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The SSNET 2024 Conference hosted by IJCLab in Orsay, France, will be held at the auditorium Pierre Lehmann (building 200 - IJCLab) in November 4-8, 2024.
As in the previous editions the conference aims at strengthening the international collaboration between the nuclear structure physicists from France, Europe and other laboratories all around the world. It allows fruitful discussions on recent experimental and theoretical aspects of nuclear structure related to the manifestation and description of the various shapes and geometrical symmetries of the nucleus as well as other symmetries and symmetry breaking.
All details of the conference (practical informations, scientific program, etc) that you can find on this website, are also gathered in the second circular.
Organizing committee: Alain Astier, Arthur Courbe, Isabelle Deloncle, Praveen Jodidar, Amel Korichi, Radomira Lozeva, Costel Petrache (chair), Jerzy Dudek (co-chair),
Conference secretaries: Émilie Bonnardel, Valérie Brouillard, Vincent Jourdain
Nuclear shapes determine the landscape of super-heavy nuclei. If it were not for shell corrections, heavy nuclei with Z$\gtrsim$104 would fission instantaneously. Deformation increases the shell corrections and enhances the stability of heavy nuclei. The evolution of deformation along the fission path determines the height of the fission barrier and its width, thereby influencing fission lifetimes. As a result, a peninsula of deformed nuclei extends from the heaviest spherical doubly magic nucleus $^{208}$Pb, towards the elusive island of super-heavy nuclei. The exact location of this island and magic numbers associated with it remain a matter of intense debate.
Trans-fermium nuclei near the Z=100, N=152 deformed shells are prolate deformed but higher order shapes play an important role for their structure. The hexacontetrapole deformation, $\beta_6$, is believed to be responsible for opening the N=152 energy gap. Studies of trans-fermium nuclei provide a stringent test of nuclear models which are used to describe the heaviest known nuclei. During the talk, recent decay spectroscopy and in-beam $\gamma$-ray spectroscopy experiments in this region using Argonne Gas-Filled Analyzer in stand-alone mode or coupled to Gammasphere will be reviewed. Among others, the observation of the ground-state rotational band in the most fissile nucleus known, $^{250}$No, the study of fast isomers in neutron-deficient Lr isotopes and the search for the rapidly fissioning nucleus, $^{252}$Rf, will be presented. These results will be compared with predictions of existing nuclear models and their impact on the shape evolution in trans-fermium nuclei will be discussed.
This material is based upon work supported by the U.S Department of Energy, Office of Science, Office of Nuclear Physics, under contract number DE-AC02-06CH11357. This research used resources of ANL's ATLAS facility, which is a DOE Office of Science User Facility.
The heaviest elements are of interest to nuclear and atomic physicists due to their peculiar properties. While nuclear shell structure effects are responsible for their very existence stabilizing them against spontaneous disintegration, the structure of their electronic shells is affected by strong relativistic effects leading to distinct atomic and chemical properties compared to their lighter homologs. The atomic structure can be probed by laser spectroscopy. which is a powerful tool to unveil fundamental atomic and, from the determination of subtle changes in atomic transitions, nuclear properties. The lack in atomic information on the heavy element of interest, the low production rates, and the rather short half-lives make experimental investigations challenging and demand very sensitive experimental techniques.
Laser spectroscopy of accelerator produced heavy nobelium (No, $Z$=102) isotopes in atom-at-a-time quantities became accessible employing the RAdiation Detected Resonance Ionization Spectroscopy (RADRIS) technique coupled to the velocity filter SHIP at GSI, Darmstadt. More recent measurements with additional advancements of the system setup and employing a novel mode of the RADRIS technique, where the desired nuclides are bred by radioactive decay on the capture filament, extended the reach of the method to $^{251,255}$No and, for the first time, to on-line produced fermium (Fm, $Z$=100) isotopes. These on-line experiments are complemented by off-line laser spectroscopy measurements at the RISIKO mass separator at Mainz University on reactor-bred heavy actinides with suitable long lifetimes. Hot-cavity laser spectroscopy on radio-chemically purified samples enabled the investigation of isotopes of the heavy actinides curium (Cm, $Z$=96), californium (Cf, $Z$=98), einsteinium (Es, $Z$=99), and fermium. This experimental endeavor is accompanied by improvements of theoretical atomic calculations which enablinge the determination of nuclear ground state properties from the extracted atomic observables of isotope shifts and hyperfine structure parameters. This provides an insight to the peculiar nuclear nature and especially the deformation of the heaviest elements. The obtained results will be discussed in view of nuclear theory predictions together with the perspectives for laser spectroscopic investigations in even heavier elements.
The study of the heaviest elements remains a compelling scientific endeavor. By investigation of nuclei in the trans-fermium region, we can learn about the single-particle structure, pairing correlations, and excitation modes in these nuclei. Berkeley Lab scientists have led several recent experiments to study the excited level structure of nuclei in this region through prompt and delayed gamma-ray spectroscopy including, notably, the odd-Z nuclei 249,251Md (Z=101). The latest results and findings from these spectroscopic studies will be discussed.
While such studies of the single-particle structure are vital to understanding the stability of the heaviest elements, the question remains as to how far we can push investigations of the heaviest nuclei. Experiments have been carried out at the 88-Inch Cyclotron using the Berkeley Gas-filled Separator (BGS) to investigate this issue. Results from recent search-and-discovery efforts for new isotopes in the region from Es-Db (Z=99-105) will be discussed. In addition, the very latest progress of studies aimed at creation of superheavy elements (Z>103) using 50Ti-induced fusion-evaporation reactions will be highlighted.
This work is supported, in part, by the US DoE under contract number DE-AC02-05CH11231.
A large body of experimental evidence and many theoretical models assessing shape-coexistence in the neutron-deficient Pb region has been acquired [1]. The quadrupole deformed shapes are associated with different intrinsic configurations that intrude down to energies close to the spherical ground state, resulting in a unique shape-triplet in $^{186}$Pb [2,3]. In the shell-model picture, the intruder configurations are associated with 2p-2h and 4p-4h proton excitations across the Z=82 shell gap.
In this region, the onset of deformation along isotopic chains varies for different elements. For example, the onset of oblate deformation in Po isotopes starts surprisingly early [4]. Since the ground state in Pb isotopes is spherical, the onset of deformation can be assessed by investigating the excited 2$^+$ states associated with different shapes. In this talk, I will present our recent experimental program to shed light on this phenomenon. In particular, I will focus on simultaneous in-beam electron and $\gamma$-ray spectroscopy experiments employing the SAGE spectrometer [5] and lifetime experiments exploiting the APPA plunger device at JYFL, Finland.
[1] K. Heyde and J.L. Wood, Rev. Mod. Phys. 83, 1467 (2011).
[2] A.N. Andreyev et al., Nature 405, 430 (2000).
[3] J. Ojala et al., Commun. Phys. 5, 213 (2022).
[4] T.E. Cocolios et al., Phys. Rev. Lett. 106, 052503 (2011).
[5] J. Pakarinen et al., Eur. Phys. J. A 50: 53 (2014).
The HISPEC/DESPEC collaboration is a part of NUSTAR (NUclear STructure, Astrophysics and
Reactions), which constitutes one of the four scientific pillars of the international FAIR facility
currently under construction in Darmstadt, Germany. Experiments are divided into two main
areas: high-resolution in-flight spectroscopy (HISPEC) and stopped-beam experiments
(DESPEC).
In the future, both HISPEC and DESPEC experiments will be provided exotic secondary beams
by the new Super-conducting FRagment Separator (Super-FRS), where the SIS-18 and SIS-100
synchrotrons will deliver high-energy beams to the Super-FRS production target. The DESPEC
setup was successfully commissioned in 2020 in the so-called ‘FAIR Phase-0’ using exotic
beams delivered by the SIS-18 and FRagment Separator (FRS) facilities of the existing GSI
campus, with several campaigns running in 2021-2024.
In this talk I will show scientific highlights from the DESPEC Phase-0 campaigns, including
investigations close to doubly-magic 100Sn and in the heavy neutron-rich regions crossing the
N=126 shell gap. Preliminary results from the worlds first in-flight fragmentation of 170Er ions,
providing a wealth of information in the highly-deformed rare-earth nuclei with A~160-170,
will also be presented. In addition, the medium- and long-term perspectives for DESPEC
experiments at the Super-FRS in the coming years will be discussed.
GANIL/SPIRAL2 presently offers unique opportunities in nuclear physics and in many other fields that arise from not only the provision of low-energy stable beams, fragmentation beams, re-accelerated radioactive species, and recently neutron beams but also from the availability of a wide range of state-of-the-art spectrometers and instrumentation. A few examples of recent highlights will be presented together with upcoming new scientific opportunities with ongoing projects.
The ATLAS facility at Argonne National Laboratory is a US DOE national user facility for low-energy nuclear physics. It provides the user community with any stable beam from proton to uranium at around Coulomb barrier energy, in addition to a suite of light radioactive beams produced in-flight by the RAISOR facility and heavier neutron-rich isotopes delivered at low or Coulomb barrier energy by the (nu)CARIBU upgrade. The facility is also host to state-of-the-art instrumentation such as Gammasphere, GRETINA, HELIOS, MUSIC, AGFA, FMA and a slew of ion trapping systems that allow it to pursue a varied research program in nuclear structure, nuclear astrophysics, fundamental interactions and applications.
The facility and its research program will be presented in this talk, together with recent upgrades such as nuCARIBU and the N=126 factory that provide increased access to new regions of the nuclide landscape.
This work is supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357.
Among the different approaches to study the structure of nuclei, thermal neutron induced reactions can be used to probe different phenomena. Capture reactions on (rare) stable or radioactive targets populate low-spin states below the neutron separation energy. With thermal neutron induced fission on actinides, neutron-rich nuclei are populated at moderately high spin. Those reactions are used at the Institut Laue-Langevin (ILL, Grenoble), at a high-resolution gamma-ray spectroscopy setup. FIPPS (Fission Product Prompt gamma-ray Spectrometer) has been used to study the structure of nuclei in different region of the nuclear chart, addressing phenomena as shape coexistence in different region of the nuclear chart.
After a general introduction about the nuclear physics activities at the Institut Laue-Langevin, recent results obtained in different experiments at FIPPS will be reported. Particular focus will be dedicated to the first fission campaigns, showing the innovative technique of fission tagging and first results. The novel use of this device for the measurement of lifetimes of medium-high spin states in neutron-rich nuclei will be shown. Preliminary results on the structure of neutron-rich Br isotopes will be highlighted, as well as the ones already published about the structure of nuclei produced after neutron-induced reactions on beta radioactive targets. The future perspectives for the coupling of the existing FIPPS setup to a fission-fragment identification system will also be outlined.
I will present several examples of shape coexistence in neutron rich doubly magic nuclei -always in the framework
of SM-CI calculations in the laboratory frame- that are the portals
to the Islands of Inversion at N=20, 40, and 50. I will pay particular attention to the case of $^{32}$Mg where
the semi-magic configuration and the deformed and superdeformed intruders mix in a very peculiar way.
I will take advantage of the Kumar invariants to discuss the meaning and limitations of the concept of nuclear shape,
We have been able to compute recently, without any
approximation, the higher order invariants (up to Q$^6$) that make it
possible to evaluate $\beta$ and $\gamma$ and their the variances. The conclusions
are that $\beta$ is softer that usually assumed, and that the $\gamma$ span at
1$\sigma$ is typically of 20-30$o$, at odds with the image of rigid triaxiallity.
In the traditional view, most heavy nuclei are like axially-symmetric prolate ellipsoids, rotating about one of the short axes. In the present picture, however, the triaxial shape appears in many heavy deformed nuclei, which actually well reproduce experimental data, as confirmed by state-of-the-art Configuration Interaction calculations. Two origins are suggested for the triaxiality: (i) binding-energy gain by the symmetry restoration for triaxial shapes, and (ii) another gain by specific components of the nuclear force, like tensor force and high-multipole (e.g. hexadecupole) central force. While the origin (i) produces basic modest triaxiality for virtually all deformed nuclei, the origin (ii) produces more prominent triaxiality for a certain class of nuclei. An example of the former is $^{154}$Sm, a typical showcase of axial symmetry but is now suggested to depict a modest yet finite triaxiality. The latter, prominent triaxiality, is discussed from various viewpoints for some exemplified nuclei including $^{166}$Er, and experimental findings, for instance, those by multiple Coulomb excitations obtained decades ago, are re-evaluated to be supportive of the prominent triaxiality. Many-body structures of the $\gamma$ band and the double-$\gamma$ band are clarified, and the puzzles over them are resolved. Regarding the general features of rotational states of deformed many-body systems including triaxial ones, the well-known J(J+1) rule of rotational excitation energies is derived, within the quantum mechanical many-body theory, without resorting to the quantization of a rotating classical rigid body. This derivation is extended to the J(J+1)-K$^2$ rule for side bands with K$\ne$0. Thus, two long-standing open problems, (i) occurrence and origins of triaxiality and (ii) quantum many-body derivation of rotational energy, are resolved.
In this talk we analyse the structure of super-heavy nuclei in a Beyond Mean Field Approach.
The calculations include the restoration of the particle-number and angular-momentum symmetries and the mixing of different shapes using the generator coordinate method. The importance of the $\gamma$ degree of freedom is highlighted by comparing the triaxial to axial-symmetric calculations performed within the same framework. In the calculations, the effective finite-range density-dependent Gogny force is used.
Calculations for the even Flerovium isotopes towards the supposed $N$=184 neutron shell closure were performed [1] .
For the three even Fl isotopes between the prolate $^{288}$Fl and the oblate $^{296}$Fl triaxial ground-state shapes are predicted, whereas axial-symmetric calculations suggest a sharp
prolate-oblate shape transition between $^{290}$Fl and $^{292}$Fl. A novel type of shape coexistence, namely that between two different triaxial shapes, is predicted to occur in $^{290}$Fl.
Finally, the existence of a neutron shell closure at $N$=184 is confirmed, while no evidence is found for $Z$=114 being a proton magic number.
In the same framework, we present the study of the excitation spectra of super-heavy nuclei. As representative examples, we have chosen the members of the $\alpha$-decay chains of $^{292}$Lv and $^{294}$Og [2,3],
the heaviest even-even nuclei which have been synthesized so far using $^{48}$Ca-induced fusion-evaporation reactions.
Rapidly varying characteristics are predicted for the members of both decay chains, which are further accentuated when compared to the predictions of simple collective models. The calculations will be compared to the available experimental data [2] and the prospect of observing $\alpha$-decay fine structures in future experiments discussed. Additionally, the excitation spectra along the $\alpha$-decay chains of the odd-A nucleus $^{289}$Fl is discussed [4]. \
Transverse wobbling (TW) and longitudinal wobbling (LW) are novel rotational modes in the triaxial nuclei [1]. As the spin increases, the TW changes into LW, caused by the coupling between the angular momenta of particle and core, or in other words, by the entanglement between the particle and core angular momenta. In this talk, we will adopt the von Neumann entropy as a measurement of such entanglement for the wobbling motion in the odd mass nucleus $^{135}$Pr and even-even nucleus $^{130}$Ba [2]. Furthermore, we will address the loss of coherence during the transition from the TW to the LW using the spin coherent states (SCS) [3] and spin squeezed states (SSS) plots [4].
References
[1] S. Frauendorf and F. Doenau, Phys. Rev. C 33, 014322 (2014).
[2] Q. B. Chen and S. Frauendorf, in preparation.
[3] Q. B. Chen and S. Frauendorf, Eur. Phys. J. A 58, 75 (2022).
[4] Q. B. Chen and S. Frauendorf, Phys. Rev. C 109, 044304 (2024).
Nuclei in the mass region 130 uniquely exhibit many different shapes and underlying symmetries, and have drawn considerable research interest. In $^{127}$I, we studied the phenomenon of shape coexistence at low excitation energy, and band termination at higher energy. Interestingly, the collective feature ceases at band termination due to rapid nuclear rotation and particle alignment. A pattern of irregular single-particle levels develops with the rotation of oblate shaped nuclei around the symmetry axis. Similar research works exist in literature for $^{121, 123, 125}$I [1, 2] as well. In our study, the reduced transition probabilities B(M1) and B(E2) are the crucial observables, obtained from the lifetime measurement in ps-fs range using the Doppler shift attenuation method (DSAM).
The high spin states of $^{127}$I were populated via the fusion-evaporation reaction $^{124}$Sn($^7$Li, 4n)$^{127}$I at the beam energy of 50 MeV delivered by the 15UD Pelletron accelerator at the Inter University Accelerator (New Delhi, India). The de-exciting $\gamma$-rays were detected by the Indian National Gamma Array consisting of 15 Compton suppressed clover detectors placed at 32$^{\circ}$, 57$^{\circ}$, 90$^{\circ}$, 123$^{\circ}$, and 148$^{\circ}$ with respect to the beam direction. The list mode data were sorted offline into angle-dependent asymmetric E$_{\gamma}$-E$_{\gamma}$ matrices to extract lifetimes. The details of DSAM-lineshape analysis are described in our earlier works [3, 4].
The latest research on $^{127}$I by Ding et al [5] has investigated many bands. But, our present study of lifetime measurement using DSAM is entirely new. Moreover, we have extended the negative-parity band based on $\pi$h$_{11/2}$ to higher spins up to band termination. At low spins, the band shows a sequence of E2 transitions which is a typical of near prolate-shaped nuclei. The theoretical results based on total Routhian surface (TRS) calculation predicted $\gamma$-softness ($\beta$ $\approx$ 0.2, $\gamma$ = 8$^{\circ}$-30$^{\circ}$ in Lund convention) below the particle alignment. When the band terminates, the shape becomes nearly oblate ($\beta$ $\approx$ 0.2, $\gamma$ $\approx$ 55$^{\circ}$). Our experimental result on B(E2) lies within 0.4 - 0.6 e$^2$b$^2$ for low spins with a sharp increase at 23/2$^-$ (2.7 e$^2$b$^2$) due to particle alignment. At high spin 27/2$^-$, the B(E2) value becomes low (0.07 e$^2$b$^2$). We estimated the B(E2) values using particle rotor model (PRM) and obtained a good comparison with the experimental results. Furthermore, this band shows a strong decoupling behaviour in comparison to the ground band of $^{126}$Te. The yrast positive-parity band was identified predominantly as $\pi$g$_{7/2}$ admixed with d$_{5/2}$. The band shows signature splitting and inversion at 17/2$^+$. The experimental B(E2) values remain roughly constant 0.47 e$^2$b$^2$ up to the signature inversion, and it abruptly decreases to 0.15 e$^2$b$^2$ at 19/2$^+$. The nuclei are triaxial ($\beta$ $\approx$ 0.23, $\gamma$ = 30$^{\circ}$) as predicted by TRS and confirmed by the PRM.
In summary, we have performed an exhaustive spectroscopic investigation for $^{127}$I, and inferred the coexistence of near prolate and triaxial shapes at low spins; while, an oblate structure emerges at high spins due to band termination.
References
[1] D. L. Balabanski et al., Phys. Rev. C 56 (1997) 1629.
[2] C. B. Moon and T. Komatsubara, J. Korean Phys. Soc. 45 (2004) L791.
[3] H. K. Singh et al., Phys. Rev. C 100 (2019) 064306.
[4] U. Lamani et al., Nucl. Phys. A 1014 (2021) 122220.
[5] B. Ding et al., Phys. Rev. C. 85 (2012) 044306.
Octupole deformation, an exotic nuclear deformation that breaks reflection symmetry, is a recurrent theme of interest in nuclear structure physics. This presentation highlights recent studies on the signatures of octupole correlations and related collective excitations using the interacting boson model that is based on the nuclear density functional theory. By mapping the self-consistent mean-field solutions obtained with a given energy density functional and pairing interaction onto the corresponding boson system, the interacting-boson Hamiltonian describing the low-energy spectra and electromagnetic transition properties is completely determined. Octupole correlations are shown to be relevant in a number of neutron-rich and proton-rich nuclei with mass A=70-250 including actinides and lanthanides, and in particular, in some challenging cases of the neutron-rich nuclei near N=60, and the N~Z~34 regions, where triaxiality and coexistence of quadrupole shapes play a crucial role along with the octupole degree of freedom.
With the construction and operation of next-generation large-scale radioactive nuclear beam facilities worldwide, numerous novel phenomena have been discovered through the excitation and decay of unstable exotic atomic nuclei, such as shape coexistence, shape phase transitions, octupole deformation, and more. These findings have brought about a fresh understanding of nuclear physics and posed significant challenges to traditional nuclear theories. To this end, we have developed a collective Hamiltonian model based on covariant density functional theory (CDFT), and conducted a series of research works in the field of nuclear shapes and collective motions.
(1) Using a five-dimensional collective Hamiltonian model based on CDFT, we have systematically explored even-even nuclear masses, quadrupole deformations, low-lying spectra, and more. We have reproduced the known regions of shape coexistence and predicted new coexistence regions [1]. Following this, we established a triaxial-and-pairing collective Hamiltonian that describes the triaxial shape vibrations, rotations, and coupling with pairing vibration. The coupling between triaxial shapes and pairing degrees of freedom, and its impact on the low-energy spectra, transition rates, and shape coexistence have been analyzed [2-4].
(2) Using a quadrupole-octupole collective Hamiltonian model and a microscopic core-quasiparticle coupling model based on CDFT, we have performed a comprehensive study on the octupole deformation and low-energy negative parity bands in the actinide region, including both even-even and odd-A nuclei. The theoretical calculations reproduce the experimental data well and yield configurations of parity doublets [5,6]. New parity doublets based on excitation states are also predicted. Furthermore, we have also incorporated the non-axial octupole deformation in the microscopic collective Hamiltonian framework and take 152Sm as an example to do an illustrative calculation [7].
Reference
[1] Y. L.Yang, P. W. Zhao, and Z. P. Li, Shape and multiple shape coexistence of nuclei within covariant density functional theory. Phys. Rev. C, 107, 024308 (2023).
[2] J. Xiang, Z. P. Li, T. Nikšić, D. Vretenar, and W. H. Long, Coupling of shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals. Phys. Rev. C, 101, 064301(2020).
[3] J. Xiang, Z. P. Li, T. Nikšić, D. Vretenar, W. H. Long, and X. Y. Wu. Coupling of shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals. II. Low-energy excitation spectra of triaxial nuclei. Phys. Rev. C, 109, 044319(2024).
[4] J. Xiang, Z. P. Li, et. al., The impact of pairing vibration on nuclear shape coexistence. In preparation.
[5] W. Sun, S. Quan, Z. P. Li, J. Zhao, T. Nikšić, and D. Vretenar, Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei with octupole correlations. Phys. Rev. C, 100, 044319(2019).
[6] R. N. Mao, X. Zhao, Z. P. Li, et.al., Systematic study of parity doublets in radiums and actinides within the microscopic core-quasiparticle coupling model. In preparation.
[7] J. Xiang, J. Zhao, Z. P. Li, et.al., Triaxial quadrupole-octupole collective Hamiltonian based on covariant density functional theory. In preparation.
The phenomenon of quantum phase transitions (QPTs) is highly investigated in many fields on physics, and, in particular, nuclear structure. QPTs in atomic nuclei refer to (mostly) abrupt changes in the structure of the spectrum. The changes are identified in the nuclear shapes of the ground state, with varying nucleon number - from one shape evolving to another (Type I QPT) or when another state is associated with a different coexisting shape that crosses and becomes the ground state shape (Type II QPT, also called configuration mixing and crossing).
In this talk, I will introduce the topic of QPTs in the algebraic frameworks of the interacting boson model (IBM) and interacting boson-fermion model (IBFM), both with configuration mixing (shape coexistence). Such frameworks allow us to explore shape evolution and coexistence of even-even (IBM) and odd-mass (IBFM) nuclei. I will present how these frameworks are applied to different chains of isotopes exhibiting QPTs and, in some cases, how both Type I and II QPTs can be recognized in the same chain. The latter situation, named intertwined QPTs (IQPTs) was recently identified in both even-even and odd-mass chains of isotopes around $A\approx100$.
A central motivation for the program of ultra-relativistic nuclear collisions is to access bulk properties of QCD matter that emerge in conditions similar to those found in the early Universe or in extreme astrophysical objects. A prime example is the quark-gluon plasma (QGP), the hot phase of QCD matter that behaves like a near-perfect fluid. The spatio-temporal evolution of the QGP can be well described within the relativistic hydrodynamic framework [1]. In particular, the spatial anisotropy of the intial condition of the QGP plays a major role in its subsequent evolution and translates, in fine, in an anisotropy of the momentum distribution of the emitted particles later observed in experimental detectors.
It turns out that nuclear deformation, an emergent phenomenon well studied in nuclear structure, participates in the creation of this initial spatial anisotropy. Indeed, in the most central collisions, i.e, collisions with a very small impact parameters, nuclear deformation strongly accentuates the asymmetry of the overlap region between the two colliding nuclei where the QGP is formed. For example, the quadrupole deformation of the colliding ions can be directly linked to an excess of elliptic flow in the distribution of observed charged hadrons compared to a spherical baseline. Therefore, a good description of the spatial arrangement of nucleons inside the nucleus is of interest in the determination of the initial conditions of ultra-relativistic nuclear collisions.
In this talk, I will present some recent theoretical efforts to generate these initial conditions from state-of-the-art nuclear structure calculations [2]. Also, I will show how our knowledge of nuclear deformation can be used to better analyze high-energy data [3] as well as propose new experiments [4]. In particular, I will discuss the idea of using the large ground-state deformation of $^{20}$Ne to shed light on the collectivity in small colliding systems [4].
[1] Ollitrault, Eur. Phys. J. A, 59, 236 (2023).
[2] Bally et al., Eur. Phys. J. A, 59, 58, (2023).
[3] Bally et al., Phys. Rev. Lett., 128, 082301 (2022).
[4] Giacalone et al., arXiv:2402.05995 (2024)
The nucleus is described as a system of fermions interacting via the exchange of different mesons in covariant density functional theory (CDFT). It is very successful in the description of many nuclear phenomena [1]. However, at present the absolute majority of covariant energy density functionals (CEDFs) are fitted to only spherical nuclei. This does not allow to improve the global description of nuclear phenomena (for example, nuclear masses) and creates some theoretical uncertainties.
To overcome this problem, a new anchor-based optimization method of defining energy density functionals (EDFs) has been proposed by us in [2]. In this approach, the optimization of the parameters of EDFs is carried out for a selected set of spherical anchor nuclei, the physical observables of which are modified by the correction function, which takes into account the global performance of EDFs. It is shown that the use of this approach leads to a substantial improvement in the global description of binding energies for several classes of covariant EDFs. The computational cost of defining a new functional within this approach is drastically lower as compared with the one for the optimization which includes the global experimental data on spherical, transitional, and deformed nuclei in the fitting protocol [2,3].
On-going efforts to further global improvement of CEDFs include taking into account infinite basis corrections in the calculations of nuclear binding energies and accounting spin-orbit contributions to the charge radii in the fitting protocol [4]. Moreover, total electron binding energies are subtracted when defining nuclear binding energies. To achieve that they were calculated for the first time for superheavy elements. The consequences of recent developments of CEDFs on the predictions of nuclear shapes across the nuclear chart will be discussed.
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award No. DE-SC0013037.
[1] D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Rep. 409, 101 (2005).
[2] A. Taninah and A.V.Afanasjev, Phys. Rev. C 107, L041301 (2023).
[3] A. Taninah, B. Osier, A.V. Afanasjev, U.C. Perera and S. Teeti, Phys. Rev. C 109, 024321 (2024)
[4] B. Osei, A. V. Afanasjev, A. Taninah, U. C. Perera, V. A. Dzuba, and V. V. Flambaum, in preparation, to be submitted to Phys. Rev. C
A recent survey extracted the implied effective $E2$ charges from $B(E2;2_1^+ \rightarrow 0_1^+)$ values in doubly magic nuclides plus or minus two like nucleons [1]. A similar survey of the effective $g$ factors in the $M1$ operator as determined empirically from the magnetic moments of nuclei adjacent to closed shells will be presented. The patterns will be discussed and compared with previous work.
Selected cases where the data indicate unexpected effective $g$ factors and/or effective charges will be considered. Such cases indicate additional configuration mixing beyond that implicit in the effective operator. A stand-out case is $^{210}$Po where the experimental $2_1^+ \rightarrow 0_1^+$ transition strength is much smaller than expected [2]. Such behavior is unusual; configuration mixing usually increases $E2$ collectivity and hence $B(E2)$ values.
The octupole vibration of the $^{208}$Pb core is known to mix the single-particle states in trans-Pb nuclei and has a profound influence on the $g$ factors and $E3$ decays of the high-spin isomers [3]. An analysis of the effect of octupole coupling on the $g$ factors of the 8$^+$ isomers in the $N=126$ isotones and their $E2$ decays, was given some years ago [4]. The possible effect of octupole mixing on the $E2$ decays in $^{210}$Po will be revisited [4]. Such mixing was not included in the evaluation of the $E2$ effective charge in [1].
The feasibility of a $g$-factor measurement by the transient-field method on a $^{210}$Po beam, to assess whether neutron components are present in its $2_1^+$ state, will be evaluated.
[1] A.E. Stuchbery and J.L. Wood, Physics 4, 697 (2022).
[2] D. Kocheva et al., Eur. Phys. J. A 53, 175 (2017).
[3] S.J. Poletti et al., Nucl. Phys. A 448, 189 (1986).
[4] A.E. Stuchbery et al., Nucl. Phys. A 555, 355 (1993).
Single-j calculations for (𝑗)𝑛 configurations with n = 3,..,2j+1 can be performed using a semi-empirical approach, provided that the energies and absolute electromagnetic transition rates are known for the two-particle (hole) nucleus. This approach was already successfully applied in the case of protons in the (𝜋ℎ9/2)3 nucleus 211𝐴𝑡 [1]. At the Cologne Tandem Accelerator of the Institute for Nuclear Physics we have tested these relations by measuring lifetimes of excited states in the (𝜋𝑔9/2)𝑛 isotones with N = 50. We started the studies in the two proton nucleus 92𝑀𝑜 where the previously unknown B(E2:4+1 → 2+1 ) value, was measured with high precision using the electronic 𝛾 −𝛾 fast timing technique [2]. Subsequently we applied the same technique in 93𝑇𝑐 and 94𝑅𝑢 [3].
Work supported by DFG Grant JO391/18-2.
[1] V. Karayonchev, et al., Phys. Rev. C 106, 044321 (2022).
[2] M. Ley, L. Knafla, J. Jolie, A. Esmaylzadeh, A. Harter, A. Blazhev, C.
Fransen, A. Pfeil, J.-M. Regis, P. Van Isacker, Phys. Rev. C 108 (2023).
[3] M. Ley, J. Jolie, A. Blazhev, L. Knafla, A. Esmayalzadeh, C. Fransen, A Pfeil, J.M. Régis, P. Van Isacker et al., submitted to Phys. Rev. C.
In the last decade, a considerable progress in the understanding of the structure of nuclei in the vicinity of $^{132}$Sn, the heaviest doubly-magic nucleus far-off stability accessible for experimental studies, was achieved. The many results obtained in several experimental campaigns performed at the Radioactive Isotope Beam Facility (RIBF) in Japan, in combination with state-of-the-art theoretical investigations, contributed in a significant way to this progress [1-4]. In the present contribution, new results from an experiment dedicated to decay spectroscopy in the $^{132}$Sn region performed during the EURICA campaign in 2014 will be discussed [5]. In particular, the known I$^\pi$ = 8$_1^+$, E$_x$ = 2129-keV isomer in the semi-magic nucleus $^{130}$Cd$_{82}$ was populated in the projectile fission of a $^{238}$U beam and the high counting statistics of the accumulated data allowed to determine the excitation energy, E$_x$ = 2001.2(7) keV, and half-life, T$_{1/2}$ = 57(3) ns, of the I$^\pi$ = 6$_1^+$ state based on $\gamma\gamma$ coincidence information. The new experimental results, combined with available data for $^{134}$Sn and large-scale shell model calculations, allowed to extract proton and neutron effective charges for $^{132}$Sn, a doubly-magic nucleus far-off stability. A comparison to analogous data for $^{100}$Sn provided first reliable information regarding the isospin dependence of the isoscalar and isovector effective charges in heavy nuclei.
[1] J. Taprogge et al., Phys. Rev. Lett. 112, 132501 (2014)
[2] G.S. Simpson et al., Phys. Rev. Lett. 113, 132502 (2014)
[3] V. Vaquero et al., Phys. Rev. Lett. 118, 202502 (2017)
[4] V. Vaquero et al., Phys. Rev. Lett. 124, 022501 (2020)
[5] A. Jungclaus et al., Phys. Rev. Lett. 132, 222501 (2024)
Recently, our understanding of three-nucleon forces (3NFs) in nuclei was notably advanced by the advent of the chiral effective field theory [1], which offers a systematic and unified approach to constructing two-body forces (2NFs) and 3NFs on equal footing. These modern 3NFs and 3NFs have been extensively utilized in many-body calculations, firmly establishing the role of 3NFs in describing spectroscopic properties. Special attention has been drawn to the relationship between chiral 3NFs and variations in shell structure observed when transitioning from stable to exotic nuclei. These 3NFs are found to be crucial in explaining the nonuniversality of magic numbers (see, for instance, [2] and references therein), highlighting their potential to influence the spin-orbit (SO) splitting,
Here, in order to better understand the specific mechanism through which chiral 3NFs influence the SO splitting, I discuss a decomposition scheme of the chiral 3NF at next-to-next-to-leading order [3] by the rank of the irreducible tensors, leading to a categorization of the 3NF in terms of the number of exchanged pions and rank. It is worth noticing that this procedure is based on decomposition of the 3NF rather than on the decomposition of the corresponding matrix elements, as it is instead usually done for analyzing the tensorial structure of 2NFs.
As a test case, calculations for p-shell nuclei have been performed within the shell-model framework to investigate the role of the different rank 3NF components.
Results show that the SO is essentially influenced by the rank-1 component, which originates exclusively from the 2 pion-exchange term. We can therefore conclude that our findings do not depend on the choice of the new low-energy constants introduced by the 3NF, although to assess the robustness of our conclusions it is essential to extend the analysis to heavier mass regions.
References
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[3] T. Fukui, G. De Gregorio, A. Gargano, to be published in Phys. Lett. B.
EURO-LABS is a European project, which brings together, for the first time, the three research communities of nuclear physics, accelerator and detector technologies for high energy physics, in a pioneering super-community of sub-atomic scientists. It is a network of 33 research and academic institutions from 18 countries (25 beneficiaries and 8 associated partners) from European and non-EU countries, involving 47 Research Infrastructures in the Nuclear physics, Accelerators and Detectors pillars.
One of the main important work packages of the project is the WP2 “Access to Nuclear Physics Facilities”. It supports the transnational access to 14 nuclear physics laboratories in Europe, to ECT* and also to the virtual access distributed facility Theo4Exp. In addition, it offers a variety of services helping in the access to these facilities.
In the presentation I will briefly describe the status of the project as well as recent achievements of the work package WP2.
Coulomb excitation experiments enable measurements of both electric quadrupole transition strengths between nuclear states as well as static E2 moments of the excited states. As such, these experiments provide direct and sensitive probes of quadrupole collectivity and correlations in nuclei, which enables stringent tests of nuclear theory. An overview of the Coulomb excitation experimental technique will be given, and results from experiments performed at both the ReA facility at FRIB and the ISAC II facility at TRIUMF will be presented. I will focus primarily on results from a recent CoulEx measurement of 78Kr performed at TRIUMF, and I will mention more briefly results from experiments at FRIB.
Nuclear collectivity has been thought to emerge through spherical quadrupole vibrations, especially in transitional regions between shell closures and deformed nuclei. The Cd isotopes ($Z=48$) were long considered textbook examples of vibrational nuclei. However, in recent years this narrative has been challenged, with elecromagnetic matrix element data showing major discrepancies with the vibrational model [1]. Results from multi-step Coulomb excitation data of $^{106,116}$Cd on $^{208}$Pb will be presented [2]. Excitation of many low-lying states, including two excited $0^+$ states was observed. The experimental $E2$ matrix elements are used to construct $E2$ rotational invariants for the ground- and low-lying excited states, providing a model independent view of nuclear shapes in the Cd isotopes. The rotational invariant behaviour as a function of spin can be compared to, and test state-of-the-art nuclear models. The experiments were performed using the GRETINA-CHICO2 arrays at Argonne National Laboratory, using the ATLAS accelerator.
[1] P. E. Garrett, T. R. Rodriguez, A. Diaz Varela et al., Phys. Rev. Lett. 123,142502 (2019)
[2] T. J. Gray, J. M. Allmond, R. V. F. Janssens et al., Phys. Lett. B 834, 137446 (2022)
The study of shapes and collective properties of atomic nuclei is a vast area of research, and low-energy Coulomb-excitation is one of the most powerful experimental techniques for such studies. It provides information not only about the reduced transition probabilities, describing the collectivity of the transitions, but also about the spectroscopic quadrupole moments of excited states, as well as the relative signs of the extracted transitional and diagonal matrix elements.
Typically, following low-energy Coulomb-excitation experiments, a set of matrix elements is determined leading to the use of the Kumar–Cline’s sum rules [1] that allows the determination of the deformation parameters together with their widths.
Coulomb excitation measurements have been performed to study structural changes and the presence of coexisting shapes in the zirconium isotopes, which are particularly interesting as, in recent years, evidence has come to light that they are excellent cases for exhibiting type II shape evolution. In most cases, however, the nuclear matrix elements required to perform precision tests of state-of-the-art nuclear theory in this region are lacking. These isotopes span a wide range of masses from a mid-open-shell region (80Zr40)[2], which is thought to be deformed, through a closed neutron shell at 90Zr50, to a closed neutron subshell (96Zr56), and then to a sudden reappearance of deformation (100Zr60)[3], which has been shown to persist to another mid-open-shell region as far as 110Zr70[4] . This variety of behaviour is unprecedented elsewhere on the nuclear mass surface. It is, therefore, not surprising that the zirconium region has been the subject of intensive experimental and theoretical work in order to gather insight into a variety of different nuclear structure phenomena. Of particular interest is how collectivity evolves in these isotopes and the coexistence observed between various configurations. For this reason we decided to perform Coulomb excitation measurement allowing for an in-depth comparison with theoretical predictions, shedding light on the structure of low-lying excitations in these nuclei.
In this talk, our experimental results will be presented focussing on the Coulomb-excitation measurements performed on the 94-96Zr isotopes.
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We studied cross-section distributions measured as a function of scattering angle for multiple excited states in $^{106}$Cd, populated via inelastic scattering on a $^{92}$Mo target. The balance between Coulomb and nuclear interaction in the population of individual states was explored by comparing the experimental $\gamma$-ray yields with the predictions obtained with the GOSIA Coulomb-excitation code. We demonstrated that from such an ``unsafe'' Coulomb-excitation measurement it is possible to correctly evaluate reduced transition probabilities between certain low-lying states. In this way, we obtained new information on the collectivity of the presumably oblate structure built on the 0$^+_3$ state, as well as on the role of octupole correlations in this nucleus. By comparing our observations with the results of previous spectroscopic studies of $^{106}$Cd, we were also able to propose a rearrangement of the level scheme including notably K=2 and K=4 structures. These results, as well as remaining puzzles concerning the low-energy part of the $^{106}$Cd level scheme, motivated a future high-precision beta-decay study into $^{106}$Cd, which has been recently accepted at TRIUMF.
Nuclear Excitation by Electron Capture (NEEC) was predicted by Goldanskii and Namiot as the the inverse process of internal conversion in 1976$^{[1]}$. It was predicted to play an important role in the isomer depletion, which is a potential path for releasing nuclei energy stored in isomer$^{[2]}$.
The first experimental observation on NEEC was reported in the slowing down process of $^{93m}$Mo$^{[3]}$. The observed isomer depletion probability was too large to be reproduced by Coulomb excitation, and thus attributed to NEEC. However, it also failed to be reproduced by NEEC in the following theoretical works$^{[4,5]}$. On the experimental side, a comment was addressed on the influence of complex γ background which may cause the overestimation of isomer depletion probability$^{[6]}$. Later, an independent experiment was performed using a $^{93m}$Mo secondary beam, but no isomer depletion was observed with an accuracy of 2×10$^{-5}$, which was reported as the upper limit of the excitation probability$^{[7]}$. However, this measurement was performed with lower recoiling energies than the previous experimental work.
Now, a new experiment has been performed with higher recoiling energy and purity of the $^{93m}$Mo isomer beam in the Heavy Ion Research Facility in Lanzhou. Both lead and carbon foils were used to stop the $^{93m}$Mo ions. Isomer depletion is observed, and the excitation probability is about 2×10$^{-5}$ for lead, and 2×10$^{-6}$ for carbon. These results agree well with the calculated probabilities for inelastic reactions, which are thus suggested to be the main mechanisms exciting the $^{93m}$Mo isomer during its stopping process.
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[3] C. J. Chiara et al., Nature 554 (2018) 216.
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In this talk I address the problem of quantifying the probability of formation of a deuteron or an alpha particle in a shell-model wave function. The method relies on the application of the Talmi-Moshinsky transformation for a deuteron and its repeated application for an alpha particle. Once this transformation is carried out, it is then assumed that the neutron-proton pair or 2n-2p quartet in the shell-model wave function has the same intrinsic structure as a deuteron or an alpha particle in the s shell.
I will present results of schematic calculations to illustrate the dependence of deuteron and alpha clustering in the shell model on nucleon numbers, isospin, isoscalar/isovector interaction strengths, etc.
The emergence and interplay of effective degrees of freedom, which include collective shape variables, pairing correlations, near-threshold collectivities due to coupling to the continuum, and clustering, represent one of the central questions of modern nuclear physics and quantum many-body physics more broadly. In this talk, I aim to provide specific perspectives on these phenomena and their study using configuration interaction approaches that incorporate continuum physics, as well as methods relying on symmetry and underlying many-body complexity.
In particular, I will highlight our recent advancements in studying clustering using configuration interaction methods that stem from fundamental nucleon-nucleon interactions. I will discuss specific applications of our theoretical studies of light nuclei and recent works on experimental validations.
Proton-neutron pairing and α-like quartet condensation in N=Z nuclei
Nicolae Sandulescu
National Institute of Physics and Nuclear Engineering, Magurele-Bucarest, Romania
A specific feature of N = Z nuclei is the occurrence of α -like quartet structures, composed by two neutrons and two protons, which have strong internal correlations and interact weakly with each other. Various studies have shown that the ground states of N=Z systems interacting by proton-neutron pairing interactions can be described by a condensate of α-like quartets [1-10]. This quartet condensate is the analogous of the Cooper pair condensate, commonly employed to treat the neutron or proton pairing correlations. As shown recently, the quartet condensation is also related to the band-like structures of even-even N=Z nuclei [11-13]. More precisely, the low-lying excitations of these nuclei are associated to the breaking of a quartet from the ground state quartet condensate and replacing it with an excited quartet.
In the first part of the talk I will present an overview of the issues mentioned above. Then I will discuss how the fingerprints of the α-like quartet condensation might show up in the α transfer reactions along a chain of even-even N=Z nuclei. Finally I will discuss the possibility of exciting light tin isotopes in pair condensate states [14].
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A range of theoretical approaches, including ab initio calculations, have predicted that well-developed cluster states can be found in the low-lying states of light neutron-rich nuclei, including the ground-state. We have realized a pioneering study at RIKEN based on the measurement of triple differential cross-sections of the cluster knockout reactions (p,p) with proper kinematical conditions on neutron-rich unstable beams for the first time. Such an approach probes the spatial distribution of clusters in the nucleus of interest. In this first study clustering in the neutron-rich Beryllium isotopes was investigated. The analysis of the differential cross-sections validated the molecular-type structure of the ground state of 10Be predicted by state-of-the-art microscopic models THSR and AMD. These results [1] bring experimental evidence that clustering plays a crucial role in the ground-state of light neutron-rich nuclei, challenging the conventional Ikeda picture. In a next step, the completion of the data analysis of 12,14Be(p,pa) will allow to infer the evolution of alpha-clustering with increasing neutron number up to the dripline, e.g pinpoint the role of the extra-neutrons. Beyond alpha clustering, the present knockout experiment though optimized for (p,p) gave us a first opportunity to investigate triton clustering in neutron rich light nuclei.
[1] P.Li et al., Phys. Rev. Lett. 131, 212501 (2023)
Neutron-proton pairing is the only pairing that can occur in the T=0 and the T=1 isospin channels. T=1 particle-like pairing (n-n or p-p) has been extensively studied unlike T=0 neutron-proton pairing. The over-binding of N=Z nuclei could be one of its manifestation.
Neutron-proton pairing can be studied by spectroscopy as in ref.[1].We have here studied it through transfer reactions in order to get more insight into the relative intensities of the two aforementioned channels. Indeed, the cross-section of np pair transfer is expected to be enhanced if the number of pairs contributing to the populated channel is important. The observable of interest is the ratio of the two-nucleon transfer cross-sections to the lowest 0+ and 1+ states.
Neutron-proton pairing is predicted to be more important in N=Z nuclei with high J orbitals so that the best nuclei would belong to the g9/2 shell [2]. However, considering the beam intensities in this region, we have focussed on fp-shell nuclei.
Measurements of the two-nucleon transfer reaction (p,3He) were performed at GANIL with three radioactive beams produced by fragmentation and purified by the LISE spectrometer: 56Ni, 52Fe, 48Cr. The set-ups were based on the coupling of the MUST2 Silicon array for charged particle detection with the EXOGAM gamma-ray array and a zero-degree detection (ZDD) for the last experiment.
The two first measurements with 52Fe (N=Z=26) beam, which is a partially occupied 0f7/2 shell nucleus and 56Ni (N=Z=28) beam, which has a fully occupied 0f7/2 shell allowed us to study np pairing according to shell occupancy [2]. The last measurement with 48Cr beam will allow to study the interplay between np pairing and deformation.
I will present the cross-sections measured in both channels (T=0 and T=1) and discuss the consequence for each pairing channel. The aforementioned ratio of cross-sections and the angular distribution for the ground state of 54Co will be compared with DWBA calculations. Preliminary results for 48Cr(p,3He) will also be presented.
[1] B. Cederwall et al, Nature 469 (2011) 469.
[2] B. Le Crom, M. Assié et al, Phys. Lett. B 829 (2022) 137057.
Neutron-rich, heavy, EXotic nuclei around the neutron shell closure at N=126 and in the transfermium region are accessible via multinucleon Transfer reactions which feature relatively high cross sections. The wide angular distributions of the multinucleon transfer products lead to experimental challenges in their separation and identification.
In my presentation, I will give an overview on how we plan to overcome these challenges with the new NEXT experiment at the PARTREC facility in Groningen. Furthermore, I will highlight some latest results from multinucleon transfer studies at the RITU separator at the University of Jyväskylä
NEXT is designed in such a way that a large fraction of the target-like transfer products emitted in a forward angel of 10° to 40° from the target will be separated and focuses towards a gas-catcher. From there they will be injected into a MultiReflection Time-of-Flight Mass Spectrometer for precision mass measurement and sample preparation for back-ground free decay spectroscopy. Thus, even very long-lived, heavy transfer products can be identified and studied with NEXT.
The RITU separator combined with the JUROGAM detector array is complementary to NEXT. With this setup the reaction Ca-48+Bi-209, Cu-65+Bi-209, and Ni-64+U-238 have been investigated. Target-like transfer products emitted in 0° from the target have been studied with the GREAT focal plane detector. The JUROGAM detector array at RITU took “snapshots at the target” through the detection of prompt-γ from the projectile-like and target-like fragments.
Transfer reactions play a crucial role in studies of nuclear structure and reaction mechanism. In heavy-ion transfer reactions, multiple nucleons can be transferred along with significant energy and angular momenta from the relative motion to the intrinsic degrees of freedom in a single collision [1,2]. This makes multinucleon transfer reactions a valuable tool for investigating various topics, ranging from nucleon-nucleon correlations to reaction dynamics [3].
Recent experiments conducted at the Legnaro National Laboratories (LNL, INFN) have focused on studying nucleon-nucleon correlations using heavy-ion beams on medium-mass targets in inverse kinematics [4,5]. Reaction products were detected at forward angles using the large solid angle magnetic spectrometer PRISMA. Transfer cross sections were measured across a wide range of energies, from near to far below the Coulomb barrier. The results were interpreted through excitation functions, extending down to very low energies corresponding to large distances of closest approach, where nuclear absorption is minimal.
Additionally, experiments were conducted to investigate the production mechanism of neutron-rich nuclei [6-8]. Transfer processes between heavy ions at energies near the Coulomb barrier have emerged as a competitive method for producing exotic species, particularly heavy neutron-rich nuclei.
This presentation will provide an overview of these experiments, with a particular emphasis on the main results and challenges encountered. New achievements will also be discussed, especially in connection with the AGATA array currently coupled to PRISMA.
[1] L. Corradi, G. Pollarolo, and S. Szilner, J. Phys. G: Nucl. Part. Phys. 36, 113101 (2009).
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[3] T. Mijatović, Front. Phys. 10:965198 (2022).
[4] D. Montanari et al., Phys. Rev. Lett. 113, 052601 (2014), Phys. Rev. C 93, 054623 (2016).
[5] L. Corradi et al., Phys. Lett. B 834 (2022) 137477.
[6] T. Mijatović et al., Phys. Rev. C 94, 064616 (2016).
[7] P. Čolović et. al., Phys. Rev. C 102, 054609 (2020).
[8] J. Diklić et. al., Phys. Rev. C 107, 014619 (2023).
Two-nucleon transfer is a powerful probe, providing insights into single-particle and collective aspects of nuclear structure and complementing data from single-nucleon transfer and inelastic scattering measurements. While the latter has become commonplace in reaction studies in inverse kinematics, particularly with solenoidal spectrometers such as HELIOS (at ATLAS), SOLARIS (at FRIB), and the ISS (at ISOLDE), the use of the ($t$,$p$) reaction has been infrequent. The ($t$,$p$) reaction, with modest reaction $Q$ values, enables access to more neutron-rich nuclei. Still, the challenges of achieving good resolution and acquiring suitable targets have limited its use. In this talk, I will show recent results from HELIOS and SOLARIS, where the ($t$,$p$) reaction has been used to explore neutron-rich nuclei $^{12}$Be and $^{34}$Si. The structure of $^{12}$Be has remained particularly elusive. While the $^{10}$Be($t$,$p$)$^{12}$Be reaction has been studied in normal kinematics, the inverse approach in a solenoidal spectrometer can reveal information on decay channels to support spin assignments. The region around 34Si has been studied extensively of late in connection to weak-binding effects in the N$\sim$20 region. An overview of the experimental technique and broader physics themes will be explored. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract Number DE-AC02-06CH11357.
Studies of the beta decay of 71Kr cannot be said free of controversy. The first study by Oinonen et al. [1] showed a relatively too small ground state to ground state feeding for a mirror pair and prompted an immediate alternative explanation by Urkedall and Hammamoto [2] calling possible shape effects and isospin breaking in the mirror system. Later a detailed in-beam study [3] restored the earlier interpretation of Oinonen, that since then has prevailed [4]. Recently, new insights have been obtained based on a high-statistics experiment performed at RIKEN Nishina Center. In this talk, I will present these new results from the perspective of deformation and isospin effects in the A= 70 region.
[1] M. Oinonen et al., Physical Review C 56, 745 (1997).
[2] P. Urkedall and I. Hammamoto, Physical Review C 58, R1889 (1998)
[3] S. Fisher et al., Physical Review C 72, 024321 (2005).
[4] S. Waniganeththi et al., Physical Review C 106, 044317 (2022).
Neutron-rich nuclei and their 𝛽 decays play an essential role in reactor physics. The spectra of escaping antineutrinos produced in 𝛽 decay of these nuclei show 6-10% discrepancies above and below modern theoretical predictions. This Reactor Antineutrino Anomaly (RAA) was previously suggested as evidence for hypothetical sterile neutrinos however recent evidence point towards deficiencies within the model predictions themselves. The 𝛽-decay of 92Rb is one of the main contributors to the reactor high-energy antineutrino spectrum and, consequently, is an important contributor to the RAA. Its decay has been recently studied in Total Absorption Spectroscopy (TAS) and shows significant differences with previous High-Resolution Spectroscopy performed in the early 70s which can be attributed to the pandemonium effect.
We have thus revisited the 𝛽-decay of 92Rb (I = 0-; t1/2 = 4.48(3) s) with the GRIFFIN spectrometer at TRIUMF that consists of up to 16 Compton-supressed HPGe clover detectors. Due to the high intensity radioactive beam of 92Rb of 106 pps and the high efficiency for detecting 𝛾 rays of GRIFFIN to obtain an unparallel picture of 92Sr with over 180 levels and 850 𝛾-ray transitions up to and beyond the neutron separation energy of ~7.3 MeV, and performed comprehensive 𝛾-ray spectroscopy, including angular correlations to assign spins to the new states.
The decay the I = 0- ground state of 92Rb takes place with a large 𝑄𝛽 value of 8095 keV and populates numerous high-lying 1− levels in 92Sr. These 1- states are situated in the region of the Pygmy Dipole Resonance (PDR) that manifests as an enhancement of 𝐸1 strength below the neutron separation energy, located at the low-energy tail of the Giant Dipole Resonance. The PDR is interpreted as an out-of-phase oscillation between the neutron-skin and an isospin saturated core, however, this remains a matter of debate. The new information of nuclear levels in 92Sr points to the possibility of to investigate the PDR via 𝛽-decay experiments.
The results of this study are also compared to recent TAS experiments and with theoretical shell model calculations and show a great agreement despite of the large density of levels and fragmented decay in 92Sr.
Investigating the properties of individual nucleons leads to a more detailed exploration of
nuclear physics. We employ the relativistic mean-field model to study the behavior of nuclei and nuclear matter. Nuclear density is treated as a fundamental variable, and an energy function is employed to depict the interactions between the nucleons. The conventional Hartree-Fock Bogoliubov model is expanded relativistically (RHB) [1], offering a unified approach to nuclear mean-field and pairing correlations, enabling an accurate portrayal of ground and excited states of nuclei. This framework is further refined with density-dependent meson exchange (DDME) [2] functional, enhancing the description of asymmetric nuclear matter, neutron matter, and nuclei far from stability.
The region of the nuclear landscape abundant in neutrons showcases captivating phenomena,
including the formation of exotic structures like clusters and halos, the coexistence of various
shapes, phase transitions, and the suppression of shell effects [3,4]. Here, we try to analyze the
cluster structures and low-energy monopole strength in neutron-rich nuclei.
References
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Shape coexistence is a very important phenomenon that takes place in several regions of the nuclear chart. Among these regions, the isotopic chain of Krypton has been the subject of several experimental investigations and thus it can be considered as an excellent candidate to test the systematic behaviours of theoretical models. [1]
By going from the neutron deficient to more neutron rich Kr isotopes one observes a variety of shapes and trends that, still nowadays, represent a challenge for the most advanced theoretical models.
Among the various many-body methods, the Bohr Hamiltonian (BH) [2] based on microscopic Hartree-FockBogoliubov calculations is particularly interesting as it gives access to the position of low-lying excited states as well their electromagnetic transitions at a very low computational cost. This makes the BH an ideal method to perform large-scale calculations along the entire nuclear chart in order to identify global trends [3].
In my presentation, I will show some systematic calculations using various Gogny interactions in Kr isotopic chains. Identifying possible correlations among trends of low lying states and bulk properties of the effective interaction may be useful in order to include beyond mean field calculations within the adjustment protocol of effective nucleon-nucleon interactions.
[1] Nomura, K., and al., (2017). Structure of krypton isotopes within the interacting boson model derived from the Gogny energy density functional. Physical Review C 96(3): 034310.
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[3] Delaroche, J.P., and al. , (2010). Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction. Physical Review C, 81(1), p.014303.
We have systematically studied the one-particle structure at low excitation energy for the mass region A = 150 using the quasiparticle-phonon coupling plus rotor method (QPRM). The interactions involved in this approach are the deformed mean field of Nilsson, the monopole pairing interaction described in the BCS formalism and the quadrupole-quadrupole forces. The microscopic structure of the quadrupole phonon is given by the Tamm-Dancoff approximation (TDA). Under the assumption of an axially symmetric rotational motion, the effects of recoil and Coriolis forces are included. The theoretical calculations are performed for the rich proton odd-A, where the configuration of the intrinsic states has both quasi-particle and quasi-particle-phonon coupling components. The structural evolution through the ground and low-lying single quasi-proton states of 155Tb is discussed and compared with the available experimental data.
This study examines the use of a sextic oscillator in the 𝛽 degree of freedom of the Bohr Hamiltonian to understand critical point solutions in nuclear transitions from spherical to deformed forms. We begin by examining critical point solutions such as E(5), which model the 𝛽 degree of freedom using an infinite square-well (ISW) potential. This model is essential for examining phase transitions in nuclear forms, and differs mainly in its treatment of the 𝛾 degree of freedom. By replacing the ISW potential with a quasi-exactly soluble sextic potential, we obtain exact solutions for the low-energy spectrum and analyze these results in detail. In addition, various forms of the sextic potential, although not exactly solvable, can be treated numerically, providing benchmarks for criticality in shape transitions. We also review two decades of related research, including a map of nuclide regions where these models apply, summarizing their implications in nuclear structure studies.
Shape of nuclei is determined by a fine balance between the stabilizing effect of closed shells and the pairing and quadrupole forces that tend to induce deformation [1]. In the mass region around A=100, there exist clear cut examples of the rapid appearance of deformation such as Zr (even-even) [2] and Nb isotopes (odd-even) [3], which can be understood in terms of the coexistence of two different configurations, i.e., shape coexistence. Sr [4] isotopes are also good candidates to study the onset of nuclear deformation and the influence of shape coexistence, while Ru and Mo [5] isotopes seem to be placed at the border of dilution of shape coexistence In addition, the structural evolution of odd-mass isotopes in this region is significant due to the diversity of configurations and coexisting shapes and to the enhancement of the onset of deformation [3].
In this contribution will be used as framework the Interacting Boson-Fermion Model [6] with Configuration Mixing (IBFM-CM) to introduce a mean-field view (intrinsic state) for studying the evolution of the nuclear deformation in A=100 region, focussing on the case of odd-even Nb isotopes. Two complementary approaches will be used for studying shape evolution: first, an algebraic approach employing a laboratory frame of reference, and secondly, a geometric-oriented method within the context of an intrinsic state formalism. The objective is to compare the onset of deformation in Nb isotopes with the even-even cases, such as Sr and Zr, extracting information from the intrinsic state, but also from spectroscopic properties.
To conclude, by applying the IBFM-CM framework and employing both algebraic and geometric approaches, this contribution aims at providing insights into the evolution of nuclear shapes in even-even and odd-even nuclei in the mass region around A=100.
[1] K. Heyde and J. L. Wood, Rev. Mod. Phys. 83, 1467 (2011).
[2] J.E. García-Ramos and K. Heyde, Phys. Rev. C 100, 044315 (2019).
[3] N. Gavrielov, A. Leviatan, and F. Iachello, Phys. Rev. C 106, L051304 (2022).
[4] E. Maya-Barbecho and J.E. García-Ramos, Phys. Rev. C 105, 034341 (2022).
[5] E. Maya-Barbecho, S. Baid, J.M. Arias, and J.E. García-Ramos, Phys. Rev. C 108, 034316 (2023).
[6] F. Iachello and P. Van Isacker, The interacting boson-fermion model (Cambridge University Press, Cambridge, 1991).
We study the shape coexistence in the nucleus $^{28}$Si with the nuclear shell model using numerical diagonalizations complemented with variational calculations based on the projected generator-coordinate method. The theoretical electric quadrupole moments and transitions as well as the collective wavefunctions indicate that the standard USDB interaction in the $sd$ shell describes well the ground-state oblate rotational band, but misses the experimental prolate band.
Guided by the quasi-SU(3) model, we show that the prolate band can be reproduced in the $sd$ shell by reducing the energy of the $0d_{3/2}$ orbital. Alternatively, in the extended $sdpf$ configuration space the SDPF-NR interaction, which describes well other Si isotopes, also reproduces the oblate and prolate bands. Finally, we address the possibility of superdeformation in $^{28}$Si within the $sdpf$ space. Our results disfavour the appearance of superdeformed states with excitation energy below 20 MeV.
The stability of nuclei has traditionally found explanation through the concept of magic numbers, comprehensively elucidated by the interplay of central and spin-orbit interactions. However, as we venture into the domain of unstable nuclei, these foundational ingredients begin to exhibit limitations. Roughly two decades ago, the tensor interaction was introduced as an attempt to address these limitations, yet it might not fully capture the dynamic evolution of nuclear magicity within specific mass regions, prompting the search for missing universal mechanisms.
We introduce a novel perspective where the Dirac mass kinetic term, which stems from the distinctive participation of a spin-0 boson in the nuclear strong force, plays a pivotal role in generating the nuclear shell structure. Namely, the combination of the Dirac mass kinetic term with the spin-orbit term redefines magic numbers both in stable and exotic nuclei. The identification of this mechanism allows to provide a broad understanding of the origin and evolution of nuclear magic numbers.
Abstract: Understanding the structural transition of nuclei at fission limits is a fascinating and ongoing investigation in nuclear physics. The Giant Dipole Resonance (GDR) is a significant probe for investigating the shape evolution of an atomic nucleus [1]. However, it is challenging to differentiate GDR γ-ray emissions before and after the fission reaction, as validated by existing experimental results. It is important to choose the deformation parameters and suitable parametrization method for calculating the total potential energy surfaces and GDR observables [2]. In the present work, we employed the Lublin Strasbourg Drop (LSD) model to calculate the potential energy surface (PES) of Thorium isotopes [3]. The LSD model includes curvature and congruence energy terms not previously included in liquid drop models, which are essential at the limit of fission [3]. Various mathematical functions have been adopted as shape parametrization methods in recent years. These include the traditional Quadrupole Bohr (β, γ) and Cassini (c, r) and the Funny-Hills (c, h, α) shape parametrizations to compute deformation-dependent energy terms. These parametrizations do not have any convergence properties. In this circumstance, K. Pomorski [4] and their research team developed a novel parametrization method based on Fourier series expansion, which we employed to compute the potential energy surface of different thorium isotopes with new collective coordinates, including non-axiality (ε), elongation (q1), left-right asymmetry (q2), and neck thickness (q3). Investigating the GDR observables, such as the GDR width and GDR cross-section, in hot and rotating nuclei at the fission limit will shed to understand the shape transition [5]. The study of the dependence of the GDR observables on nuclear shape transitions at fission limits is in progress.
Reference
1. J. J. Gaardhoje, Ann. Rev. Nucl. Part. Sci. 42, 483 (1992).
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Significant progress has been made in comprehending the structure of nuclei near the doubly closed $^{208}$Pb core nucleus (N=126, Z=82) through the use of the shell model. The shell-model structure calculations for valence protons in N = 126 nuclei and for valence neutrons in Z = 82 nuclei are largely complete [1],[2]. However, for nuclei that contain both valence protons and neutrons, the shell-model space expands significantly, rendering complete calculations essentially impossible.
Studies on N = 124 nuclei have focused on understanding how the two neutron holes
($^{}$v$^{-2}$) in the core influence the valence proton structure observed in N = 126 nuclei [3],[4]. Various theoretical approaches were used to evaluate the experimental results for N = 124 nuclei and investigate these effects. However, the lack of experimental data for the N = 124 proton-particle nuclei hindered analogous studies in these situations.
This study aims to theoretically predict the low-lying spin states in N=124 isotones with mass numbers ranging from A=207 to A=213. The results will be compared with existing experimental data to assess the influence of the ($^{}$v$^{-2}$) states of the core and the effect of added protons on the nuclear structure of these isotones.
In the present work, we investigate the structure of low-spin states in four N=124 isotones: $^{207}$Bi (Z=83), $^{209}$At (Z=85), $^{211}$Fr (Z=87), and $^{213}$Ac (Z=89). With valence nucleons consisting of both proton particles and neutron holes, these nuclei provide an opportunity to examine the competition between proton-particle and neutron-hole excitations.
The quasiparticle-phonon coupling plus rotor model, or QPRM, was used in this study [5]. The deformed Nilsson averaged field, which incorporates the deformation parameters, is used in this method to determine the wave function of the states and single-particle energies.
The odd-mass system could be treated as a separate quasiparticle motion using the BCS (Bardeen, Cooper, and Schrieffer) approach [6], which makes it possible to determine the quasiparticle energies and the occupation probability coefficients of the intrinsic states.
The quadrupolar excitation mode can be explored using the TDA (Tamm-Dancoff approximation).
The recoil energy is also considered, and the rotational energy of these nuclei is treated using intermediate coupling (deformation alignment and rotation alignment). The decoupling parameter, coriolis effect, and rotational parameter are adjusted for both positive and negative parity bands to reproduce the observed energies of low spin states.
We used the QPRM technique [7], to investigate the low spin states of these nuclei. The systematic of the four N=124 isotones is analyzed to determine the configuration of low spin states. The impact of each correction: pairing, quadrupolar force, zero point rotational energy, and the Coriolis effect is demonstrated to understand the nuclear structure of these nuclei.
Key words: level structure, collectivity, deformation parameter, moment of inertia, coriolis effect
References :
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In the study of thermal neutron-induced fission of \textsuperscript{235}U, a dispersion in the experimental data concerning the average prompt neutron multiplicity $\overline{\nu}$ as a function of the pre-neutron mass $A$ of the fragments was observed [1]. To identify the source of this dispersion, we have conducted a Monte Carlo simulation of the measurement process carried out with the 2E technique. The input data include the pre-neutron fragment mass yield ($Y(A)$), kinetic energy distribution $E$, number $n$ of prompt neutrons emitted, and their corresponding kinetic energy $\eta$ relative to the center of mass (CM). These data are based on the experimental results by Al-Adili et al. [1].
In the simulated experiment, the fragments with pre-neutron masses $(A,A')$ arrive at the detector after emitting $(n,n')$ neutrons, with resultant masses $(m,m')$, and due to recoil effects, kinetic energies $(e,e')$. In each fission event, the quantities simulated as measured are the masses $(A_s,A_s')$ and kinetic energies $(E_s,E_s')$, which are calculated using the relations $A_s+A_s'=236$ and $A_s E_s=A_s' E_s'$, representing the conservation of mass and linear momentum conservation, where $E_s\approx e/(1-n/A_s)$ and $E_s'\approx e'/(1-n'/A_s')$.
Based on the $n$ values corresponding to the mass $A_s$ we construct the curve $\overline{\nu}_s (A)$. The results show that $\overline{\nu}_s (A)>\overline{\nu}(A)$ in regions around $A=115$ and $A>150$, respectively. The source of these discrepancies lies in the dispersion of $e$ relative to $E$ due to the recoil effects, which produces a dispersion in the calculated mass relative to the pre-neutron one. The discrepancy is greater if, in each fission event, the correction is performed using $\overline{\nu}(A)$ instead of $n$. Using the same input data, we also simulated the measurement of the kinetic energy distribution $e$ as a function of mass $m$. The result demonstrates that $\sigma_e(m)$ exhibits a peak around $m=109$, in agreement with the experimental data from Belhafaf et al. [2]. The origin of this peak, not simulated in the pre-neutron curve $\sigma_E(A)$, is due to dispersion of $m$ and $e$ relative to pre-neutron mass $A$ and kinetic energy $E$ values.
In summary, to trace back to the primary distributions of quantities associated with the fission fragments, it is necessary to adjust the results of the simulation of the experiment with the values from the experiment itself.
References
[1] A. Al-Adili et al., “Prompt fission neutron yields in thermal fission of U 235 and spontaneous fission of Cf 252,” Phys. Rev. C, vol. 102, no. 6, 2020.
[2] D. Belhafaf et al., “Kinetic energy distributions around symmetric thermal fission of U234 and U236,” Zeitschrift für Phys. A Atoms Nucl., vol. 309, no. 3, pp. 253–259, Sep. 1983.
Pairing in atomic nuclei reveals profound insights into the intrinsic behavior and properties of nuclear systems [1]. Numerous theories have arisen in the exploration of this field, with particular significance attributed to the BCS theory [2]. Extending the boundaries of this theory, the Finite Temperature BCS (FTBCS) theory, with the inclusion of angular momentum [3], has emerged as an important framework for understanding the properties of atomic nuclei [4]. Lately, there has been a notable emphasis on the integration of quasi-particle number fluctuations into the FTBCS theory (FTBCS1) [5].
This study focuses on the Dysprosium (Dy) nucleus, employing the FTBCS1 model to investigate the impact of quasi-particle number fluctuations on pairing gaps, heat capacity, entropy, and level density. Contrary to the expectations from FTBCS theory, the findings reveal that the gap parameter, instead of vanishing at a specific temperature, experiences a gradual reduction, maintaining a finite value. Similar effects are observed in entropy and heat capacity plots, which can be attributed to quasi-particle number fluctuations. Notably, a smooth super-fluid to normal phase transition is observed in FTBCSemphasized text1, a phenomenon absent in traditional FTBCS theory.
References
[1] T. Vu Dong et.al, Phys. Rev. C 107 (2023) 064319.
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[4] N. Q. Hung and N. D. Dang, Phys. Rev. C 78 (2008) 064315.
[5] N. Q. Hung and N. D. Dang, Phys. Rev. C 84 (2011) 054324.
Abstract:
The potential energy surface of 182-186Pt, 184-188Hg, and 186-190Pb in the 4D deformation parameters space (c,ŋ,a3,a4) are evaluated within the macroscopic-microscopic approach using the so-called Fourier-over-Spheroid shape parametrization [1]. The LSD formula [2] is used to evaluate the macroscopic part of the energy, while the microscopic energy correction was obtained using the Yukawa-folded single-particle potential [3]. Pairing correlations are taken within the BCS approximation using an approximate particle-number projection. Each potential energy point at the (β, γ) plane was minimized with respect higher-order deformation parameters (a3 and a4).
A possible shape coexistence and appearance of the shape isomers is discussed.
References:
The Gogny-type density functionals have finite-range and density-dependent terms. The parameters of the functionals are designed not only to reproduce the basic properties of finite nuclei but also to satisfy the saturation properties of nuclear matter. Consequently, calculations using a single density functionals can describe experimental data in various mass regions. However, the mean-field calculations using the functionals miss some corrections. Especially, the odd nuclei are often treated with the equal filling approximation. In contrast, there are semi-empirical methods that construct a shell-model Hamiltonian by fitting experimental values. The shell-model (configuration interaction) calculations can take into account correlations beyond mean fields, but we have to determine the model space and then fit the effective interactions with experimental results.
In this study, a hybrid approach is attempted by applying a method using the Gogny-type density functionals to shell-model calculations. The resultant density-dependent interaction of the shell-model Hamiltonian is self-consistently determined. In contrast to semi-empirical methods, this hybrid model can compute shell-model Hamiltonian including the density-dependent force on the ground-state density. The purpose of this calculation is to investigate which nucleon-nucleon interactions make important contributions to the shell structure systematically from stable nuclei to unstable nuclei. We investigate excitation spectra of the odd nuclei with correlations beyond the mean-field.
In this presentation, we will present results for the pf-shell nuclei in comparison with the experimental results. In particular, we will focus on the calculation with the isospin-dependent tensor force, and show that the isospin dependence is necessary to describe characteristics in neutron-rich nuclei.
In order to measure the lifetimes of low-lying excited states in Xe, Cs and Ba isotopes in the A=120 mass region, two fusion-evaporation experiments have been recently performed at HIL, Warsaw. The experimental setup is composed of NEDA (52 liquid scintillators, for neutron detection), EAGLE (15 HPGe detectors, for gamma detection), and a Plunger device that allows to apply the recoil-distance Doppler shift (RDDS) method.
Among the lifetimes of interest to be measured, we first aim to give a solid support to the prolate-oblate shape coexistence and chiral bands recently discovered in 119Cs [1,2] by extracting the intra- and inter-band B(E2) transition probabilities of several key levels.
A second aim is to measure the B(E1) transition probabilities between the negative-parity bands and the ground-state bands of 118Xe and 120Ba, which will shed light on the extent of octupole correlations in the light xenon and barium nuclei.
The third aim is to measure the half-lives of several isomers recently identified in a thin-target experiment which was performed at JYFL, Finland using the JUROGAM3+ MARA setup.
The data analysis of these two experiments and the latest results obtained will be presented during this conference.
[1] K. K. Zheng et al., Phys. Lett. B 822 (2021) 136645
[2] K. K. Zheng et al., Eur. Phys. J. A 58 (2022) 50
Tellurium isotopes in the A $\approx$ 125 mass region are good candidates to study shape changes owing to their transitional nature. The h$_{11/2}$ intruder orbitals in this region drives the nuclear shape. The protons occupying the low-$\Omega$ h$_{11/2}$ orbitals drive the nucleus to a prolate shape while the neutrons in the mid to high $\Omega$ orbitals result in an oblate shape. Furthermore, the neighboring even-even nuclei -$^{124,126}$Te are said to possess E(5) critical point symmetry, corresponding a shape-phase transition between a spherical vibrator and a $\gamma$ unstable one[1]. As the $^{125}$Te nucleus can be considered a neutron hole coupled to the even-even core $^{126}$Te, we can also expect to observe various shape-change phenomena in this nucleus.
The excited nuclear states of $^{125}$Te were populated in the $\alpha$ induced reaction $^{124}$Sn($\alpha$, 3n)$^{125}$Te. The K-130 cyclotron at VECC, India, provided the $\alpha$ beam at an energy of 35 MeV. The de-exciting $\gamma$ rays were detected by the Indian National Gamma Array (INGA) spectrometer, comprising 7 Compton-suppressed HPGe detectors. The detectors were arranged as follows - 4 detectors at 90$^{\circ}$, 2 at 125$^{\circ}$ and one detector at 40$^{\circ}$. The digital data acquisition system was
based on PIXIE-16 (XIA LLC, USA) 12-bit 250 MHz digitizer modules[2]. Further analysis was performed using the RADWARE package[3].
In the present work, the previously obtained level scheme for $^{125}$Te[4,5] has been verified and expanded to about 39/2$\hbar$ by adding 83 new $\gamma$ transitions. In particular, the bands based on the 1/2$^{+}$ and 3/2$^{+}$ levels have been identified as signature partners. The signature splitting between the bands indicates triaxial deformation[6]. PES calculations show a change in $\gamma$ from -50.5$^{\circ}$ to 39.2$^{\circ}$. We interpret the results within the Particle Rotor model(PRM) framework. The calculations were performed with an even-even triaxial core of $^{126}$Te while considering a VMI (Variable Moment of Inertia) treatment for the core spectrum. We discuss probable configurations for the possible band structures obtained in the present work and the shape change effects observed.
References:
[1] S.F Hicks et al., Phys. Rev C 95:034322, (2017).
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[6]L-C He et al., Chinese Phys. C 41(4):044003, (2017).
The valence nucleons are subject to Coriolis and centrifugal forces caused by the rotation of the core of the nucleus. These forces lead to an energy shift between the states with even and odd spins within a rotational band based on the total angular momentum of the states, resulting in the formation of two bands with a ΔI = 2 connection through M1/E2 transitions. Each band is characterized by a quantum number known as signature, which reflects the signature splitting in an axially symmetric nucleus. The unfavoured states experience an increase in excitation energy due to this effect, while
the excitation energy of the favoured states decreases. In cases of odd-odd nuclei where bands are built on specific configurations like πh11/2 ⊗ νh11/2, at lower excitation energy and spin, the unfavoured states exist lower in energy, making them more yrast compared to the favoured states. The system reverts to normal behaviour at higher excitation energies and spin, with the spin at which this occurs being termed the point of inversion; this is referred to as signature inversion. Various factors contribute to the inversion, such as pairing effects, triaxiality, and neutron-proton interaction.
Studying this phenomenon experimentally often involves using gamma-spectroscopy. Research in this area can be particularly challenging when dealing with neutron-deficient isotopes, as their low formation cross-sections make them difficult to study using the available stable beams. Additionally, even if these isotopes are formed, they often have very short half-lives, necessitating in-beam spectroscopy or high-speed separation techniques.
In a recent experiment conducted with JUROGAM3+MARA at Jyv¨askyl¨a, Finland, using a 64Zn beam directed at a thin 58Ni target, we have discovered new bands and transitions in 114I, 117Cs, 118,120Ba, and 120La. Our current research is focused on investigating the phenomenon of signature inversion and its impact on our current understanding of nuclear shapes, particularly in the neutron-deficient isotopes of I, Cs, and La, using in-beam gamma spectroscopy and recoil decay tagging techniques.
During this presentation, I will mainly present the new results obtained for the odd-odd isotopes of I, Cs, and La from the perspective of collectivity and signature inversion.
The tungsten isotopes 165W and 169W have been studied by using fusion-evaporation reactions $^{92}$Mo($^{78}$Kr,4p1n)$^{165}$W and $^{92}$Mo($^{84}$Kr,1α2p1n)$^{169}$W at the Accelerator laboratory of the University of Jyväskylä, Finland. Beam energies of 380 and 402 MeV were used for the $^{165}$W and $^{169}$W experiments, respectively. The vacuum-mode separator MARA [1], the JUROGAM 3 germanium-detector array [2], and the MARA focal-plane detector setup [3] were utilised to select the reaction channels of interest and determine energies and half-lives for the previously unknown isomeric state properties. The structure above these 13/2$^+$ isomers is relatively well known in both nuclei [4,5], allowing us to use the in-beam gamma rays in addition to mass and X-ray information to identify the isomeric transitions observed at the focal plane. The new results and systematics of isomerism in tungsten isotopes will be discussed.
[1] J. Uusitalo et al., Acta Phys. Pol. B 50 (2019) 319-327.
[2] J. Pakarinen et al., Eur. Phys. J. 56 (2020) 149.
[3] J. Sarén et al., Nucl. Instrum. Methods Phys. Res. B 541 (2023) 33-36.
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In this report, the design and performance of the Modular Total Absorption Spectrometer (MTAS) built and commissioned at the Oak Ridge National Laboratory is presented [1]. The MTAS results of the β feeding intensities of 88Rb, fission products with large cumulative yields in nuclear reactors [2]. By comparing MTAS results with previous measurements, 88Rb provides a validation of MTAS’s ability to determine ground-state feedings in β decays. The deconvolution of 88Rb decay spectra suggests that MTAS can distinguish an allowed β spectral shape from a first forbidden unique β spectral shape. Furthermore, a new data analysis technique is proposed and verified to deal with nuclei with no information about the decay scheme.
References:
[1] Nucl. Inst. Meth. Phys. Res. A 836 (2016) 83-90
[2] Phys. Rev. C 105, 054312 (2022)
Double alpha decay, a simultaneous emission of two alpha particles by the nucleus, is a possible rare decay mode first discussed in 1979 [1]. This decay was considered as two competing processes: immediate two particle emission or the emission of a 8Be-cluster with its instantaneous disintegration. However, the predicted half-lives for trans-lead isotopes were found to be too long for simple observation [2]. Recent microscopic calculations [3] show that expected kinematics of two-particle decay is symmetric, back-to-back emission of alpha particles, and the predicted branching ratio of the double alpha mode is on the order of 10-8 compared to conventional alpha decay, which would allow detection of such rare events in a coincidence measurement.
A dedicated experiment to the search for double alpha decay was conducted in 2022 at the FRS Ion Catcher (GSI), a universal system to perform decay and laser spectroscopy and mass measurements of heavy ions. An offline 228Th source was used to produce 224Ra recoil ions that were transported to a high geometry detector. Two sensitive silicon strip detectors detected all charged particles emitted by 224Ra. The number of registered decay events is on the order of 109 which should be sufficient to test the theoretical prediction. Details on the design and performance of the experiment have been recently published [4].
Data obtained during a 4-month measurement are currently being analyzed. In this talk, we will present intermediate results necessary for the complete estimation of the background from decay products of 224Ra. In particular, details of the energy and time calibrations will be shown. A detailed geometry model used with the hit-pattern information and Monte Carlo simulations that describe random coincidences will be discussed.
The semi-magic 120
50 Sn70 lies in the neutron mid-shell among the other
stable Sn isotopes, where shape coexistence was observed with the signature
of deformed bands built on excited 0+ states intruding into the yrast band
that is built on the spherical ground state. However, the lifetime of the
excited 0+3 only has a lower limit of 6 ps in the literature, which prevents the
study of transition strengths, and as a result, its structure is obscured.
The 0+3 lifetime was measured in the first thermal neutron capture experiment,
119Sn(n,γmany)120Sn, at the Institut Laue-Langevin, where the world’s
highest-flux thermal neutron beam was delivered at 108 n/cm2/s at the target
position on an isotopically enriched 119Sn target. Low-spin states in 120Sn
were populated up to the neutron separation energy Sn = 9.1 MeV, and
the decaying gamma-ray cascades were detected with the Fission Product
Prompt Gamma-ray Spectrometer (FIPPS) comprised of eight Comptonsuppressed
HPGe clovers coupled to an array of 15 LaBr3(Ce) scintillation
detectors. The LaBr3(Ce) scintillators, which were used for gamma-ray detection
and lifetime measurement using the Generalized Centroid Difference
(GCD) method, have fast timing responses and are ideal for extracting lifetimes
between 10 and a few hundred ps.
In total, there are 4 × 109 counts in the γγγ cube where two LaBr3(Ce)
events were in coincidence with one HPGe.
Lifetime measurement for the 0+3 state in 120Sn using the GCD technique
will be presented. Additional lifetimes will also be measured where the γγγ
cascade’s statistics permit, and detailed gamma-ray spectroscopy will be performed
using the FIPPS data to significantly extend the 120Sn level scheme.
Nuclear mass measurements have recently been extended conspicuously to proton-rich region in the upper $fp$ shell. The new data are utilized to study isospin symmetry breaking phenomena using Coulomb displacement energy (CDE) and triplet displacement energy (TDE) as probes. The new mass data, either measured for the first time or with greatly improved accuracy, removed several previously found ``anomalies" in the systematical behavior in the $fp$ shell. Remarkably, more regular odd-even staggering patterns can be established in both CDE and TDE, calling for a uniform explanation in terms of isospin-nonconserving (INC) forces across the $sd$, $f_{7/2}$, and upper $fp$ shells. By extending the large-scale shell-model calculation [Phys. Rev. Lett. 110, 172505 (2013)] to the upper $fp$-shell region, we found that, in order to describe the new data, the same INC force is required as previously used for the $f_{7/2}$ shell. Especially, we propose the $T=1$ TDE for those triplet nuclei, that have $pp$, $nn$, and $pn$ pairs on top of a common even-even $N=Z$ core, to be a good indicator for the isotensor component of isospin violating interactions, which is estimated here to be 150 keV.
The β-delayed γ-ray spectroscopy of neutron-rich Ru isotopes is investigated at the Radioactive Isotope Beam Factory of RIKEN. The β-decay schemes of these nuclei are established with the use of prompt-prompt and prompt-delayed γ-γ-coincidence measurement by EURICA γ-ray detection array [1]. The systematic trends of low-lying states and their implications on single-particle orbit and shape evolution far below 132Sn will be discussed.
References
[1] P.-A. Söderström et al., Nucl. Instr. Meth. Phys. Res., Sect. B 317, 649 (2013).
The ab initio description of nuclei has seen major advances combining innovative many-body developments with nuclear forces and currents based on chiral effective field theory. This has led to ab initio calculations up to heavy nuclei, and highlighted the importance of uncertainty quantification as well as the development of accurate interactions for medium-mass to heavy nuclei. This talk will discuss novel chiral low-resolution interactions that accurately describe bulk properties from oxygen to lead, including uncertainty estimates from the effective field theory truncation. Moreover, we will discuss the role of two-body currents for electroweak properties of nuclei and present applications of ab initio calculations to tests of the standard model and beyond.
This presentation will explore the shell evolution across the neutron dripline by showing recent experimental results on the spectroscopy of exotic nuclei around N=20, utilizing the SAMURAI (large-acceptance multi-purpose spectrometer) at RIBF, RIKEN. The O-Ne dripline region represents the neutron-rich frontier, offering unique opportunities to study phenomena near and beyond the neutron dripline. We will focus on two key topics: the deformed halo nucleus 31Ne and the doubly-magic candidate nucleus 28O (Z=8, N=20).
For 31Ne (Z=10, N=21), we present kinematically complete measurements conducted with both Pb and C targets. The Pb-target-induced reactions are primarily governed by Coulomb breakup, while the C-target-induced reactions involve inelastic excitation, one-proton removal from 32Na, and one-neutron removal from 32Ne. These experimental results provide insights into the shell-evolution, deformation, and halo properties of 31Ne.
Regarding 28O, we discuss the recent observation of this nucleus and the phenomenon of shell melting at N=20 beyond the neutron dripline [1]. We will also cover future perspectives on the spectroscopy of extremely neutron-rich nuclei, emphasizing the implications for shell evolution.
[1] Y. Kondo et al., Nature 620, 964 (2023).
The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) [1-2] considers the effects of axial deformation, pairing correlation and continuum in a self-consistent and microscopic way, and has been successfully applied in many studies on exotic nuclei. Recently, the DRHBc theory was extended to include the nuclear magnetism, i.e., the time-odd DRHBc (TODRHBc) [3], and to incorporate triaxial deformation, i.e., the triaxial RHB theory in continuum (TRHBc) [4]. Based on the DRHBc and TODRHBc theories, nuclear magnetism in the halo nucleus $^{31}$Ne is explored [3]. A possible binding mechanism from nuclear magnetism is revealed, contributions of the halo and the core to nuclear current are studied, and a layered feature in the spatial distribution of current is observed. Based on the DRHBc and TRHBc theories, the proton dripline nucleus $^{22}$Al is investigated [5]. The possibility of a proton halo is examined by analyzing the single-particle levels, density profiles and root-mean-square radii. It is found that triaxiality plays an indispensable role in the appearance of s-wave component for the valence proton in $^{22}$Al.
References:
[1] S.-G. Zhou, J. Meng, P. Ring, et al., Neutron halo in deformed nuclei, Phys. Rev. C 82, 011301 (2010)
[2] L.-L. Li, J. Meng, P. Ring, et al., Deformed relativistic Hartree-Bogoliubov theory in continuum, Phys. Rev. C 85, 024312 (2012)
[3] C. Pan, K. Zhang, and S. Zhang, Nuclear magnetism in the deformed halo nucleus $^{31}$Ne, Phys. Lett. B 855, 138792 (2024)
[4] K.Y. Zhang, S.Q. Zhang, and J. Meng, Possible neutron halo in the triaxial nucleus $^{42}$Al, Phys. Rev. C 108, L041301 (2023)
[5] K.Y. Zhang, C. Pan, S. Wang, Is there a proton halo in $^{22}$Al?, submitted to Phys. Rev. C (2024)
There have been tremendous efforts studying the possible effect of neutron-proton (np) pairing on various nuclear properties. Most studies have focused on its impact on the nuclear binding energy and spectroscopy. In this contribution, I will start by a simple systematics of alpha correlation energies and illustrate how alpha clustering is affected by the like-particle pairing. It has ben expected that super-allowed alpha decay may be observed in N~Z nuclei with the further enhancement of alpha clustering by the np pairing. We tend to argue now that it may not be the case. On the other hand, our large-scale shell model calculations seem to indicate that the np correlation may enhance significantly the proton decay rate from odd-odd nuclei.
If time allows, I would also like to discuss the effect of np pairing on Gamow-Teller decays of nuclei below $^{100}$Sn.
The recently observed abnormal bifurcation of the double binding energy differences $\delta V_{pn}$ between the odd-odd and even-even nuclei along the $N=Z$ line from Ni to Rb has challenged the nuclear theories. To solve this problem, a shell-model-like approach based on the relativistic density functional theory is established, by treating simultaneously the neutron-neutron, proton-neutron, and proton-proton pairing correlations both microscopically and self-consistently. Without any ad hoc parameters, the calculated results well reproduce the observations, and the mechanism for this abnormal bifurcation is found to be due to the enhanced proton-neutron pairing correlations in the odd-odd $N=Z$ nuclei, compared with the even-even ones. The present results provide an excellent interpretation for the abnormal $\delta V_{pn}$ bifurcation, and provide a clear signal for the existence of the proton-neutron pairing correlations for nuclei close to the
$N=Z$ line.
The well-explored A~190 Hf-Ta-W nuclei near the valley of stability feature robust axially symmetric prolate shapes and associated high-K isomerism. The very-neutron-rich isotopes of these elements are far less explored experimentally as they cannot be accessed via fusion-evaporation or neutron-transfer reactions, and varying predictions of prolate-to-oblate shape transitions in different theoretical models remain untested. To access this neutron-rich region, a 198Pt primary beam at NSCL was fragmented for the first time, populating a wide palette of isotopes in high-spin metastable states. Following momentum-analysis by the A1900 fragment separator over a ~400 ns flight path, the isotopes were implanted in a Si detector stack surrounded by the GRETINA array to detect delayed gamma rays correlated with the implants. A range of new as well as previously observed isomers, with half-lives from a few hundred ns to few hundred μs, were populated in 72<Z<77 nuclei. With the available gamma-gamma resolving power of GRETINA, collective band structures were populated in some cases and level schemes deduced from the isomeric decays. These first spectroscopic data on high-spin excitations in this rather inaccessible region of the nuclear chart will be presented and discussed within the framework of available model predictions.
This collaborative work, spearheaded by UMass Lowell, involved researchers from Michigan State, Central Michigan and Western Michigan universities, RIKEN, Lawrence Livermore and Lawrence Berkeley National Laboratories, and the National Nuclear Data Center at Brookhaven National Laboratory. The work is supported by the U.S. Department of Energy and the National Science Foundation.
In 2021, the MAJORANA DEMONSTRATOR experiment concluded its investigation into neutrinoless double beta decay involving $^{76}$Ge. Proven to be one of the world's ultra-low-background facilities, we adapted the apparatus to explore the rare decay of a distinct isotope. Notably, in nature $^{180m}$Ta stands as the sole known isotope existing in an isomeric state rather than the ground state. This unobserved isomeric decay is hindered by spin suppression. However, measuring its rate will provide insight into the strength of its production, for example, through neutrino-induced reactions. Beyond understanding the underlying mechanisms of the decay this exceptional state the measurement of the decay rate holds potential of probing dark matter through stimulated decay as an addition to ton-scale sized detectors. To this end, we introduced Ta samples amidst the Ge detectors, capitalizing on the deep-underground ultra-low background environment, the exceptional resolution of the MAJORANA detectors, and established analytical methodologies to search for both, the nuclear decay and potential DM-induced emissions. The first year of data was dominated by backgrounds from surface activation yet still was able to set world-leading limits. I plan to present the findings from our latest data collection and discuss their implications for the dark sector.
This material is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, the Particle Astrophysics and Nuclear Physics Programs of the National Science Foundation, and the Sanford Underground Research Facility. We acknowledge the support of the U.S. Department of Energy through the LANL/LDRD Program.
The radioisotope thorium-229 features a nuclear isomer with an exceptionally low excitation energy of ≈ 8.3 eV and a favourable coupling to the environment, making it a candidate for a next generation of optical clocks allowing to study fundamental physics such as the variation of the fine structure constant [1,2]. While first indirect experimental evidence for the existence of such a nuclear state dates from almost 50 years ago, the proof of existence has been delivered only recently by observing the isomer’s internal electron conversion decay [3]. This discovery triggered a series of successful measurements using the α-decay of uranium-233 of several properties, including its energy, an important input parameter for the development of laser excitation of the nucleus. In spite of recent progress, the difficulties to observe the isomer’s radiative decay remains a dark spot of this research field. The development towards a "nuclear clock" was further hindered by a too large uncertainty on the isomer energy. The study of the β-decay of actinium-229 inside a large-bandgap crystal at the ISOLDE facility at CERN lead to the first observation of the radiative decay [4] and set the scene for direct laser excitation of the thorium-229 nucleus [5]. In this contribution, the nuclear clock concept is introduced and recent developments are discussed.
[1] E. Peik et al., Europhys. Lett. 61, 2 (2003).
[2] E. Peik et al. Quantum Sci. Technol. 6 (3), 034002 (2021).
[3] L. von der Wense et al. Nature 533 (7601), 47–51 (2016).
[4] S. Kraemer et al. Nature 617, 706-710 (2023).
[5] J. Tiedau et al. Phys.Rev.Lett. 132 182501 (2024).
First-order electromagnetic processes are the primary mechanism by which excited states in atomic nuclei relax, most-often via single γ-ray emission. Since both the initial- and final-state wave functions possess a well-defined spin and parity, conservation laws impose a characteristic multipolarity for each discrete transition. Nature favours pathways that proceed via the lowest-available multipole order. Yet, situations arise in which the only available decay pathway is hindered by a larger spin-change requirement.
The only proposed observation of a discrete, hexacontatetrapole (E6) transition in nature occurs from the isomeric, T1/2 = 2.54-minute decay of 53mFe. However, there are conflicting claims concerning its γ-decay branching ratio, and a rigorous interrogation of γ-ray sum contributions is lacking in the published work [1]. Experiments performed at the Australian Heavy Ion Accelerator Facility were used to study the decay of 53mFe, and confirm the existence of the E6 transition. For the first time, sum-coincidence contributions to the weak E6 decay have been firmly quantified using complementary experimental and computational methods [2]. Shell-model calculations were also performed in the full pf model space to investigate the nature of high-multipolarity transitions in atomic nuclei. This presentation will provide an overview the experiments, results obtained from this work and their interpretation.
This work is supported by the Australian Research Council Grants No. DP170101673 and DP170101675, the International Technology Centre Pacific (ITC-PAC) under Contract No. FA520919PA138, and NSF Grant PHY-2110365. Support for the ANU Heavy Ion Accelerator Facility operations through the Australian National Collaborative Research Infrastructure Strategy program is acknowledged.
References
[1] J. N. Black, W. C. McHarris, and W. H. Kelly, Phys. Rev. Lett. 26, 451 (1971); J. N. Black, W. C. McHarris, W. H. Kelly, and B. H. Wildenthal, Phys. Rev. C 11, 939 (1975); D. Geesaman, Spin gap isomers in 52Fe, 53Fe, and 54Co, Ph.D. thesis, State University of New York, Stony Brook (USA) (1976).
[2] T. Palazzo et al., Phys. Rev. Lett. 130, 122503 (2023).
The `island' of fission isomers identified in the actinide region (Z = 92 - 97, N = 141- 151) originates from multi-humped fission barriers, which can be understood as the result of superimposing microscopic shell corrections to the macroscopic liquid drop model description. For the first time, the in-flight fragmentation and electromagnetic dissociation methods were applied at GSI for populating fission isomers. With the fragment separator (FRS) at GSI, the fragmentation of 1 GeV/u $^{238}$U projectiles gives access to isotopes that are hard or impossible to reach by light particle-induced reactions that are so far in use. In-flight separation with the FRS allows studying fission isomers with half-lives as short as 100 ns. Most importantly, it provides beams with high purity and enables event-by-event identification. Two detection methods were employed to study fission isomers with half-lives in the range of approximately 100 ns to 50 ms: beam implantation in a fast plastic scintillator, and beam thermalization in a cryogenic stopping cell at the FRS Ion Catcher followed by subsequent detection [1]. Production and measurements of fission isomers $^{240f,242f}$Am with a background-free method have been developed at the IGISOL facility in Jyväskylä, Finland. Results from these experiments will be presented in this contribution.
[1] J. Zhao et al., Procedings of Science 419 (2023) PoS (FAIRness2022) 063.
Nuclear electromagnetic moments provide essential information in our understanding of nuclear structure. Observables such as electric quadrupole moments are highly sensitive to collective nuclear phenomena. In contrast, magnetic dipole moments offer sensitive probes to test our description of microscopic properties such as those of valence nucleons. Although great progress was achieved in describing the electromagnetic properties of light nuclei and experimental trends in certain isotopic chains, a unified and consistent description across the Segré chart of nuclear electromagnetic properties remains an open challenge for nuclear theory.
In nuclear-DFT, we align angular momenta along the intrinsic axial-symmetry axis with broken spherical and time-reversal symmetries. We fully account for the self-consistent charge, spin, and current polarizations – in particular through the inclusion of the crucial time-odd mean-field components of the functional. Spectroscopic moments are then determined for symmetry-restored wave functions without locally adjusting parameters or using effective charges or effective g-factors.
Systematic DFT results were so far obtained in the unpaired odd near doubly magic nuclei [1], heavy paired odd open-shell nuclei [2,3], and in indium [4], silver [5], tin [6], and potassium [7] isotopes. In this talk, I will focus on those obtained for the ground and excited states in even-Z odd-N (82<N<126) deformed isotopes of elements between gadolinium and osmium. The comparison of calculated and measured values is presented in the Figure.
[1] P.L. Sassarini et al., J. Phys G 49 (2022) 11LT01
[2] J. Bonnard et al., Phys. Lett. B 843 (2023) 138014
[3] H. Wibowo et al., to be published
[4] A.R. Vernon et al., Nature 607 (2022) 260; L. Nies et al., Phys. Rev. Lett. 131 (2023) 022502; J. Karthein et al., submitted to Nature Physics; A.R. Vernon et al., to be published
[5] R.P. de Groote et al., Phys. Lett. B 848 (2024) 138352
[6] T.J. Gray et al., Phys. Lett. B 847 (2023) 138268
[7] A. Nagpal et al., to be published
Clustering is an intriguing phenomenon in nuclear structure. Correlations between nucleons result in the formation of subunits (cluster) inside the nucleus. The most typical cluster is the alpha particle, which is present not only in light nuclei, but also observed in heavy nuclei as the alpha decay phenomena.
Recently, we have proposed a quantity "local alpha strength function" $S_\alpha(\mathbf{r},E)$ [PRC 108 (2023) 014318], as a measure of localized four nucleons $(p\uparrow,p\downarrow,n\uparrow,n\downarrow)$. When we remove an alpha particle at the position $\mathbf{r}$ from a nucleus, the final state in the residual nucleus can be expanded in the energy eigenstates. Thus, the local alpha strength function $S_\alpha(\mathbf{r},E)$ corresponds to the strength to produce the state at energy $E$ in the residual nucleus. Introducing approximations, such as the mean-field with no rearrangement, the calculation becomes feasible.
In this talk, we present several improvements and extensions, such as finite-size effect, alpha reduced width, and applications to transfer reactions.
The energy density functional (EDF) approach in nuclear physics often utilizes mean-field wave functions that intentionally break certain symmetries of the Hamiltonian to incorporate static correlations.
To achieve a precise description of nuclear properties and recover quantum numbers, the restoration of these broken symmetries is essential. While symmetry-restored calculations are common for studying ground-state properties and low-lying excitations, their application to nuclear responses remains largely confined to theoretical studies and schematic models. This work investigates the effects of angular momentum projection (AMP) on the monopole and quadrupole responses of deformed nuclei.
Using deformed Skyrme-random-phase-approximation (RPA) calculations, an exact AMP in the multipole strength function calculations is implemented, establishing a projection after variation (PAVRPA) scheme. This method is applied for the first time in a realistic study to examine AMP’s impact on the coupling of monopole and quadrupole modes in the intrinsically deformed nucleus 24Mg [1].
Results reveal that the monopole PAV-RPA response function exhibits a significant amount of low-energy strength, in addition to the giant resonance peaks. The characteristics and nature of this strength are analyzed and discussed. In the quadrupole channel, AMP leads to the suppression of all strength except that corresponding to the isoscalar giant quadrupole resonance.
The anomalous low-lying monopole strength is interpreted as contamination of the excited states due to coupling with the non-infinitesimal rotational motion in deformed RPA phonons. This spurious strength was also identified in projected generator coordinate method (PGCM) calculations using a similar PAV approach, but was absent in full variation after projection (VAP) calculations [2]. Although the spurious strength was effectively subtracted in this study, these findings highlight the need for future implementation of full VAP-RPA to achieve more accurate results.
References
[1] A. Porro, G. Colo, T. Duguet, D. Gambacurta, and V. Som
a, “Symmetry-restored Skyrme-randomphase-approximation calculations of the monopole strength in deformed nuclei,” Phys. Rev. C,
vol. 109, no. 4, p. 044315, 2024.
[2] A. Porro, T. Duguet, J.-P. Ebran, M. Frosini, R. Roth, and V. Som`a, “Ab initio description of monopole resonances in light- and medium-mass nuclei: IV. Angular momentum projection effects and rotation-vibration coupling,” In preparation, 2024.
The isospin symmetry breaking part of the nuclear interaction is a small part of the whole; however, it sometimes gives important contributions to nuclear properties, such as the difference of mirror nuclei, the isobaric analog states, and the neutron-skin thickness. The isospin symmetry breaking terms also affect the estimation of the slope parameter of the nuclear symmetry energy.
In this talk, I will first summarize our recent study on the isospin symmetry breaking in nuclear properties and point out the lack of precise determination of the effective nuclear interaction or energy density functional for the isospin symmetry breaking terms. Then, I will introduce our recent attempt to determine the energy density functional of the isospin symmetry breaking terms. Finally, I will present some future perspectives.
Observations of spectroscopic properties in some nuclei suggest the existence of shape fluctuations and shape coexistence phenomena. To describe such phenomena, it is obvious that a mean-field approach, which treats small-amplitude dynamics around a single-reference state, is not enough, and a beyond-mean-field approach is necessary. The five-dimensional quadrupole collective Hamiltonian method, which describes large-amplitude collective dynamics in the $\beta$--$\gamma$ deformation space, has been often employed. Recently, we have developed the local QRPA with the Skyrme EDF to evaluate the collective inertial functions at any triaxial shapes in the $\beta$--$\gamma$ plane in the collective Hamiltonian method [1].
In this talk, we will show the results of low-lying states obtained using the collective Hamiltonian method for neutron-rich Cr isotopes and $N=40$ isotones, where recent advances in experiments have started providing much spectroscopic information. The improved inertial functions give better reproduction of the excitation energies of the experimental low-lying levels. In particular, the low-lying excited $0^+$ states are considerably affected by the improved inertial functions using the local QRPA in these neutron-rich nuclei.
[1] K. Washiyama, N. Hinohara, and T. Nakatsukasa, Phys. Rev. C 109, L051301 (2024).
The development of worldwide rare isotope beam facilities has brought many new insights in nuclear physics. In particular, nuclei with exotic deformation have acquired great interest over the years for the challenges and implications it involves. Theoretically, relativistic density functional theory has achieved great success in describing many nuclear phenomena over the past several decades.
In a series of our recent works [1,2,3,4], we have developed the three-dimensional cranking relativistic density functional theory to study the high-order deformation in atomic nuclei. In particular, by overcoming the variational collapse and the fermion doubling problem, relativistic density functional theory has been solved in three-dimensional lattice space, and the corresponding time-dependent relativistic density functional theory has been established. It allows a unified description of the static and dynamic properties of nuclei without assuming any spatial symmetry restrictions. In this talk, I will review recent progress in the development of time-dependent relativistic density functional theory in space lattice and its application for the emergence of high-order deformation in nuclei.
In recent years there has been an increasing interest in studies of exotic nuclear shapes and underlying symmetries. Combining a realistic phenomenological mean-field approach based on an arbitrarily deformable Woods-Saxon potential, numerous large scale calculations of nuclear energies in multidimensional deformation spaces were performed indicating rich realisations of nuclear shape coexistence and shape evolution mechanisms. Combining those with powerful applied mathematics methods including inverse problem theory and graph-theory provided powerful extra tools to study both shape and symmetry properties, shape transitions, fission and and exotic fission channels such as tripartition and more.
A specially intriguing evolution was witnessed recently which follows applications of group-, and group representation theories, see especially Tagami et al., ref. [1], which allows formulating the experimental identification criteria of symmetries known in the literature as molecular symmetries traditionally applying to the distant atoms in a molecule, for instance four atoms placed at the tips of a pyramid (tetrahedral symmetry) and compact atomic nuclei bound by totally different forces.
In the present project we address similar issues, extending the strategies of the first discovery of nuclear tetrahedral and octahedral symmetries in a heavy, non-cluster nucleus $^{152}$Sm, ref. [2], to even heavier non-cluster nucleus $^{236}$U, in which we have identified, ref. [3], using experimental results from other authors, the signals of the point group symmetry C$_{\rm 2v}$ (symmetry of the water, H$_2$O, molecule). We found specific rotational structures predicted by group theory according to which C$_{\rm 2v}$ symmetry generates rotational bands composed of both odd and even spin members with both parities:
$A_1 \leftrightarrow I^{\pi}:
\,0^+, 1^-, \{2 \times 2^+, 2^-\}, \{3^+, 2 \times 3^-\},$
$\phantom{A_1 \leftrightarrow I^{\pi}:
\,}\{3 \times 4^+, 2 \times 4^-\}, \{2 \times 5^+, 3 \times 5^-\},$
$\phantom{A_1 \leftrightarrow I^{\pi}:
\,}\{4 \times 6^+, 3 \times 6^-\}, \{3 \times 7^+, 4 \times 7^-\},\; \ldots\; \leftarrow \,^{236}{\rm U} $
with degeneracies marked by curly brackets. We present mathematical details and physics discussion.
References
[1] S. Tagami, Y. R. Shimizu, and J. Dudek, Phys. Rev. C 87, 054306 (2013)
[2] J. Dudek, D. Curien, I. Dedes, K. Mazurek, S. Tagami, Y. R. Shimizu, and T. Bhattacharjee, Phys. Rev. C 97, 021302(R) (2018).
[3] I. Dedes, J. Dudek, A. Baran, D. Curien, A. Gaamouci, A. Góźdź, A. Maj, A. Pędrak, D. Rouvel, J. Yang, submitted to Phys. Rev. C
The cadmium isotopes ($Z\!=\!48$) since long have been considered as textbook examples of spherical-vibrator motion and U(5) dynamical symmetry in nuclei. On the other hand, detailed studies, using complementary spectroscopic methods, have provided evidence for marked deviations from such a structural paradigm [1,2]. Previous attempts to explain the observed discrepancies in $E2$ decays relied on strong mixing between vibrational and intruder states and ultimately proved unsuccessful. Two approaches have been proposed to address these unexpected findings. The first questions the spherical-vibrational character of the $^{110,112}$Cd isotopes, replacing it with multiple shape coexistence of states in deformed bands, a view qualitatively supported by a beyond-mean-field calculation with the Gogny D1S energy density functional [3,4]. A second approach is based on the recognition that the reported deviations from a spherical-vibrator behavior show up in selected non-yrast states, while most states retain their vibrational character. In the terminology of symmetry, this implies that the symmetry in question is broken only in a subset of states, hence is partial [5]. Such a U(5) partial dynamical symmetry (PDS) approach was applied to $^{110}$Cd [6].
In the present contribution, we show that the empirical data in $^{110-116}$Cd is consistent with a vibrational interpretation and good U(5) symmetry for the majority of low-lying normal states, coexisting with a single deformed $\gamma$-soft band of intruder states. The observed deviations from this paradigm are properly treated by an Hamiltonian with U(5) PDS acting in the sector of normal states, which are weakly coupled to SO(6)-like intruder states [7]. The results demonstrate the relevance of persistent symmetries and related notion of U(5) PDS to this series of isotopes.
This work was done in collaboration with J.E. Garcia-Ramos (Huelva), N. Gavrielov and P. Van Isacker (GANIL).
[1] P. E. Garrett, K. L. Green and J. L. Wood, Phys. Rev. C 78 (2008) 044307.
[2] P. E. Garrett, J. Bangay, A. D. Varela, G. C. Ball et al., Phys. Rev. C 86 (2012) 044304.
[3] P. E. Garrett, T. R. Rodriguez, A. D. Varela et al., Phys. Rev. Lett. 123 (2019) 142502.
[4] P. E. Garrett, T. R. Rodriguez, A. Diaz Varela et al., Phys. Rev. C 101 (2020) 044302.
[5] A. Leviatan, Prog. Part. Nucl. Phys. 66 (2011) 93.
[6] A. Leviatan, N. Gavrielov, J. E. Garcia-Ramos and P. Van Isacker. Phys. Rev. C 98 (2018) 031302(R).
[7] N. Gavrielov, J.E. Garcia-Ramos, P. Van Isacker and A. Leviatan, Phys. Rev. C 108 (2023) L031305.
We would like to present new results addressing the issues of nuclear stability induced by the presence of exotic symmetries in heavy nuclei. These mechanisms can in turn be seen as resulting from the specific shell effects (significant shell gaps in the single nucleon energy spectra) described using the language of magic numbers. In our context, we refer to them as 4-fold magic numbers, since the corresponding gaps are present at the same nucleon numbers, yet at non-vanishing all four octupole deformations $\alpha_{3\mu=0,1,2,3}\neq0$, often at $\alpha_{20}=0$. In our recent calculations, we were able to establish those properties in nuclei with neutron numbers close to $N=136$ (actinide region), cf. Ref.[1] and, independently, $N=196$ (superheavy region), cf. Ref.[2].
Our theoretical predictions are calculated by employing a realistic phenomenological mean-field approach with the deformed Woods-Saxon potential and its newly optimized parametrization, which contains no parametric correlations. Among 12 Woods-Saxon parameters, the presence of the correlations between 4 parameters was detected and removed using the Monte Carlo approach. The potential energy surfaces are deduced from the standard multidimensional deformation space ($\alpha_{20}$, $\alpha_{22}$, $\alpha_{3\mu}$, $\alpha_{40}$) in both actinides and superheavy nuclei regions, and show the well-pronounced double energy minima generated by the octupole shell gaps, which in turn generate the exotic group symmetries $C_{2v}$, $D_{2d}$, $T_d$, and $D_{3h}$, respectively.
With the help of the representation theory of the point groups, we produced the rotational bands generated by the symmetries. By analyzing the specific properties of the collective rotational bands generated by the symmetries, we formulate the quantum mechanical criteria for experimental identification of these exotic symmetries.
Our calculations show that among the four octupole deformations, octupole-tetrahedral $\alpha_{32}$ deformation plays an important role in stabilizing the superheavy nuclei around the $N=196$ region cf. Ref.[2]. In addition, in superheavy nuclei region $110\leq Z\leq 138$ and $166\leq N\leq 206$, the islands of the $D_{3h}$ symmetry with the nuclear equilibrium deformations with $\alpha_{33}\neq0$ combined with normal-deformed oblate $\alpha_{20}\approx-0.15$, super-deformed oblate $\alpha_{20}\approx-0.50$ and hyper-deformed oblate $\alpha_{20}\approx-0.85$ are predicted cf. Ref.[3].
[1] J. Yang, J. Dudek, I. Dedes, A. Baran, D. Curien, A. Gaamouci, A. Góźdź, A. Pedrak, D. Rouvel, H. L. Wang, and J. Burkat, Phys. Rev. C 105, 034348 (2022).
[2] J. Yang, J. Dudek, I. Dedes, A. Baran, D. Curien, A. Gaamouci, A. Góźdź, A. Pedrak, D. Rouvel, and H. L. Wang, Phys. Rev. C 106, 054341 (2022).
[3] J. Yang, J. Dudek, I. Dedes, A. Baran, D. Curien, A. Gaamouci, A. Góźdź, A. Pedrak, D. Rouvel, and H.-L. Wang, Phys. Rev. C 107, 054304 (2023).
Symmetries play a determining role in physics, guiding the frontier research of quantum systems, in particular on the sub-atomic level. The results of the group theoretical analysis supported by realistic mean field calculations predict existence of tetrahedral symmetry in many atomic nuclei throughout the Mass Table. Corresponding nuclear configurations are associated with relatively strong shell energy effects related with tetrahedral magic numbers, which were identified long ago [1-3]. Tetrahedral symmetry has been of interest in molecular physics but there exist so far only one proposed structure in nuclear domain [4]. Experimental efforts are underway in identifying and understanding this exotic symmetry [5-7] and its relation with the octahedral symmetry both giving rise to the four-fold degeneracy of certain single nucleon levels.
VECC, Kolkata has few setups for gamma ray spectroscopic measurement aiming at nuclear structure studies using beams from cyclotrons. In addition, detectors can be augmented through national collaborations giving rise to different national campaigns.
In our recent efforts, we could identify two structures in 152Sm presenting symmetry competition, and symmetry breaking criteria. The newly observed band structure was investigated via high-resolution gamma spectroscopic techniques with neutron evaporation reaction, 150Nd (, 2n) 152Sm @ 26 MeV beam. An array of twelve Clover HPGe detectors was used for the measurement. The mixed parity sequence with absence of E2 and presence of candidate E3 transitions encourage interpretation in terms of excited tetrahedral structure. We formulated arguments stipulating that this structure manifests tetrahedral symmetry accompanied by the octahedral symmetry breaking following the group representation theory calculations. Details of the experimental interpretation will be presented and discussed.
References:
[1] J. Dudek, A. Gozdz, N. Schunck and M. Miskiewicz, Phys. Rev. Lett. 88, 252502 (2002).
[2] J. Dudek, D. Curien, N. Dubray, J. Dobaczewski, V. Pangon, P. Olbratowski, and N. Schunck, Phys. Rev. Lett. 97, 072501 (2006).
[3] S. Tagami, Yoshifumi R. Shimizu and J. Dudek, Phys. Rev. C 87, 054306 (2013).
[4] J. Dudek, D. Curien, I. Dedes, K. Mazurek, S. Tagami, Y. R. Shimizu and T. Bhattacharjee, Phys. Rev. C 97, 021302(R) (2018).
[5] M. Jentschel, W. Urban, J. Krempel, D. Tonev, J. Dudek, D. Curien, B. Lauss, G. de Angelis and P. Petkov, Phys. Rev. Lett. 104, 222502 (2010).
[6] R. A. Bark, J. F. Sharpey-Schafer, S. M. Maliage, T. E. Madiba, F. S. Komati, E. A. Lawrie, J. J. Lawrie, R. Lindsay, P. Maine, S. M. Mullins, el. al, Phys. Rev. Lett. 104, 022501 (2010).
[7] A. Saha, T. Bhattacharjee, D. Curien, J. Dudek, I. Dedes, K. Mazurek, A. Gozdz, S. Tagami, Y. R. Shimizu, S. R. Banerjee et al., J. Phys. G: Nucl. Part. Phys. 46, 055102 (2019).
Atomic nuclei exhibit multiple energy scales ranging from hundreds of MeV in binding energies to fractions of an MeV for low-lying collective excitations. Describing these different energy scales within an ab-initio framework is a long-standing challenge that we overcome by using high-performance computing, many-body methods with polynomial scaling, and ideas from effective-field-theory. With this approach we accurately describe the first 2+ and 4+ energies and the quadrupole transitions from the first 2+ to the ground-state in neon isotopes. For 32,34Ne less is known and we predict that they are strongly deformed and collective. For 30Ne we interestingly find that a deformed and nearly spherical shape coexist, similar to what is seen in 32Mg. We also confirm that 78Ni has a low-lying rotational band, and that deformed ground states and shape coexistence emerge along the magic neutron number N = 50 towards the key nucleus 70Ca. On the neutron-deficient side we also addressed structure of nuclei around the strongly deformed N = Z = 40 nucleus 80Zr, although there are challenges our results are competitive with mean-field calculations. With this talk I hope to convey that the accurate computation of multiscale nuclear physics demonstrates the predictive power of modern ab initio methods.
The magnetic dipole moment is one of the fundamental observable in finite nuclei and can tell us how much the nucleus is dominated by the single-particle picture. Reproducing magnetic dipole moments has been one of the major challenges in nuclear ab initio theory. With the valence-space in-medium similarity renormalization group (VS-IMSRG), one of the ab initio calculation methods applicable for medium-mass and heavy nuclei, it was found that the absolute size of the magnetic dipole moments is underestimated. The effect of two-body current (TBC, also known as the meson exchange current) is non-negligible in light nuclei, as studied by Green's function Monte Carlo and no-core shell model. Thus, including TBC effects in medium-mass and heavy nuclei calculation is a natural step forward. In this presentation, using the VS-IMSRG, I will discuss the TBC effect on the magnetic dipole moments of the proximity of doubly magic nuclei from oxygen to bismuth.
Ab Initio methods aim at providing a unified description of nuclei from realistic two- and three-body interactions. The last ten years have witnessed great progresses in their range of applicability. This includes the possibility to describe higher mass systems, but also the generalization of many-body formalisms to singly and doubly open-shell nuclei. While symmetry-broken single-reference expansion methods have recently proven their ability to provide an accurate description of ground state properties up to Sn isotopes, collective properties of ground and excited (related to deformation, rotation, vibration) states are difficult to grasp through pure particle-hole expansions. For these reasons, Projected Generator Coordinate Method (PGCM) has gained a renewed interest for it's ability to naturally incorporate long range correlations in its formulation.
The ability to grasp coherently static and dynamical (long and short range) correlations in a unified formalism is a necessary step towards the unified description of ground and excited state properties of mid-mass nuclei independently of their closed and open-shell character. Adapting the recently formulated non-orthogonal perturbation theory to the nuclear many-body problem, we introduce a new formalism (coined as PGCM-PT) that consistently merges PGCM with perturbation theory. Combined with recently introduced many-body reduction of three-body interactions, it offers a promising way to tackle all even-even mid-mass doubly open-shell nuclei.
A numerical implementation if the new formalism at second order in the perturbative expansion (i.e. PGCM-PT2) has been achieved and tested on open-shell and doubly open-shell nuclei in the O-Ne region. In this talk, PGCM-PT2 formalism will be introduced and discussed. Based on the comparison between PGCM and PGCM-PT2, applications of PGCM in medium-mass systems will be presented.
References:
H. Burton and A. Thom, J. Chem. Theory Comput. (2020), 16, 9, 55865600
M. Frosini, T. Duguet, J.-P. Ebran, V. Somà, Eur. Phys. J. A 58 (2022) 4, 62
M. Frosini, T. Duguet, J.-P. Ebran, B. Bally, T. Mongelli, T. R. Rodrìguez, R. Roth, V. Somà, Eur. Phys. J. A 58 (2022) 4, 63
M. Frosini, T. Duguet, J.-P. Ebran, B. Bally, H. Hergert, T. R. Rodrìguez, R. Roth, J. Yao, V. Somà, Eur. Phys. J. A 58 (2022) 4, 64
The emergence of collective modes such as nuclear clustering has a profound effect on reactions that occur in stellar interiors. Thus, a good description of astrophysical reaction rates needs to properly take into account the clustering (and deformation) aspects of nuclear structure. To demonstrate how this phenomenon arises from the fundamental nuclear interaction we apply the no-core shell model with continuum (NCSMC), a unified approach for structure and reactions. We will discuss applications of the NCSMC to various reactions of astrophysical interest, the description of alpha clustering, as well as leverage its unique properties to connect existing experimental data to currently unmeasured reaction rates.
This work was performed in part by LLNL under Contract DE-AC52-07NA27344.
The discrepancy between the average measured lifetime of trapped ultracold neutrons (τtrap = 879.4 ± 0.6 s) and the average beam measured lifetime of neutrons (τbeam = 888.0 ± 2.0 s) remains unresolved up to now. In 1990 Green and Thomson tried to resolve this puzzle by entering the two-body decay of neutrons (the decay into a hydrogen atom and antineutrino) into consideration. From the analysis of the experiments performed up to 1990, they deduced that the explanation of the puzzle in this way would require the corresponding branching ratio (BR) < 3%, which constituted four orders of magnitude discrepancy with the theoretical BR of 4x10-6. In 2018 Czarnecki et al analyzed more recent experiments on the neutron lifetime, as well as on the axial-current coupling, and deduced that the explanation of the puzzle in this way would require the corresponding BR < 0.27%, which still constituted 3 orders of magnitude discrepancy with the theoretical BR of 4x10-6. In the present paper we bring to the attention of the research community that with the allowance for the second solution of Dirac equation for hydrogen atoms, the theoretical BR is increased by a factor of 200, that it to 0.08%. (The hydrogen atoms, corresponding to the second solution of Dirac equation, have only the s-states, so that due to the selection rules they practically do not couple to the electromagnetic radiation; their existence is evidenced by four different types of atomic/molecular experiments.) Thus, the difference between the experimental limit of 0.27% and the theoretical BR is dramatically reduced: from 3 orders of magnitude to just a factor of 3. Consequently, the two-body decay of neutrons in the beam experiments (that count only the protons) plays a much more significant role in the overestimated neutron lifetime in these experiments than previously thought. I show that the two-body decay of neutrons has profound cosmological implications. Namely, it is the mechanism by which neutron stars are slowly but continuously producing baryonic dark matter (in the form of hydrogen atoms, corresponding to the second solution of Dirac equation), and this process goes on at the present time as well.
Storage of freshly produced secondary particles in a storage ring is a straightforward way to achieve the most efficient use of the rare species as it allows for using the same secondary ion multiple times. Employing storage rings for precision physics experiments with highly-charged ions (HCI) at the intersection of atomic, nuclear, plasma and astrophysics is a rapidly developing field of research. The number of physics cases is enormous. In the focus of this presentation will be the most recent results obtained at the Experimental Storage Ring ESR of GSI in Darmstadt and the Experimental Cooler-Storage Ring CSRe of IMP in Lanzhou.
Both the ESR and CSRe rings are coupled to in-flight fragment separators and are employed for precision mass spectrometry of short-lived rare nuclei. At CSRe, the enabled measurement of the velocity of every stored particle—in addition to its revolution frequency—has boosted the sensitivity and precision of mass measurements, which lead to accurate determination of the remaining masses constraining matter flow though 64Ge waiting point in the rp-process nucleosynthesis.
The ESR is presently the only instrument dedicatedly utilized for precision studies of decays of HCIs. Radioactive decays of HCIs can be very different as known in neutral atoms. Some decay channels can be blocked while new ones can become open. Such decays reflect atom-nucleus interactions and are relevant for atomic physics and nuclear structure as well as for nucleosynthesis in stellar objects.
Furthermore, both the CSRe and the ESR are utilized for nuclear reaction studies, where the beam cooling combined with internal ultra-thin ultra-pure windowless gas targets enables high angular and energy resolution. A significant extension of experimental capabilities is achieved with the installation of a dedicated low-energy storage ring CRYRING behind the ESR, where investigations of reactions at low centre-of-mass energies, that is relevant for astrophysical scenarios, are being started.
The experiments performed at the ESR, CRYRING@ESR, and CSRe will be put in the context of the present research programs in a worldwide context, where, thanks to fascinating results obtained at the presently operating storage rings, a number of projects is planned.
Transfer reactions at the high-precision Q3D spectrometer at the University of Munich have shown that there are many low-lying excited K=0+ states in well-deformed nuclei. Historically, 0+ states were difficult to measure and hindered testing and verification of numerous nuclear models due to the absence of the predicted and essential 0+ states. This entire process changed, since starting in 2002, one of the first Q3D measurements showed the existence of 13 0+ states [1] in one nucleus below 3.1 MeV. This work was followed by many others to reveal that in some cases, tens of 0+ states exist in the low-lying structure of numerous deformed nuclei. The discovery of these states and their characterization continues to be a lively contributor to the discussions and debates between coexistence and vibrational collectivity.
In the many instances where several 0$^+$ states were identified, we have followed investigations with lifetime measurements where possible using a variety of techniques and developed criteria for assigning the nature of these states using both transition probabilities, moments of inertia if the members of the bands built on these 0+ states could be identified, and reaction cross sections [(p,t) and (t,p)]. We have focused on the Z=50-82 region of the chart of nuclides and correlate these with the shape evolution of nuclei from spherical shapes near the closed shells, to deformed in the middle of the shells. We compare the experimental results with the universal CHFB+5DCH theoretical calculations [2] for the entire chart of nuclides and show some specific examples within the IBA [3].
References:
[1] S.R. Lesher et al., Phys. Rev. C 66, 051305 (R) (2002)
[2] J.P. Delaroche et al., Phys. Rev. C 81, 014303 (2010)
[3] R. Bijker and J. Mas Ruiz, Conference Proceedings of Simposia Fisica Nuclear, in press (2024)
One of the pillars for the study of exotic nuclides is the precise knowledge of the nuclear binding energy, which is directly and model-independently deduced from atomic-mass data. Tackling the increasing challenge to determine the mass of isotopes having low production yields and short half-lives, multi-reflection time-of-flight (MRTOF) mass spectrometry has grown from an initially rarely-used technology to the world’s most commonly-used method for measurements with a relative mass precision down to $\delta m/m = 10^{-8}$. This technology has been developed at RIKEN's RIBF facility for about two decades in combination with gas-filled ion catchers for low-energy access of isotopes produced in-flight.
In the recent past, three independent systems operating at different access points at RIBF, have provided substantial data in the medium- and heavy-mass region of the nuclear chart, reaching out to the superheavy nuclides. Recent achievements like high mass resolving power [1] followed by installations like $\alpha$/$\beta$-TOF detectors [2] and in-MRTOF ion selection have tremendously increased the selectivity of the systems, allowing for background-free identification of the rarest isotopes.
In this contribution, I will give a short overview about the success of MRTOF atomic mass measurements using BigRIPS in the recent past [3-5], and further focus on very new achievements from this year. Furthermore, the future plans for instrumentation of MRTOF devices at RIBF will be discussed with a view to the combination of established methods for decay spectroscopy and the mass selectivity provided by MRTOF-MS.
References:
[1] M. Rosenbusch et al., Nucl. Instrum. Meth. A 1047, 167824 (2023).
[2] T. Niwase et al., Theo. Exp. Phys. 2023(3), 031H01 (2023).
[3] S. Iimura et al., Phys. Rev. Lett. 130, 012501 (2023).
[4] D. S. Hou et al., Phys. Rev. C 108, 054312 (2023).
[5] W. Xian, S. Chen et al., Phys. Rev. C. 109, 035804 (2023).
Shape coexistence dominates the exotic structure and dynamics revealed by neutron-rich nuclei in the A=100 mass region. Sudden variations in the structural evolution with spin, excitation energy, and particle number, the occurrence of isomeric states, their decays and the exotic features of the daughter states represent various facets of shape coexistence and mixing. We addressed different open questions concerning shape coexistence phenomena in odd-odd and even-even nuclei including the nature of low-lying isomeric states and their allowed and first-forbidden β decay.
Aiming to a simultaneous description of the multifaceted impact of shape coexistence and mixing we investigated the structure and dynamics of neutron-rich Rb, Sr, Y, and Zr nuclei in the frame of the beyond-mean-field complex Excited Vampir variational model using the effective interaction derived from a nuclear matter G matrix based on the charge-dependent Bonn CD potential in a large model space. Recent results on the comprehensive treatment of the exotic behavior manifested in the structure and dynamics of these nuclei will be presented and compared to available data.
A quadrupole-octupole axially symmetric geometric model is proposed for the description of alternate parity bands observed in heavy [1] and medium mass even-even nuclei [2]. The shapes and the dynamical behaviour of the considered nuclei are ascertained from the phenomenology of the adopted model and the obtained parameters [2,3]. The model parameters exhibit a regular evolution as a function of neutron number [2,4]. As a result, the quadrupole shape phase transition around N=90 is found to be accompanied by the increase of the vibrational character for the octupole deformation. A similar critical point is also identified in the A = 224–228 mass region of the Ra and Th nuclei. It marks different stages of the transition between static and dynamic octupole deformation with a specific spin dependence for the electromagnetic transitions. Model extrapolations are performed for various types of excited states, for which distinguishing spectral signatures are forwarded.
[1] R. Budaca, P. Buganu, A. I. Budaca, Phys. Rev. C 106, 014311 (2022).
[2] R. Budaca, A. I. Budaca, P. Buganu, Phys. Scr. 99, 035309 (2024).
[3] R. Budaca, P. Buganu, A. I. Budaca, Eur. Phys. J. A 59, 242 (2023).
[4] R. Budaca, P. Buganu, A. I. Budaca, Il Nuovo Cimento C 47, 25 (2024).
Present status and perspectives of the superheavy element (SHE) research at RIKEN are presented. In April 2018, we formed the new SHE Research Group (nSHE RG) and started an experiment to synthesize a new element 119 in the 248Cm(51V,xn)299–x119 reaction using GAs-filled Recoil Ion Separator II (GARIS-II) at RIKEN Ring Cyclotron [1]. The 248Cm target material was supplied from Oak Ridge National Laboratory. In January 2020, RIKEN heavy-ion Linear ACcelerator (RILAC) was upgraded with the 28-GHz superconducting ECR ion source and the superconducting RILAC (SRILAC). We developed the new separator GARIS-III at SRILAC. An optimal reaction energy in the 248Cm + 51V fusion reaction was deduced from the quasielastic barrier distribution extracted by measuring the excitation function of quasielastic backscattering [2–4]. Since October 2020, we have continued the synthesis experiment of element 119 with GARIS-III at SRILAC.
Long-lived isotopes of 261Rf, 262Db, 265Sg, and 266Bh useful for SHE chemistry were synthesized in the 248Cm(18O,5n)261Rf, 248Cm(19F,5n)262Db, 248Cm(22Ne,5n)265Sg, and 248Cm(23Na,5n)266Bh reactions, respectively, and their production and decay properties were investigated using a rotating wheel apparatus for α and SF spectrometry coupled to the GARIS gas-jet system [5,6]. In the conference, the chemistry studies of SHEs such as Rf and Db at the RIKEN AVF cyclotron are also presented.
[1] H. Sakai et al., Eur. Phys. J. A 58, 238 (2022).
[2] T. Tanaka et al., J. Phys. Soc. Jpn. 87, 014201 (2018).
[3] T. Tanaka et al., Phys. Rev. Lett. 124, 052502 (2020).
[4] M. Tanaka et al., J. Phys. Soc. Jpn. 91, 084201 (2022).
[5] H. Haba, EPJ Web Conf. 131, 07006 (2016).
[6] H. Haba et al., Phys. Rev. C 102, 024625 (2020).
The rotation of deformed nuclei generates easily recognizable patterns of excited nuclear states, called rotational bands. If the nucleus has axial asymmetry, the rotational bands are more complex, for instance, in addition to the ground-state band of an even-even nucleus, excited gamma bands are created. These sets of bands are formed because the nucleus rotates simultaneously around its three axes, a motion that looks like tilted precession (TiP) of the total angular momentum around the axis with largest moment of inertia (MoI).
The most unambiguous way to establish the axial asymmetry of the nuclear shape are direct Kumar-Cline measurements carried out within multi-step Coulomb excitation experiments. While such an analysis is model-independent and in general is the most robust proof of stable axial asymmetry, the technique is experimentally challenging and have been carried out only for a limited number of deformed nuclei. In these circumstances, the axial asymmetry of the nuclear shape is often derived based on observed features of rotational bands and on theoretical expectations, for instance energy staggering in the gamma band of even-even nuclei, tilted precession and wobbling in odd-mass nuclei, chiral bands, and others. In this presentation an alternative way of deducing axial asymmetry will be presented and discussed.
The presentation also aims at a discussion of the terminology of “wobbling” [1] and “tilted precession” [2]. Wobbling was introduced by Bohr and Mottelsson as a harmonic vibration coupled to a simple one-dimensional rotation [1]. They used a harmonic approximation of the three-dimensional rotational Hamiltonian at high spins, where the TiP motion is dominated by the rotation around the axis with largest MoI, while the tilt of the precession can be considered as caused by harmonic vibrational excitations. The motion was called wobbling, and the bands were labelled by the number of excited vibrational phonons.
However, in the last decade, bands at low spins, where the harmonic approximation does not hold and thus the bands have purely rotational character, were also associated with wobbling [3]. Such a modification in the meaning of the term “wobbling” causes conflicts with past research works. For instance, the gamma bands at low spins produced by the triaxial rotor model would, within such changed terminology, qualify as wobbling bands. This is in contrast with the past, where such low-spin bands were not considered wobbling. The differences between wobbling within its original definition (simple rotation coupled to harmonic vibration) and TiP (three-dimensional rotation causing precession) will be detailed, the terminology issues will be discussed, and a way forward will be proposed [4].
References:
[1] A. Bohr and B. Mottelson, Nuclear Structure Volume II, (W. A. Benjamin, New York, 1975).
[2] E. A. Lawrie, O. Shirinda, and C. M. Petrache, Phys. Rev. C 101, 034306 (2020).
[3] S. Frauendorf and F. Dönau, Phys. Rev. C 89, 014322 (2014).
[4] E.A. Lawrie, Chapter 6 in “Chirality and Wobbling” by C. M. Petrache, Edited by Taylor & Francis Group, 2024.
Absolute transition strengths between excited states yield fundamental information on nuclear structure. These observables can be determined from level lifetimes. The recoil distance Doppler-shift (RDDS) technique employing so-called plunger devices provides a valuable method for the determination of lifetimes in the picosecond range and has been in the focus of our Cologne group since many years.
In this talk, new results from RDDS measurements of our group especially in tellurium isotopes close to neutron midshell and neutron-deficient nuclei in the A=170 region are discussed. Special emphasis is paid to the evolution of collectivity including hints for shape coexistence. In the tellurium isotopes, among other results, also lifetimes of excited $0^+$ states were measured allowing the calculation of $\rho^2(E0)$ strengths that are indicators of the mixing of coexisting structures. In the A=170 region, signatures for a structural change with decreasing neutron number were found that cannot be reproduced with nuclear models so far. Further, we will discuss recent experiments with the RDDS technique on neutron-rich nuclei in the A=40-50 region with respect to the evolution and a possible weakening of the N=28 shell closure.
We will also present our latest developments of the RDDS technique with respect to the application with very different kinematic conditions and reactions techniques, e.g., multinucleon transfer, fusion-evaporation reactions and direct reactions, also employing radioactive beams, and the required detection techniques to identify the reaction products. The related recoil velocities of the reaction products range from few percent of the speed of light up to the relativistic regime with v/c ≈ 60%. For this purpose, our group developed sophisticated plunger devices adopted to the respective spectrometers and beam geometries.
Funded by the German Research Foundation (DFG), grant No. FR 3276/3-1
Octupole phonon excitations on the shell-model states in Xe, Cs, and Ba isotopes up to mass 142
Large-scale nuclear shell-model calculations are performed in Xe, Cs, and Ba isotopes up to mass 142 (Z > 50 and N > 82) beyond 132Sn. All the single-particle levels in the one-major shells, six neutron (1f7/2, 2p3/2, 2p1/2, 0h9/2, 1f5/2 and 0i13/2) orbitals and five proton (0g7/2, 1d5/2, 1d3/2, 0h11/2, and 0s1/2) orbitals are considered. For an effective two-body interaction, only one set of the multipole pairing, quadrupole-quadrupole interactions is employed and the strengths of the two-body interactions are set constant for all the nuclei considered. These interactions are phenomenologically determined to reproduce the experimental energy spectra in two-body systems. Some of the isomeric states are analyzed in terms of the shell-model configurations. Octupole correlated states are discussed by phenomenologically introducing a collective octupole phonon on top of each shell model state.
References
N. Yoshinaga, K. Higashiyama, C. Watanabe, and A. Odahara,
Phys. Rev. C 109, 064313
The structure of the neutron-rich Zn isotopes was studied via beta-decay, Coulomb excitation, beam fragmentation and multi-nucleon transfer experiments. In most of the cases, states with spins below 6 ћ were populated except for 78Zn. The semi-magic nickel isotopes present a spherical ground-state structure. However, for N<40 Ni isotopes, low-lying 0+ states were understood as proton or neutron excitations across the Z=28 or N=40 gaps, respectively [1 and references therein]. In more neutron-rich Ni isotopes, in particular in 78Ni [2], low-lying excited structures are predicted to be based on deformed intruder configurations. The island of inversion at N=40 was known to extend up to Z=26 (Fe). Recent experimental work in 74Zn indicates that it extends further to larger atomic numbers [1].
Se isotopes around N=50 present axially deformed structures with gamma softness [3] whereas Ge isotopes are mainly triaxial. A Coulomb excitation study suggests even a rigid triaxial character in 76Ge [4]. Zn isotopes are therefore transitional nuclei between spherical and triaxial with configuration coexistence which complex structures deserve dedicated studies.
In the present work, even neutron-rich isotopes from N=43 to 49 were produced at GANIL in fusion-fission 238U on 9Be reactions. The light fragments were identified in mass and atomic number using the VAMOS++ spectrometer [5]. The emitted gamma-rays were detected in AGATA composed of 24 Ge capsules. In order to gain statistics, the array was placed closer to the target (13.3 cm) [6]. Fragment-gamma coincidences enable to firmly assign transitions to given isotopes. Fragment-gamma-gamma coincidences were observed enabling to complete level schemes of the even mass Zn fragments.
The experimental results are compared with the most advanced shell-model calculations using the most updated interaction for this region of the nuclear chart.
Both the experimental and theoretical information will be presented.
References:
[1] M. Rocchini et al., Phys. Rev. Lett. 130, 122502 (2023).
[2] R. Taniuchi et al., Nature (London) 569, 53 (2019).
[3] NNDC
[4] A. D. Ayangeakaa et al., Phys. Rev. Lett. 123, 102501 (2019).
[5] M. Rejmund et al., Nucl. Instrum. Meth. A 646, 184 (2011), M. Vandebrouck et al., Nucl. Instrum. Meth. A 812, 112 (2016)
[6] E. Clément et al.,Nucl. Instrum. Meth. A 855,1 (2017)
The fission process of the excited $^{250}$Cf produced in reaction $^{238}$U on $^{12}$C at E$_{\rm lab}$= 1461 MeV in the GANIL [1,2] is described using the Langevin equation coupled to the Master equation for the neutron evaporation [3]. The 4D potential energy surface of the considered nucleus is evaluated within the macroscopic-microscopic approach using the so called Fourier-over-Spheroid shape parametrization [4]. The LSD formula [5] is used to evaluate the macroscopic part of the energy while the microscopic energy correction was obtained using the Yukawa-folded single-particle potential [6]. Pre-scission neutron emission, charge equilibration at scission, and de-excitation of the primary fragments after scission are evaluated within a Weisskopf-type theory [7]. A good agreement of our estimates on the fission fragment mass and TKE yield, neutron multiplicities with the existing data is obtained. The evaluated isotopic distributions of the fission fragments underestimate the measured yields for the neutron reach isotopes what gives an assumption to reconsidering the isospin dependence of the model parameters.
References:
1. M. Caamano, O. Delaune, F. Farget, X. Derkx, K.-H. Schmidt, L. Audouin, C.-O. Bacri, G. Barreau, J. Benlliure, E. Casarejos, A. Chbihi, B. Fernandez- Dominguez, L. Gaudefroy, C. Golabek, B. Jurado, A. Lemasson, A. Navin, M. Rejmund, T. Roger, A. Shrivastava, and C. Schmitt, Phys. Rev. C 88, 024605 (2013), with errata in Phys. Rev. C 89, 069903(E) (2014).
2. D. Ramos, M. Caamano F. Farget, C. Rodriguez-Tajes, L. Audouin, J. Benlliure, E. Casarejos, E. Clement, D. Cortina, O. Delaune, X. Derkx, A. Dijon, D. Dore, B. Fernandez-Dominguez, G. de France, A. Heinz, B. Jacquot, C. Paradela, M. Rejmund, T. Roger, M.-D. Salsac, C. Schmitt, Phys. Rev. C 99, 024615 (2019).
3. K. Pomorski, B. Nerlo-Pomorska, J. Bartel, C. Schmitt, Z. G. Xiao, Y. J. Chen, L. L. Liu, submitted to Phys. Rev. C
4. K. Pomorski, B. Nerlo-Pomorska, C. Schmitt, Z.G. Xiao, Y.J. Chen, L.L. Liu, Phys. Rev. C 107, 054616 (2023).
5. K. Pomorski, J. Dudek, Phys. Rev. C 67, 044316 (2003).
6. A. Dobrowolski, K. Pomorski, J. Bartel, Comp. Phys. Comm. 199, 118 (2016).
7. K. Pomorski, B. Nerlo-Pomorska, A. Surowiec, M. Kowal, J. Bartel, K. Dietrich, J. Richert, C. Schmitt, B. Benoit, E. de Goes Brennand, L. Donadille, C. Badimon, Nucl. Phys. A 679, 25 (2000).
Abstract:
Nuclear fission is a crucial process at the heart of contemporary nuclear technology. Pairing interactions are the most important residual interactions beyond the mean-field framework, profoundly influencing the characteristics of the fissioning nucleus and the resulting fission products. For instance, the amount of pairing interactions strongly influences quantities such as spontaneous fission lifetimes, the shape of the barriers separating the ground state from scission, and fission fragment distributions.
In this presentation, we will present a comprehensive study on the fission process in Th, U, Pu, and Cm isotopes using a Yukawa-Folded mean-field plus standard pairing model. Our study provides an accurate description of pairing interactions in nuclear fission, avoiding the artificial effects produced by the BCS calculation. The analysis focuses on the effects of pairing interactions on fission barriers, static fission paths, total kinetic energy, mass distributions, and fission half-lives. The potential energy surface calculations are based on the macroscopic-microscopic model framework, with shape descriptions during fission using the Fourier series expansion method. Utilizing the three-dimensional collective model within the Born-Oppenheimer approximation (BOA), we analyze the impact of pairing interactions on fission fragment mass distributions.
References:
[1] X. Guan, C. Qi, Comp. Phys. Comm. 275, 108310 (2022).
[2] J. Dukelsky, S. Pittel, and G. Sierra, Rev. Mod. Phys. 76, 643 (2004).
[3] C. Schmitt, K. Pomorski, B. K. Nerlo-Pomorska, and J. Bartel, Phys. Rev. C 95, 034612 (2017).
[4] K. Pomorski, A. Dobrowolski, R. Han, B. Nerlo-Pomorska, M. Warda, Z. G. Xiao, Y. J. Chen, L. L. Liu, and J. L. Tian, Phys. Rev. C 101, 064602 (2020).
[5] X. Guan, Y. Xin, Y. J. Chen, X. Z. Wu, and Z. X. Li, Phys. Rev. C 104, 044329 (2021).
[6] X. Guan, T.C. Wang, W.Q. Jiang Yang Su , Yong-Jing Chen, and Krzysztof Pomorski., Phys. Rev. C 107,034307 (2023).
The nuclear structure of the transfermium nuclei are studied within the framework of the cranked shell model (CSM) with pairing correlation treated by a particle-number-conserving (PNC) method. The single-particle level structure, high-K isomers, rotational properties and α-decay energies of the transfermium nuclei are investigated. Particular emphasis will be place on the newly obtained Nilsson parameters set of κ µ and their effect on the nuclear shell gap. The single-particle level structure of the light superheavy and superheavy mass region will be discussed in detail. High-order deformation ε 6 plays an important role both in the single-particle orbitals and in the multi-particle states of the transfermium mass region. A reverse of the single-particle energy levels is resulted by including ε 6 deformation. The octupole correlation is used to explain the rotational properties of the reflection asymmetric nuclei in U and Pu isotopes.
We investigate the Extended Lipkin Model (ELM), whose phase diagram mirrors that of the Interacting Boson Approximation (IBA) model. Our goal is to implement the ELM on a quantum platform, leveraging Machine Learning techniques to identify its quantum phase transitions and critical lines. To achieve this, we offer: i) ground state energy calculations using a variational quantum eigensolver; ii) a detailed formulation for ELM dynamics within quantum computing, facilitating experimental exploration of the IBA phase diagram; and iii) a phase diagram determination using various Machine Learning methods. We successfully replicate the ELM ground-state energy using the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) algorithm across the entire phase space. Our framework ensures ELM implementation on quantum platforms with controlled errors. Lastly, our ML predictions yield a meaningful phase diagram for the model.
The Relativistic Configuration-interaction Density functional (ReCD) theory that combines the advantages of large-scale configuration-interaction shell model and relativistic density functional theory is extended to study nuclear chiral rotation. The energy spectra and transition probabilities of the chiral doublet bands are reproduced satisfactorily without any free parameters. By analyzing the probability amplitudes of the wavefunctions, the significant roles of configuration mixing and four quasiparticle states to the chiral doublets are revealed. The evolution from chiral vibration to static chirality is clearly illustrated by the K plot and azimuthal plot. The investigation provides both microscopic and quantal descriptions for nuclear chirality for the first time and demonstrates the robustness of chiral geometry against the configuration mixing as well as the four quasiparticle states.
Recently, high-energy nuclear collisions have been proposed as a powerful tool to image the global structure of heavy atomic nuclei, such as their shapes and radial profiles. We present the first quantitative demonstration of this method by extracting the quadruple deformation and triaxiality for the U238 nucleus known for its large prolate shape. We achieve this by comparing several flow observables in collisions of U with collisions of near-spherical Au. Though the extraction of U is consistent with low-energy experiments, the measurements indicate a non-zero triaxiality of U238 in its ground state. A similar comparative measurement is carried out in collisions of Ru96 and Zr96. Large differences are observed in almost all flow observables in the two collision systems, reflecting strong impacts from the structure differences between the pair of isobars. In particular, our measurements suggest an intriguing octupole deformation in Zr96 which is not predicted by mean field model calculations, as well as a larger neutron skin in Zr96. We also firstly studied the light nuclue O16 structure in the high energy collisions, compared to the ab initio calculations. The prospect of the imaging method for studying nuclear structure is also discussed.