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Description
The isospin symmetry is a consequence of the charge-independence of the nucleon-nucleon nuclear interaction. However, the Coulomb interaction breaks the isospin symmetry. Despite the small size of the isospin breaking, it is fundamental to know its value in the best possible way to understand the properties of the isobaric analog state and its role in Fermi $\beta$ decay.
In the case of self-conjugated nuclei with N=Z, the selection rules for electromagnetic transition forbid the $\gamma$ decay of electric dipole type. The presence of E1 decay and the measurement of its intensity is a tool to deduce isospin mixing. The giant dipole resonance (GDR)is an E1 decay that can be used as a probe to measure the value of the isospin mixing [1-3].
We used this approach to measure the E1 decay of the GDR in nuclei produced with N=Z. In this framework, we deduced the isospin mixing in the compound nucleus $^{72}$Kr at a low nuclear temperature, around 1.3 MeV, from the $\gamma$ decay of the GDR. The $\gamma$ rays from two compound-nucleus reactions were measured: from the $^{32}$S + $^{40}$Ca at bombarding energy of 90 MeV characterized by isospin I = 0, and from the $^{31}$ P + $^{40}$Ca at 82 MeV used as a reference (I $\neq$ 0). We employed the ELIGANT array at the Bucharest Tandem Laboratory, consisting of Compton-suppressed large-volume scintillator detectors (LaBr$_3$:Ce and CeBr$_3$) [4].
The statistical-model analysis of the measured spectra provided a mixing parameter of $(3.5\,\pm\,0.8)\%$ [5]. This datum, being at the lowest temperature compared with the few other existing ones, validates the predictions of the temperature dependence of the isospin mixing. Moreover, we studied the isospin mixing parameter, measured via GDR, as a function of nucleus mass and temperature.
We extracted the isospin-symmetry-breaking correction, $\delta_c$, from the isopin mixing parameter used for the Fermi super-allowed transitions. It is consistent with $\beta$ decay data, theoretical predictions, and previous experimental results [5].
References
[1] A. Corsi et al., “Measurement of isospin mixing at a finite temperature in $^{80}$Zr via giant dipole resonance decay,” Physical Rewiev C, vol. 84, p. 041304(R), 2011
[2] S. Ceruti et al., “Isospin mixing in $^{80}$Zr: From finite to zero temperature,” Physical Rewiev Letters, vol. 115, p. 222502, 2015.
[3] G. Gosta et al., “Probing isospin mixing with the giant dipole resonance in the $^{60}$Zn compound nucleus,” Physical Rewiev C, vol. 103, p. L041302,
2021.
[4] P.-A. Söderström et al., “Eligant-gn — eli gamma above neutron threshold: The gamma-neutron setup,” Nuclear Inst. and Methods in Physics Research, A, vol. 1027, p. 16617, 2022.
[5] A. Giaz et al., “Probing the Isospin Mixing in the $^{72}$Kr Compound Nucleus via GDR γ Decay” to be pubblished on Physics Letters B
