Speaker
Description
There are two common approaches for calculating cross-sections for weak probes: one involves using square-integrable basis functions [1-5], while the other relies on response functions (dynamical polarizabilities) [6]. For multi-open-channel problems, all methods struggle to some extent. Considering these issues, we develop a powerful novel alternative which takes advantage of the randomness of the Stochastic Variational Method (SVM) [7].
Our method extracts response functions (dynamical polarisabilities) directly from a bound-state approach for perturbation-induced reactions [7]. Explicitly, we express the response as a sum of 𝛿 functions (inspired by the Lorentz integral transform (LIT) method [2, 8, 9]). In the LIT formalism, an analogous sum is convoluted with a Lorentzian, yielding a smooth function, which then gives the response function after a numerical inversion. We determine this latter function directly by solving an inhomogeneous bound-state problem while avoiding the problems that the inversion can ill-pose.
Instead of folding the response with a smearing function as in the LIT, we use the integrated response, that is, the integral up to some energy of a response function. Hence, the sum of 𝛿 distributions becomes a stepwise continuous function of energy, which we fit with a differentiable function. This facilitates a robust derivation of the smooth physical response function. Ostensibly, we have replaced one hard problem (robust inversion of the LIT) with another (fitting of a function). However, the fitting procedure seems to be very robust. We will demonstrate this advantage by using a stochastic basis choice that covers the dominant important areas of the spectrum. We benchmark our method with both an analytically solvable model and results from the LIT for photo-dissociation of the deuteron. We also intend to discuss our preliminary results for the photo-dissociation of 3He.
1. W. Horiuchi, et. al., Few-Body Systems 50(1), 455 (2011).
2. V.D. Efros, Physical Review E 86(1), 016704 (2012).
3. L.E. Marcucci, et. al., Frontiers in Physics 8 (2020)
4. C. Drischler, et. al., Physics Letters B 823, 136777 (2021).
5. X. Zhang and R.J. Furnstahl, Physical Review C 105(6), 064004 (2022).
6. J. D. Walecka, Theoretical Nuclear and Subnuclear Physics, second edition. (World Scientific Publishing Co Pte Ltd, London, 2004).
7. Niels R. Walet, Jagjit Singh, J. Kirscher, M. C. Birse, H. W. Grießhammer, and J. A. McGovern, Few-Body Syst 64, 56 (2023).
8. G. Bampa, et. al., Physical Review C 84 (3), 034005 (2011).
9. W. Leidemann and G. Orlandini, Progress in Particle and Nuclear Physics 68, 158 (2013).
