Speaker
Description
We discuss the first theoretical identification of a low-energy enhancement (LEE) in the magnetic dipole $\gamma$-ray strength function of heavy nuclei. The LEE has been a subject of intense experimental and theoretical interest [1] since its discovery, and, if the LEE persists in heavy neutron-rich nuclei, it would have profound implications for our understanding of r-process nucleosynthesis. Standard shell-model methods used to study the LEE in medium-mass nuclei are computationally intractable in heavy nuclei. We combined beyond-mean-field many-body methods in the shell-model framework to identify the LEE in heavy nuclei.
The shell model Monte Carlo (SMMC) method [2] is a powerful method to calculate thermal observables in model spaces that are many orders of magnitude larger than those that can be addressed in conventional methods, but it cannot be used to calculate directly $\gamma$SFs. In SMMC, it is only possible to calculate the imaginary-time response function, whose inverse Laplace transform is the $\gamma$SF. However, this transform is numerically ill-defined. The standard method to carry out numerically the analytic continuation is the maximum-entropy method whose success depends crucially on a good choice of a prior strength function.
The static path plus random-phase approximation (SPA+RPA) reproduces well SMMC state densities [3]. We implemented an extension of the SPA+RPA [4] to calculate $\gamma$SFs in the framework of the CI shell model for a pairing plus quadrupole Hamiltonian [5]. We then use the SPA+RPA $\gamma$SF as a prior in a maximum-entropy method that reproduces the SMMC imaginary-time response function [5].
The SPA+RPA becomes computationally expensive for the interactions used in SMMC, and instead we use as prior strength the SPA $\gamma$SF [6,7]
We applied these methods in chains of samarium [5] and neodymium [6,7] isotopes and identified a LEE in their M1 $\gamma$SF. We also observed a scissors mode and a spin-flip mode that are built on top of excited states. We discuss how these modes change in the crossover from spherical to deformed heavy nuclei.
This work was supported in part by the U.S. DOE grant No. DE-SC0019521.
[1] J. E. Mitdbo, A. C. Larsen, T. Renstrom, F. L. Bello Garrote, and E. Lime, Phys. Rev. C 98, 064321 (2018), and references therein.
[2] For a recent review, see Y. Alhassid, in Emergent Phenomena in Atomic Nuclei from Large-Scale Modeling: a Symmetry-Guided Perspective, edited by K. D. Launey (World Scientific, Singapore, 2017), pp. 267-298.
[3] P. Fanto and Y. Alhassid, Phys. Rev. C 103, 064310 (2021).
[4] H. Attias and Y. Alhassid, Nucl. Phys. A 625, 565 (1997); R. Rossignoli and P. Ring, Nucl. Phys. A 633, 613 (1998).
[5] P. Fanto and Y. Alhassid, arXiv:2112.13772.
[6] A. Mercenne, P. Fanto, and Y. Alhassid, to be published (2023).
[7] D. DeMartini, P. Fanto, and Y. Alhassid, to be published (2023).
