Semiclassical and microscopic calculations of the spin-orbit density part of the Skyrme nucleus-nucleus interaction potential with temperature effects included

Abstract

The semiclassical formulation of the Skyrme energy density functional for spin-orbit density part of the interaction potential is compared with the microscopic shell model formulation, at both the ground state and finite temperatures. The semiclassical spin-orbit interaction potential is shown to contain exactly the same shell effects as are there in the microscopic shell model, provided a normalization of all semiclassical results to the spin-saturated case (for one or both nuclei as spin-saturated) is made. On the other hand, the \ensuremath{\alpha} nucleus structure present in microscopic shell model is found absent in semiclassical approach. The role of temperature is found not to change the behavior of shell or \ensuremath{\alpha} nucleus structure effects up to about 3 MeV, and increase or decrease the height of the (normalized) barriers in accordance with the shell structure of nuclei. Calculations are made for three two-nucleon transfer reactions forming the \ensuremath{\alpha}-nucleus $A=4n,N=Z$ compound systems ${}^{56}{\mathrm{Ni}}^{*}$ and ${}^{48}{\mathrm{Cr}}^{*}$ and the non-\ensuremath{\alpha}-nucleus compound system ${}^{52}{\mathrm{Cr}}^{*}$, and for Skyrme forces SIII and SLy4. The two parameter Fermi density, with its parameters fitted to experiments and made temperature dependent in a model way, is used for the nuclear density in semiclassical calculations, and the same in microscopic shell model is achieved via the Fermi-Dirac occupation of shell model states and particle number conservation.