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

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 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 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 alpha-nucleus A=4n,N=Z compound systems Ni-56(*) and Cr-48(*) and the non-alpha-nucleus compound system Cr-52(*), 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.