Global calculations on the microscopic energies and nuclear deformations: Isospin dependence of the spin-orbit coupling

TL;DR

This study systematically calculates microscopic energies and nuclear deformations of about 1850 even-even nuclei using different isospin-dependent Woods-Saxon parameterizations, revealing similarities and differences across nuclear regions and providing insights into the isospin dependence of the spin-orbit force.

Contribution

It introduces a comprehensive macroscopic-microscopic approach with three Woods-Saxon parameterizations to analyze nuclear shapes and energies, highlighting the isospin dependence of the spin-orbit interaction.

Findings

Ground state deformations are consistent across models.

Significant differences occur mainly in neutron-rich and superheavy nuclei.

Microscopic energies are generally within 2 MeV across models.

Abstract

The microscopic energies and nuclear deformations of about 1850 even-even nuclei are calculated systematically within the macroscopic-microscopic framework using three Woods-Saxon parameterizations, with different isospin dependences, which were constructed mainly for nuclear spectroscopy calculations. Calculations are performed in the deformation space $(\beta_2, \gamma, \beta_4)$. Both the monopole and doubly stretched quadrupole interactions are considered for the pairing channel. The ground state deformations obtained by the three calculations are quite similar to each other. Large differences are seen mainly in neutron-rich nuclei and in superheavy nuclei. Systematic calculations on the shape-coexisting second minima are also presented. As for the microscopic energies of the ground states, the results are also very close to each other. Only in a few cases the difference is larger than 2 MeV. The total binding energy is estimated by adding the macroscopic energy provided by the usual liquid drop model with its parameters fitted through the least square root and minimax criteria. Calculations are also compared with the results of other macroscopic-microscopic mass models. All the three calculations give similar values for the deformations, microscopic energies and binding energies of most nuclei. One may expect to have a better understanding of the isospin dependence of the spin-orbital force with more data on proton- and neutron-rich nuclei.