Microscopic–Macroscopic Mass Calculations with Wigner–Kirkwood expansion

Abstract

The systematic study and calculation of ground state nuclear masses continues to be one of the active and important areas of research in nuclear physics. The present work is an attempt to determine the ground state masses of nuclei spanning the entire periodic table, using the Microscopic–Macroscopic approach. The semi-classical Wigner–Kirkwood (WK) ℏ expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is achieved upto the fourth order in ℏ. The shell corrections, along with the pairing energies obtained by using the Lipkin–Nogami scheme, constitute the microscopic part of the nuclear masses. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. It is shown that the Microscopic–Macroscopic mass calculation thus achieved, yields reliable description of ground state masses of nuclei across the periodic table. The present status of the WK mass calculations and the possible future perspectives are discussed.