Global mass formula with shell corrections based on Wigner-Kirkwood method: an Overview

Abstract

Study of nuclear masses and their systematics is of great importance. Accurate knowl-edge of the nuclear masses plays s decisive role in the reliable description of processes like the astrophysical r-process. Considerable progress has already been achieved in the accurate prediction of the masses, and it is still being pursued vigorously by a number of groups around the globe. There are primarily two distinct approaches to calculate nuclear masses: the microscopic nuclear models based on density functional theory, like Skyrme Hartree Fock Bogoliubov or Relativistic Mean Field models, and the macroscopic- microscopic (Mic - Mac) models. Here, we report the mass calculation based on the Mic - Mac approach. According to the Mic - Mac approach, mass of a nucleus is written as sum of Macroscopic part (liquid drop) and a microscopic part, which comprises of shell correction and pairing energies. Here, the semi-classical Wigner - Kirkwood (WK)~expansion method is used to calculate shell corrections for spherical and deformed nu-clei. The expansion is achieved upto the fourth order in~. The pairing energies are obtained by using the Lipkin - Nogami scheme. The macroscopic part is obtained from a liquid drop formula, with six adjustable parameters. These parameters are adjusted to reproduce experimental masses of 367 spherical nuclei, which yields a rms deviation of 630 keV. It is shown that the approach based on WK expansion can be reliably used for accurate prediction of nuclear masses.