Microscopic-Macroscopic Approach for Binding Energies with Wigner-Kirkwood Method

TL;DR

This paper presents a semi-classical method combining Wigner-Kirkwood shell corrections with a liquid drop model to accurately predict nuclear binding energies, demonstrating promising results for nuclear mass predictions.

Contribution

It introduces a systematic microscopic-macroscopic approach using Wigner-Kirkwood shell corrections up to fourth order in 44, combined with a liquid drop model, to improve nuclear binding energy calculations.

Findings

Achieved an rms deviation of 630 keV for 367 spherical nuclei.

Demonstrated the effectiveness of the approach in predicting nuclear masses.

Provided a systematic study of shell corrections as a function of deformation.

Abstract

The semi-classical Wigner-Kirkwood $\hbar$ expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in $\hbar$. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a {\it rms} deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.