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

TL;DR

This paper introduces a microscopic-macroscopic model using the Wigner-Kirkwood semiclassical expansion to accurately compute binding energies of deformed nuclei, achieving results comparable to established methods and exploring corrections for improved efficiency.

Contribution

It applies the fourth-order Wigner-Kirkwood expansion to nuclear binding energy calculations, offering a simpler and faster alternative to traditional shell correction methods.

Findings

Achieved rms deviation of 610 keV in binding energies for 561 nuclei.

Found regular behavior of higher-order correction ratios as a function of asymmetry.

Demonstrated the model's predictive power near drip lines and superheavy regions.

Abstract

The binding energies of deformed even-even nuclei have been analysed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner - Kirkwood $\hbar$ expansion up to fourth - order, instead of the usual Strutinsky averaging scheme, to compute the shells corrections in a deformed Woods - Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with $Z\ge 8$ and $N\ge 8$, we find an {\it rms} deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the FRDM of M\"oller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth - order Wigner - Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth - order to the second - order corrections behaves in a very regular manner as a function of the asymmetry parameter $I=(N-Z)/A$. This allows to absorb the fourth - order corrections into the second - order contributions to the binding energy, which enables to simplify and speed up the calculation of deformed nuclei.