On the mass formula and Wigner and curvature energy terms

TL;DR

This paper evaluates various liquid drop mass formulas, analyzing the impact of curvature and Wigner terms, to improve the accuracy of atomic mass predictions through least squares fitting.

Contribution

It systematically assesses the independent effects of curvature energy and Wigner term in mass formulas, providing optimized parameters for better atomic mass predictions.

Findings

Wigner term and curvature energy independently enhance mass formula accuracy.

Surface energy coefficient around 17-18 MeV identified.

Optimal charge radius r₀ approximately 1.22-1.23 fm.

Abstract

The efficiency of different mass formulas derived from the liquid drop model including or not the curvature energy, the Wigner term and different powers of the relative neutron excess $I$ has been determined by a least square fitting procedure to the experimental atomic masses assuming a constant R$_{0,charge}$/A$^{1/3}$ ratio. The Wigner term and the curvature energy can be used independently to improve the accuracy of the mass formula. The different fits lead to a surface energy coefficient of around 17-18 MeV, a relative sharp charge radius r$_0$ of 1.22-1.23 fm and a proton form-factor correction to the Coulomb energy of around 0.9 MeV.