On the coefficients of the liquid drop model mass formulae and nuclear radii

TL;DR

This paper analyzes various liquid drop model mass formulae, determining their coefficients by fitting to experimental nuclear masses, and explores how different terms affect the accuracy and predictions of nuclear masses and radii.

Contribution

It systematically evaluates the impact of additional correction terms on the accuracy of nuclear mass formulas and charge radius predictions, providing optimized coefficients and expressions.

Findings

Coulomb diffuseness correction significantly improves mass formula accuracy.

Wigner and curvature energy terms can be used separately for better fits.

Surface energy coefficient around 17-18 MeV and charge radius r₀ ≈ 1.22-1.23 fm.

Abstract

The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and different powers of the relative neutron excess $I=(N-Z)/A$ have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction $Z^2/A$ term or the charge exchange correction $Z^{4/3}/A^{1/3}$ term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an $|I|$ dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more effective than an $I^4$ dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17-18 MeV and a relative equivalent rms charge radius r$_0$ of 1.22-1.23 fm.