Global phenomenological descriptions of nuclear odd-even mass staggering

TL;DR

This paper provides a comprehensive phenomenological analysis of nuclear odd-even mass staggering, revealing dependencies on neutron excess and shell structure, and proposing an improved global description for nuclear binding energy models.

Contribution

It introduces a new global phenomenological expression for odd-even mass differences that outperforms previous models and accounts for shell and neutron excess effects.

Findings

Clear change in neutron excess dependence at Z=50

Accurate local descriptions for odd and even nucleon numbers

Global expression significantly better than previous models

Abstract

We examine the general nature of nuclear odd-even mass differences by employing neutron and proton mass relations that emphasize these effects. The most recent mass tables are used. The possibility of a neutron excess dependence of the staggering is examined in detail in separate regions defined by the main nuclear shells, and a clear change in this dependency is found at $Z=50$ for both neutrons and protons. A further separation into odd and even neutron (proton) number produces very accurate local descriptions of the mass differences for each type of nucleons. These odd-even effects are combined into a global phenomenological expression, ready to use in a binding energy formula. The results deviate from previous parametrizations, and in particular found to be significantly superior to a recent two term, $A^{-1}$ dependence.