Odd-even staggering in nuclear binding and the liquid-drop model

TL;DR

This paper investigates odd-even staggering in nuclear binding energies, identifies background effects using the liquid-drop model, and proposes a new term to better explain observed differences between even and odd measures.

Contribution

It introduces a new term to the liquid-drop model to account for residual differences in odd-even staggering not explained by traditional models.

Findings

Background effects partially explain differences in OES trends.

A new liquid-drop term improves fit to experimental data.

The revised model alters the interpretation of pairing energies.

Abstract

The trends with mass number are examined for the odd-even-staggering (OES) in nuclear binding of neutrons and protons through the conventional measures $\Delta^{(3)}$. The large differences previously observed between these trends for even and odd values of these measures is found to arise, in part, from the slow variation of binding energies with mass and charge which provides a background contribution. This background is estimated with the liquid-drop model, and accounts for the greater difference found in proton removal relative to neutron removal. The differences which persist after backgrounds are removed can not be treated in the conventional liquid-drop model but require the addition of a new term. Such a term is investigated, and its effect on specific values of the OES is calcutated. The liquid-drop fitting is also applied to a set of separation energies constrained to match the specific set of nuclei used to determine the observed values for the odd $\Delta^{(3)}$. The resulting fit for the pairing term is compared to the average value of even and odd measures. The effect on this value of the new liquid-drop term is observed, and the change in background when the new term is included is also used as an alternate method for determining the difference between trends of the even and odd values of the OES.