The tightly bound nuclei in the liquid drop model

TL;DR

This paper analytically identifies the nuclei with the highest mean binding energy per nucleon using the liquid drop model and explores related nuclear properties and stellar nucleosynthesis implications.

Contribution

It provides an analytical proof of local extrema in binding energy per nucleon and discusses the shell model and nucleosynthesis context.

Findings

Local extrema at A ≈ 59 and Z ≈ 26.4, and A ≈ 62 and Z ≈ 27.75.

Identification of 62Ni as the most tightly bound nucleus.

Explanation of why 56Fe is more abundant than 62Ni in stars.

Abstract

In this paper, we shall maximise the binding energy per nucleon function in the semi-empirical mass formula of the liquid drop model of the atomic nuclei to analytically prove that the mean binding energy per nucleon curve has local extrema at A = 58.6960, Z = 26.3908 and at A = 62.0178, Z = 27.7506. The Lagrange method of multipliers is used to arrive at these results, while we have let the values of A and Z take continuous fractional values. The shell model that shows why 62Ni is the most tightly bound nucleus is outlined. A brief account on stellar nucleosynthesis is presented to show why 56Fe is more abundant than 62Ni and 58Fe. We believe that the analytical proof presented in this paper can be a useful tool to the instructors to introduce the nucleus with the highest mean binding energy per nucleon.