English

The tightly bound nuclei in the liquid drop model

Nuclear Theory 2018-03-12 v3

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.

Cite

@article{arxiv.1709.01386,
  title  = {The tightly bound nuclei in the liquid drop model},
  author = {N R Sree Harsha},
  journal= {arXiv preprint arXiv:1709.01386},
  year   = {2018}
}

Comments

16 pages, 3 figures, 3 tables, final version accepted for publication in European Journal of Physics

R2 v1 2026-06-22T21:33:33.110Z