The tightly bound nuclei in the liquid drop model

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 La...

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Bibliographic Details
Published in:European journal of physics 2018-05, Vol.39 (3), p.35802
Main Author: Sree Harsha, N R
Format: Article
Language:English
Subjects:
binding energy per nucleon
liquid drop model
nickel-62
semi-empirical mass formula
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Summary: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.
ISSN:0143-0807
1361-6404
DOI:10.1088/1361-6404/aaa345