Theoretical predictions of nuclear binding energy using a semi-empirical mass formula (SEMF): Five terms of SEMF–5T

Document Type : Original Article

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1 physics, Faculty of science, Zagazig university

2 Physics Department, Faculty of Science, Zagazig University

3 Mathematics and Theoretical Physics Department, Nuclear Research Centre, Egyptian Atomic Energy Authority, B.O. 13759, Cairo, Egypt

Abstract

This study utilizes the semi-empirical mass formula with five terms (SEMF-5T), grounded in the liquid drop model (LDM), to calculate nuclear binding energies for nuclei far from the stability line. The focus spans three mass regions: light elements (Z = 20-23, A = 39-60), heavy elements (Z = 78-93, A = 199-219), and superheavy elements (Z = 87-110, A = 230-270). Our results demonstrate high accuracy and reliability, with acceptable uncertainties when compared to experimental data and existing models. We derive the coefficients for the mass formula through a least squares fitting procedure, using a dataset of 246 stable and unstable nuclides. These coefficients allow for precise predictions of nuclear binding energies in the specified regions. To validate our findings, we compare our predicted binding energies with experimental measurements and the finite-range droplet model (FRDM), a well-regarded model in the field. Our calculations show strong agreement with both experimental data and the FRDM model, underscoring the prediction accuracy of the mass formula. Thus, the liquid drop model proves to be a reliable and precise tool for determining binding energies across the studied mass regions.

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