Activities Based on Empirical Data to Determine Coefficients in Semi-Empirical Mass Formula

Abstract

In this paper, we propose activities based on empirical data to arrive at Coulomb, asymmetry, and pairing energy coefficients in the semi-empirical mass formula (SEMF). The Coloumb energy co-efficient is obtained using mirror nuclei data. Asymmetry energy co-efficient is determined from mass parabolas. The concept of neutron separation energies is used to arrive at the pairing energy co-efficient and its dependence with regards to the power of mass number A. Using these three obtained coefficients in SEMF for binding energies (BE), a plot of BE/A vs A−1/3 has resulted in Volume and surface energy coefficients using linear regression. It has found that the five coefficients obtained using these activities are closely matching with those obtained using Least Square Minimization (LSM) and Variational Monte Carlo (VMC) techniques. The mean percentage error (MPE), calculated between obtained binding energies from the optimized coefficients and the experimental binding energies, using the three approaches are almost equal. These activities enrich the understanding of students by laying importance on the physics involved, as they confirm that alternative strategies from experimental data are able to match those obtained using mathematical optimization procedures such as LSM and VMC.