Optimization of Semi-empirical Mass Formula Based on Experimental and Microscopic Theoretical Data

Abstract

In this dissertation, I have optimized the semi-empirical Bethe-Wizsacker formula using the least-square method. I have considered the optimization to be linear multiple regression problem, considering independent terms with some physical significance. The recently available experimental mass evaluations of AME2020 [Huang et al. Chin. Phys. C 45, 030002 (2021)] and microscopic theoretical estimation of the Hartree-Fock-Bogoliubov model (HFB-24) [Goriely et al. Phys. Rev. C 88, 024308 (2013)] are used for fitting the standard semi-empirical mass formula. Further improvements are made by introducing the isospin asymmetry (I) dependence of volume, surface, and curvature coefficients. The shell corrections proposed by Myers and Swiatecki are used in this work. It is observed that isospin asymmetry dependence of volume, surface, and curvature coefficients along with the shell energy, play a predominant role in the estimation of nuclear binding energy and related data. The best fit model is obtained by considering 13 parameters in the semi-empirical mass formula with a root mean square value of 1.54 MeV and 2.46 MeV while fitting with AME2020 and HFB-24 data, respectively. The neutron and proton drip lines are also explosed using the fitted semi-empirical formulas. The correlation analysis of the coefficients of various models indicates that the I 2 dependence of the volume, surface, and curvature coefficients does not correlate with the model parameters, making it difficult to constrain.