The Study of Modified Semi-Empirical Mass Formula (SEMF) by Considering Isospin Effects in Liquid Drop Model

Abstract

We do theoretically study of Modified Semi-Empirical Mass Formula (SEMF) based on macroscopic approach in liquid drop
model by considering isospin effects. Isospin is one of internal symmetry properties in hadron group, particularly the nucleon multiplet, it
represented by isospin group. Hadron is a group of elementary particles take place in the strong interaction. The role of strong
interactions represents homogeneous nuclear force, interactions between proton-proton, proton-neutron, and neutron-neutron
are same. In other words, protons and neutrons are indistinguishable because mass (energy) between protons and neutrons is almost the same, by removing charge between them (charge independent). The dependence of isospin effects on nuclear symmetry term and oddeven (pairing) term made the formulation of SEMF should be modificated, in order to obtain nuclear mass and binding energy of a nucleus close to the experimental results. We do two accuracy testing. First, by comparing for nuclei using SEMF before and after being modified, the result shows that using SEMF before modification the value of and for modified SEMF we obtained at . The value of for modified SEMF is smaller than before modification, it indicates that Modified SEMF is a good formula to calculate the mass of nuclei. Second, by comparing Modified SEMF with other models such as FRDM, HFB-14, and HFB-17 using accuracy parameter in the form of rms deviation and number of model parameters. The results show that rms deviation decrease 21% to 0,516 and number of model parameters decrease to 15, consists of 13 macroscopic model parameters and two microscopic model parameters and . The value of model parameters was obtained by fitting to experimental results, as a reason it is called semi-empiric.