Adding a correction terms for the shell of the Liquid Drop Model and the Quark-Like Model

Abstract

This paper aims to add a corrective term to Liquid Drop Model (LDM) and Quark – Like Model (QLM), which is the term for closed shells of magic nuclei. This was done by relying on valence nucleons. Fitting to the terms volume, surface, Coulomb repulsion, asymmetry, pairing and shell term in LDM was performed using the least-square method LSM by designing a code in Fortran 95 for 261 magic nuclei within the range (2≤Z≤92), this correct and balance nuclear binding energy values, especially for magic nuclei, with experimental values. A fit of the QLM has also been made in order to correct the values of the nuclear binding energy. The standard deviation (σ) was used as a statistical tool to determine the extent to which the models can be adopted to explain the behavior of magic nuclei, in addition to the high accuracy in determining the experimental nuclear binding energy. The values of the standard deviation are σ= 0.144 and σ= 0.84 for the updated formulas of the Generalized Liquid Drop Mode (GLDM) and the Generalized Quark Like Model (GQLM) respectively.