Fitting the Nuclear Binding Energy Coefficients for Liquid Drop Model and Adding a mathematical terms to the Closed Shell of Magic Nuclei

Document Type : Original Article

Authors

1 Iraq , Mosul , University of Mosul, College of science, Physics department

2 Physics Department College of Science, Mosul University, Mosul, IRAQ.

Abstract

The present study reconsiders the formula of the Liquid Drop Model (LDM) in addition to updating the terms of the energy parameters represented by the term of volume, surface, coulomb, asymmetry and pairing. This was done using the least-squares method (LSM) by means of a computer program in the Fortran language to match the nuclear binding energy for more than 480 different nuclei, including the magic nuclei of the range (2 ≤ Z ≤ 92). A mathematical term represented by the closed shell term, in addition to the energy terms above, was derived once by the difference between the separation energy of protons and neutrons and again by the method of valence nucleons, which represents the highest energy level in any nucleus because it is the only energy that participates in spinning the nucleus. New energy parameters were obtained specifically for the Liquid Drop Model which enabled us to determine the theoretical nuclear binding energy in a good match with its experiment values for most of the nuclei used, especially the magical nuclei. The standard deviation (σ ) was used as a statistical tool to determine the extent to which the model can be adopted to explain the behavior of magic nuclei, in addition to the high accuracy in determining the theoretical nuclear binding energy. The value of the standard deviation ( σ = 0.126 ) and (σ=0.144)) for the two updated formulas of the model were the generalized liquid drop models (GLDM)₁ and (GLDM )₂, respectively.

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