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

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 performed 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 the 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.

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

“…[ By designing a code to solve the above matrix equation by Gauss's method, we get new constants that are tabulated in the equation ( 7) [18]:…”

“…Studying atoms showed that when the number of electrons is equal to one of the numbers (2, 10,18,36,54,86), it delivers high chemical stability and has a high ionization ability. According to the Pauli exclusion principle, these numbers, known as atomic magic numbers, can explain why these atoms' chemical stability is due to their closed electron shells and subshells [7].…”

Pauli Exclusion Classical Potential for Intermediate-Energy Heavy-Ion Collisions

“…The resulting fit corresponds to the blue dashed line of Figure 3. The values of Audi [47], Rholf [51], Dorso [39], and of the Generalized liquid drop model [52] are presented for comparison. It must be mentioned that the Coulomb and symmetry terms of Equation ( 4) depend explicitly on A and Z, which introduces discontinuities for different isotopes of the same element, and such fluctuations are more noticeable around A ≈ 70.…”

Estimation of Nuclear Mass Formulas Coefficients Using Least-Squares Method Based on Gauss-Seidel Scheme: A Comparative Study Between Three Models

“…Recently years, a significant number of studies have been published on the subject of nuclear masses such as the published papers [21]- [27]. Interestingly, to date no researcher has discussed the proposed LDM formula of eight parameters with making a comparison between three models.…”