Calculate the Binding Energy Using the Least Squares Method to Modify the Liquid Drop Model

AL-Fraha, Enas M.

doi:10.33899/rjs.2025.186498

	Calculate the Binding Energy Using the Least Squares Method to Modify the Liquid Drop Model
Rafidain Journal of Science
Volume 34, Issue 1, March 2025, Pages 91-99 PDF (600.95 K)
Document Type: Research Paper
DOI: 10.33899/rjs.2025.186498
Author
Enas M. AL-Fraha
Sciences College, Physics department, Mosul university, mosul
Abstract
The current research developed a new formula for calculating the theoretical value of nuclear binding energy and comparing it with the experimental binding energy. The liquid drop model was modified to show the effect of the interconnected relationship between the dead nucleus, i.e. The region of the nucleus composed of protons and neutrons (Z=N) which are in pairs, with the surface of the nucleus which represents the levels occupied by the unpaired neutrons (N>Z) surrounding the region of the nucleus through the potential energy (X₀), which allows a clearer understanding of the nuclear structure, leading to good information in the field of applied nuclear physics. The least squares method (LSM) was used to determine the constants of the proposed formula, by creating a code using the Fortran 95 language, and the code was solved using the Gaussian method, and the constants were found for more than 400 different nuclei (even-even, even-odd, odd-odd) within the range (2 ≥ Z ≥ 92). To determine the reliability of the proposed formula, a statistical measure was used the standard deviation (σ), its accuracy in calculating the theoretical binding energy, and the standard deviation (σ=0.384) of the updated formulation of the modified liquid drop model or (MLDM).
Keywords
Binding energy; standard deviation; least squares method; modified liquid drop model

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