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.

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.