A simple approach based on semiempirical mass formula and the Kelson-Garvey model by considering one, two and three body interactions has been developed to construct an analytical formula for binding energy. Binding energies for some nuclei are calculated via this method and compared with the available data. Also, an equation that expressed the relation between binding energies of the neighboring nuclei was obtained.

The mass and binding energy of atomic nuclei are the keys to the understanding of many physical processes. For this reason, it is important to construct reliable theoretical models for the values of the nuclear mass and binding energy of a nucleus as a function of mass A and atomic number Z. Generally, the binding energy is, to a first approximation, a fairly smooth function of `macroscopic' degrees of freedom that pertain to the nucleus as a whole. If we are willing to ignore small local departures, it is possible to develop simple formulae that express the binding energy E_B, or equivalently mass M (Z,N) of a nucleus in terms of these bulk coordinates. In order to keep the formulae simple, we may not wish, for instance, to make complicated calculations to relate various terms in the expression to the underlying nucleon-nucleon interactions. One of the more popular approaches to obtain nuclear binding energies is based on the analogy of a nucleus to a drop of incompressible fluid.

The Weizacker mass formula does not always give good results for the binding energy differences of nearby nuclei that are important in many applications. For this purpose the Kelson-Garvey approach (Janecke, 1988, p. 285 and Basu, 2004) is more useful. This method is a microscopic model that nuclear binding energy is considered to be the result of a sum of one and two-nucleon interaction terms. The value of these terms may vary from one mass region to another but in a small region differing only by a few nucleons, they must essentially be constant. The known binding energies of nuclei may be used to extract the values of these terms and results may then be used to predict the unknown binding energies in the same region. We illustrate this method below by considering the one and two nucleon interactions and then develop a method to calculate the binding energy with the considering three nucleon interactions. Finally, we calculate the binding energy for some nuclei and compare the obtained results with available experimental and theoretical data.

Physics Journal, Binding Energies, Semiempirical Mass Formula, Theoretical Models, Microscopic Models, Proton-Neutron Interactions, Kelson-Garvey Approach, Weizacker Mass Formula, Nucleon-Nucleon Interactions, Atomic Mass Evaluation, Nuclear Masses and Deformations.