Semi-empirical Nuclear Mass Formula: Simultaneous Determination of 4 Coefficients

Abstract

The deduction of 4 coefficients of the semi-empirical mass formula is presented as a function with two constants of proportionality:  which relates the energy of the nuclear volume with volume and  which relates volume with the mass number. Next the development of a proprietary method is presented—one that permits the simultaneous calculation of 4 of the 5 coefficients of the original semi-empirical formula. This method, which is direct and does not employ or require the use of successive approximations or iterations, is sufficiently didactic. It makes use of the experimental binding energies from 6 stable isotopes with a mass number odd-. Subsequently as validation, the coefficients are utilized for the theoretical calculation of the atomic masses of 237 stable isotopes and are compared with the experimental masses. Additionally, the calculation of the coefficients of proportionality  and , the unit nuclear radius , the coefficients of nuclear surface tension , and the nuclear density are presented as well.