The Liquid Drop Mass Formula as a Shell Model Average

Abstract

It has been previously shown1)that an expression for the binding energies of nuclei with the structure of the semiempirical Bethe-Weizsacker mass formula can be derived from a shell model with residual interactions. Pending quantitive agreement -which is the subject of this paper -this approach provides a microscopial foundation for the exceptionally good semi-empirical mass formula. To our knowledge, this constitutes the first verification of the commonly accepted, but otherwise unproven, statement that the liquid drop mass formula should emerge from a suitably averaged shell model, this being the basic assumption in the mass formulae constructed by using the liquid drop expression as a base line to which shell corrections are added.