AS A SHELL MODEL AVERAGE

It has been previously shown 1 \hat 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 comtitutes 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. The analytical expression in terms of the mass number A and the atomic number Z is obtained by evaluating the Hartree -Fock ground -state energy with a conveniently paramererized set of pheno­ menological single -particle energy levels. The coefficients of the mass formula thus obtained - volume, surface, symmetry and pair ing, as well as new ones which are predicted - are given as defi­ nite functions of the shell model parameters. The fit to the ex peri­ mental data is done through a search of the parameters associated with the single particle potential and the residual interactions. The search is limited to the range of phenomenological values consistent with nuclear spectra calculations and optical model analysis of