Atomic Mass Formula with Empirical Shell Terms

An atomic mass formula is constructed as the sum of a gross part and empirical shell terms.The gross part is adjusted so that the shell terms may remain small and accord with the charge symmetry of nuclear forces.The shell terms show marked dips at the magic numbers 28, 50, 82 and 126, but not at 8 and 20.The standard deviation is 300 ke V for even-even and odd-mass nuclei with mass number 1 to 257.For odd-odd nuclei the mass formula includes additional terms and the standard deviation is 435 keV. § 1. IntroductionMany authors made attempts to construct the atomic mass formula including effects of the nuclear shell structure.Among them, Cameron et al. 1 l~s) assumed purely empirical shell terms in addition to a liquid-drop formula.Myers and Swiatecki 4 ),o) and Seeger 6 l' 7 l calculated shell energies as arising from the nonuniformity of single-nucleon levels of spherical or deformed nuclei and added them to their own liquid-drop formulas.Kiimmel et al. 8 l started from a formal summation of single-particle energies in each shell; by dividing it into the liquiddrop part and the shell part and applying some corrections to them, they constructed a mass formula.While these formulas include the liquid-drop part as representing the general tendency of atomic masses, there are other formulas which lack such a part.Zeldes et al. 9 l described atomic masses as a simple expression in valence nucleon numbers; the parameters in it are directly related to the matrix elements of the effective interaction.Garvey et aJ.l 0 l proposed a kind of mass relation from another viewpoint.A detailed review of these formulas was given by Comay et al. 11 l At the present stage, 'each has both merits and demerits and there seems to be room for improvement.In this paper we construct a mass formula from a somewhat different viewpoint.We start from the Yamada-Matumoto systematics of nucleon separation energies, SP (proton separation energy) and Sn (neutron separation energy) .12 l It is summarized as follows : A. Cases in which no odd-odd nucleus is concerned (Z: proton number, N: neutron number): SP (fi.xed-Z, even-N) increases smoothly (almost linearly) with N.