Binding energies of the , and neutron and average two-body effective interactions

Abstract

The binding energies of the single particle or hole orbitals of the 1 g 9 2 and 1 h 11 2 neutron shells are given as a simple linear function of the active valence proton and neutron numbers. This function is derived theoretically by the assumption of constant two-body effective interactions V pn and V nn in the relevant proton and neutron shell spaces. These values, appearing in the function as the coefficients of the proton and neutron numbers, are determined from the experimental binding energies by a least-squares fit. The good quality of fit between the experimental and fitted binding energies implies the plausibility of the formula and the assumption. The determined V pn and V nn have absolute values and signs consistent with those in the literature. The effective interactions in the case of the 1 g 9 2 hole is found to decrease with increasing mass number.