Nuclear masses near N = Z from Nilsson-Strutinsky calculations with pairing corrections beyond BCS from an isospin-conserving pairing force

摘要

A model with nucleons in a charge-independent potential well interacting byan isovector pairing force is considered. For a 24-dimensional valence space,the Hartree-Bogolyubov (HB) plus random phase approximation (RPA) to the lowesteigenvalue of the Hamiltonian is shown to be accurate except near values of thepairing force coupling constant G where the HB solution shifts from a zero to anon-zero pair gap. In the limit G -> infinity the HB + RPA is asymptoticallyexact. The inaccuracy of the HB + RPA in the critical regions of G can beremedied by interpolation. The resulting algoritm is used to calculate pairingcorrections in the framework of a Nilsson-Strutinsky calculation of nuclearmasses near N = Z for A = 24-100, where N and Z are the numbers of neutrons andprotons, and A = N + Z. The dimension of the valence space is 2A in thesecalculations. Adjusting five liquid drop parameters and a power law expressionfor the constant G as a function of A allows us to reproduce the measuredbinding energies of 112 doubly even nuclei in this range with a root meansquare deviation of 0.95 MeV. Several combinations of the masses for differentN, Z, and isospin T are considered and the calculations found to be in goodagreement with the data. It is demonstrated by examples how fluctuations as afunction of A of the constant X in an expansion of the symmetry energy of theform T(T+X)/(2 theta) can be understood from the shell structure.