Role of pair-vibrational correlations in forming the odd-even mass difference

Abstract

Abstract In the random phase approximation (RPA)-amended Nilsson-Strutinskij method of calculating nuclear binding energies [1, 2], the conventional shell correction terms derived from the independent-nucleon model and the Bardeen-Cooper-Schrieffer pairing theory are supplemented by a term which accounts for the pair-vibrational correlation energy. This term is derived by means of the RPA from a pairing Hamiltonian which includes a neutron-proton pairing interaction. The method was used previously in studies of the pattern of binding energies of nuclei with approximately equal numbers N and Z of neutrons and protons and even mass number A = N + Z. Here it is applied to odd-A nuclei. Three sets of such nuclei are considered: (i) The sequence of nuclei with Z = N – 1 and 25 ⩽ A ⩽ 99. (ii) The odd-A isotopes of In, Sn, and Sb with 46 ⩽ N ⩽ 92. (iii) The odd-A isotopes of Sr, Y, Zr, Nb, and Mo with 60 ⩽ N ⩽ 64. The RPA correction is found to contribute significantly to the calculated odd-even mass differences, particularly in the light nuclei. In the upper sd shell this correction accounts for almost the entire odd-even mass difference for odd Z and about half of it for odd N. The size and sign of the RPA contribution varies, which is explained qualitatively in terms of a closed expression for a smooth RPA counter term.