New model of the average neutron and proton pairing gaps

Abstract

Abstract By use of the BCS approximation applied to a distribution of dense, equally spaced levels, we derive new expressions for the average neutron pairing gap gDn and average proton pairing gap gDp. These expressions, which contain exponential terms, take into account the dependencies of gDn and gDp upon both the relative neutron excess and shape of the nucleus. The three constants that appear are determined by a least-squares adjustment to experimental pairing gaps obtained by use of fourth-order differences of measured masses. For this purpose we use the 1986 Audi-Wapstra mid-stream mass evaluation and take into account experimental uncertainties. Our new model explains not only the dependencies of gDn and gDp upon relative neutron excess and nuclear shape, but also the experimental result that for medium and heavy nuclei gDn is generally smaller than gDp. We also introduce a new expression for the average residual neutron-proton interaction energy gd that appears in the masses of odd-odd nuclei, and determine the constant that appears by an analogous least-squares adjustment to experimental mass differences. Our new expressions for gDn, gDp and gd should permit extrapolation of these quantities to heavier nuclei and to nuclei farther removed from the valley of β stability than do previous parameterizations.