Determination of the proximity potential from sub-barrier fusion data

Abstract

Sub-barrier fusion cross sections for 12 systems involving p-shell nuclei are analyzed in an attempt to determine directly the universal form of the internucleus potential. We use a previously developed inversion procedure based on the Wentzel-Kramers-Brillouin approximation, which new model calculations presented here show to be highly accurate. The scaling implied by the proximity formulation is found to be roughly consistent with the data, with the structure of the colliding nuclei having little effect. The proximity function Φ determined from the data is consistent with the original function of Blocki et al. at intermediate separations, subject to the use of a different formula for the nuclear radii. Data for selected systems involving sd-shell nuclei lead to a more attractive potential than that found for the p-shell systems, while data for systems involving Ca isotopes exhibit reentrant barriers characteristic of a breakdown of the basic assumptions of the inversion procedure.