Multipole expansions in exact finite-range calculations of two-nucleon transfer reactions between heavy ions

Abstract

A method is developed for calculating microscopic form factors for two-nucleon transfer reactions between heavy ions in the distorted-wave Born approximation. This method utilizes a multipole expansion of the two-nucleon overlap integrals in terms of the relative angular momentum of a transferred nucleon pair, which is found to converge very rapidly. Sample calculations are carried out for the reaction $^{48}\mathrm{Ca}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$)$^{50}\mathrm{Ca}$ at ${E}_{\mathrm{lab}}=50$ MeV, leading to the ground and excited states. The calculations underpredict the experimental cross sections by a factor of about 10 for the ${0}_{1}^{+}$, ${2}_{1}^{+}$, and ${2}_{2}^{+}$ state transitions. It is also found that the singlet ($S=0$) and triplet ($S=1$) two-nucleon transfers contribute about equally to the cross section.NUCLEAR REACTIONS Multipole expansion, microscopic form factor, finite-range full recoil, DWBA, $^{48}\mathrm{Ca}$($^{18}\mathrm{O}$, $^{16}\mathrm{O}$)$^{50}\mathrm{Ca}$ ${E}_{\mathrm{lab}}=50$ MeV, 0+ ground state, ${2}_{1}^{+}$, ${2}_{2}^{+}$, and ${3}^{\ensuremath{-}}$ excited states.