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

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 $E_{\mathrm{lab}}=50\mathrm{}$ 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 ($S=0\mathrm{}$) and triplet ($S=1\mathrm{}$) two-nucleon transfers contribute about equally to the cross section.