Recoil corrections in heavy-ion-induced transfer

Abstract

A perturbative approach for rapid calculation of recoil corrections to heavy-ion distorted- wave Born approximation has been developed. Without making either the local momentum approximation or the Hankel function approximation, we expand the final scattering wave function about ${\overrightarrow{\mathrm{r}}}_f=\alpha {\overrightarrow{\mathrm{r}}}_i$. We have modified the existing no-recoil code RDRC to include exactly the first-order term, allowing one to correct for both longitudinal and transverse recoil effects. Sample calculations have been performed, including an analytically solvable test case, plus the reactions ${}_{}{}^{94}{}_{}{}^{}\mathrm{Mo}$(${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{95}{}_{}{}^{}\mathrm{Mo}$ and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$)${}_{}{}^{49}{}_{}{}^{}\mathrm{Sc}$ for which data have been taken and analyzed previously with RDRC. The relative $\alpha$ independence of the results argues strongly for convergence.