Exact Solution to Optical-Model Equations for Quasi-Elastic (p, n) Reactions

The coupled optical-model equations describing quasi-elastic ($p, n$) reactions are solved exactly and the results are compared with distorted-wave Born approximation (DWBA) solutions. It is shown that for reasonable values of the isobaric potential the DWBA deviates only slightly from the exact solution. Fits to experimental data are presented for ${\mathrm{Ti}}^{48}(p, n){\mathrm{V}}^{48}$, ${\mathrm{V}}^{51}(p, n){\mathrm{Cr}}^{51}$, and ${\mathrm{Cr}}^{52}(p, n){\mathrm{Mn}}^{52}$.