Normalization of the ( d , He 3 ) reaction

The normalization constant ${{D}_{0}}^{2}$ for distorted-wave Born approximation calculations for ($d$, $^{3}\mathrm{He}$) reactions is estimated using a $J$-dependent sum rule analysis of relative spectroscopic factors. Discrepencies in absolute spectroscopic factors for $^{51}\mathrm{V}(d, ^{3}\mathrm{He})^{50}\mathrm{Ti}$ and $^{12}\mathrm{C}(d, ^{3}\mathrm{He})^{11}\mathrm{B}$ reactions at 80 MeV are resolved. A comparison of these reactions suggests that the Coulomb part of the $d\ensuremath{-}p$ interaction should not be included in the calculations. Our analysis yields ${{D}_{0}}^{2}=(1.65\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ Me${\mathrm{V}}^{2}$${\mathrm{fm}}^{3}$. Together with other analyses, a value of ${{D}_{0}}^{2}=(2\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ Me${\mathrm{V}}^{2}$${\mathrm{fm}}^{3}$ appears to be appropriate.