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 $d-p$ interaction should not be included in the calculations. Our analysis yields ${D_0}^2=(1.65\mathrm{}\pm 0.15)\times {10}^4$ Me${\mathrm{V}}^2$${\mathrm{fm}}^3$. Together with other analyses, a value of ${D_0}^2=(2\mathrm{}\pm 0.4)\times {10}^4$ Me${\mathrm{V}}^2$${\mathrm{fm}}^3$ appears to be appropriate.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He})$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}(d, {}_{}{}^3{}_{}{}^{}\mathrm{He})$, $E=30-80\mathrm{}$ MeV; $J$-dependent sum rule analysis; deduced normalization constant ${D_0}^2$.

• Received 21 June 1976

DOI:https://doi.org/10.1103/PhysRevC.15.53