Parameters for the $d-pn$, $t-dn$, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}-dp$ overlaps obtained from dispersion relations yield for the normalization constants for ($d,p$), ($t,d$), and (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reactions the values $D^2=(1.66,3.9,\mathrm{and} 2.9)\times {10}^4$ ${\mathrm{MeV}}^2$ ${\mathrm{fm}}^3$, respectively. These constants are employed in a comparative distorted-wave Born-approximation analysis of interrelated nucleon-transfer reactions on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at energies near the Coulomb barrier. The relative normalization of the ($t,d$) and ($d,p$) reactions is almost independent of the wave function of the transferred nucleon and of the optical potentials. For the mirror ($t,d$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reactions on a self-conjugate nucleus, the relative normalization depends on the ratio between root-mean-squared radii of the transferred nucleons. This ratio is calculated using a method which always yields the same relative normalization. Good consistency is found between reaction data and the normalization constants obtained from dispersion relations.

NUCLEAR REACTIONS ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(d,p_0)$, $E=3,4, \mathrm{and} 6$ MeV. ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^3{}_{}{}^{}\mathrm{He},d_0){}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}$, $E=9, 9.85,10.7$ MeV. ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}_0^{}{}_{}{}^{}){}_{}{}^{39}{}_{}{}^{}\mathrm{K}$, $E=11\mathrm{}$ MeV. Measured $\sigma (E,\theta )$. Comparisons with ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(t,d_0){}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(d,t_{0,1}){}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p,d_{0,1}){}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$. Deduced normalization constants for ($t,d$) and (${}_{}{}^3{}_{}{}^{}\mathrm{He},d$) reactions.

• Received 24 March 1976

DOI:https://doi.org/10.1103/PhysRevC.14.2082