Systematic Distorted-Wave Born-Approximation Predictions for Two-Nucleon Transfers: Applications to (d,α) Experiments

In the case of angular-momentum-mismatch conventional distorted-wave Born-approximation (DWBA) calculations tend to give results which are strongly dependent on the opticalmodel parameters chosen and, to a lesser degree, on finite-range and nonlocality effects. We discuss reasons for this sensitivity and present systematic calculations for ($d,\alpha$) reactions on nondeformed targets ranging from ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. Satisfactory DWBA results could be obtained for the entire range of targets, provided that all potentials for the generation of scattered and bound wave functions were restrained to have nearly identical physically meaningful real well geometries and real depths of $V\approx n{V}_0$, where $V_0$ is the proton scattering potential and $n$ is the number of nucleons in the projectile. The use of well geometries with $r_0=1.2\mathrm{}$ fm, $a=0.75\mathrm{}$ fm, and retention of the basic DWBA requirement that the optical potentials should also correctly fit elastic scattering removes the familiar ambiguities for deuteron and $\alpha$ potentials. It is shown that with these parameter restrictions finite range effects are expected to be small so that a first-order correction procedure is adequate. Explicit calculations are compared with over 30 ($d,\alpha$) angular distributions of known angular momentum transfer for experimental bombarding energies ranging from 12 to 17 MeV. Consistent agreement with experiment was obtained.