It is shown that physically consistent and realistic values of all the parameters can be found for a model that represents the distorted waves in the distorted-wave Born approximation for collective $\alpha$ inelastic scattering by a properly normalized decaying plane wave. The significance of this achievement in a thoroughly understood reaction is that we are now able to obtain analytic distorted waves that are sufficiently realistic and sufficiently simple to use in off-shell distorted-wave impulse approximation calculations of reactions of current interest requiring microscopic descriptions of the reaction mechanism.

NUCLEAR REACTIONS ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}(\alpha ,{\alpha }^{\prime })$, $E=33, 50, 100$ MeV; ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ti}(\alpha ,{\alpha }^{\prime })$, $E=41\mathrm{}$ MeV; ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}(\alpha ,{\alpha }^{\prime })$, $E=42\mathrm{}$ MeV; analytic DWBA, calculated $\sigma \left(\theta \right)$.

• Received 22 April 1974

DOI:https://doi.org/10.1103/PhysRevC.10.1041