Deuteron Stripping on Deformed Nuclei

Abstract

Interference of indirect transition amplitudes with the direct transition amplitude for deuteron stripping on deformed nuclei is investigated. The indirect transitions that are considered are those that arise via intermediate rotational excitations of the target and product nuclei. These indirect transitions are introduced by generalizing the initial and final distorted waves so that they include inelastic amplitudes. A straight-forward coupled-channel treatment of the generalized distorted waves is described. However, a quantitative investigation of the coupled-channel formulation is not attempted because of the enormous numerical difficulties that such a procedure would present. Instead, the rotational motion of the target is treated adiabatically; thereby, in principle, inelastic amplitudes in all rotational channels are accounted for simultaneously. Further simplification is achieved by treating the coupling of the rotational coordinates to the projectile coordinates only to first order. Calculations are performed for deuteron stripping on ${\mathrm{Mg}}^{24}$ and ${\mathrm{U}}^{238}$. The calculations indicate that: (a) the indirect amplitudes are small; (b) the indirect amplitudes are affected more strongly by intermediate excitations in the deuteron channel than by intermediate excitations in the proton channel; (c) the indirect amplitudes generally flatten the angular distributions of the reaction protons; and (d) the ratio of the strength of the indirect transitions to that of the direct transition is fairly independent of the mass of the target. Although the spin-orbit force is neglected, the theory predicts a $J$ dependence in the angular distributions that is significant at all angles. The indirect stripping amplitudes are small; however, they produce measurable effects in the differential cross section when they add coherently to the direct amplitude. The most dramatic effects of the indirect amplitudes are changes of the angular distributions of the reaction protons. In addition, the calculated spectroscopic coefficients are changed by a significant amount when the indirect amplitudes are taken into account.