Deuteron elastic scattering and stripping processes offC12as a three-body problem

Abstract

Deuteron elastic scattering and stripping processes off a target nucleus consisting of A nucleons are treated within the framework of the few-body integral equations theory. By projecting the ($A+2$)-body operators onto target states, matrix three-body integral equations are derived that allow for the incorporation of the excited states of the target nucleons. This approach is applied to deuteron scattering off $^{12}\mathrm{C}$ when the latter is in its ground state before and after the reaction. For the nucleon-$^{12}\mathrm{C}$ subsystem three sets of (quasi-separable) potentials are employed. The first such potential is based on the one derived by Cattapan et al. [Nucl. Phys. A241, 204 (1975)] for orbital angular momentum states with $L\ensuremath{\leqslant}2$, which is valid for low energies. As second set we use the potential of Miyagawa and Koike [Prog. Theor. Phys. 82, 329 (1989)] fitted to semiphenomenological higher-energy phase shifts for states up to $L=6$. The third one finally consists for $3\ensuremath{\leqslant}L\ensuremath{\leqslant}5$ of the potential set of Miyagawa and Koike, whereas the potential parameters for $L\ensuremath{\leqslant}2$ are determined by simultaneously fitting the elastic-channel T matrix obtained as solution of multichannel two-body Lippmann-Schwinger equations, to the experimental low-energy and the semiphenomenological higher-energy phase shifts. For the nucleon-nucleon interaction we take one of the separable ${}^{3}{S}_{1}\ensuremath{-}{}^{3}{D}_{1}$ potentials of Phillips [Nucl. Phys. A107, 207 (1968)]. Differential cross sections for the elastic-scattering reaction $d+$$^{12}\mathrm{C}$ $\ensuremath{\rightarrow}d+$$^{12}\mathrm{C}$ and the transfer reaction $d+$$^{12}\mathrm{C}$ $\ensuremath{\rightarrow}p+$$^{13}\mathrm{C}$($^{13}\mathrm{C}$${}^{*}$) are calculated at deuteron bombarding energies of 4.66 and 15 MeV (up to 36-channel calculation), and at 56 MeV (up to 76-channel calculation) together with some selected analyzing powers, and are compared with experimental data. At the highest energy considered, the decomposition of the differential cross section into the near-side and the far-side components shows the appearance of nuclear rainbow scattering.