Spin-Orbit Coupling forΛ−He4Scattering Using a One-Boson-Exchange Model for theΛNInteraction

The polarization and cross sections for $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering are calculated for $\Lambda$ incident energies 1-20 MeV. A $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ potential is constructed using a phenomenological $\Lambda N$ Gaussian central potential and the empirical shape for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and a spin-orbit potential obtained from a one-boson-exchange (OBE) model for the $\Lambda N$ interaction. As indicated recently by Downs, the OBE model for $\Lambda N$ forces leads to strong antisymmetric spin-orbit terms due to vector-meson exchange. This means that the $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ potential depends only on part of the $\Lambda N$ spin-orbit interaction, since it results from summing the latter interaction over the nucleon spin states. Parameters from three quite different OBE calculations are used to predict the $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering, and these three sets of OBE parameters lead to remarkably similar predictions concerning the cross sections and polarization properties for this energy range. However, no $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ resonances are predicted, in contrast to recent Hartree-Fock calculations of $\Lambda -{}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering. The polarization effects predicted are large, and experimental data concerning them would have interesting consequences for our knowledge of the origin of spin-orbit forces in the baryon-baryon system.