The properties of ${\mathrm{Li}}^6$ and deuteron—$\alpha$-particle scattering are studied in an exact three-particle model in which the neutron, proton, and $\alpha$ particle interact through separable two-body forces. The $\alpha$ particle is assumed to be structureless, and Coulomb effects are neglected. As a representation of the nucleon—$\alpha$-particle interaction, a three-term separable potential fit to low-energy neutron-$\alpha$-particle scattering is introduced in the partial waves $s_{\frac{1}{2}}$, $p_{\frac{3}{2}}$, and $p_{\frac{1}{2}}$. The $s_{\frac{1}{2}}$ interaction is taken to be repulsive, while the other two are attractive. The three-body formalism of Amado is generalized to allow spin-dependent two-body interactions in an arbitrary partial wave. Numerical solution of the resulting three-body equations gives the binding energies of the $T=0\mathrm{}$ and $T=1\mathrm{}$ states of ${\mathrm{Li}}^6$ as well as phase shifts, angular distributions, and deuteron polarization in $d-\alpha$ scattering, and also the total cross section for $d+\alpha \to n+p+\alpha$ up to 30 MeV. Most of the calculations have used only an $s$-wave $n-p$ interaction, but a limited number have been done with the $d$ state of the deuteron included in order to assess its importance. Given the assumptions of the model, the agreement of the calculated quantities with experiment is very good. Some discussion of the results with respect to phenomenological optical-model fits to deuteron-nucleus scattering is also given.

• Received 27 June 1969

DOI:https://doi.org/10.1103/PhysRev.187.1328