The spin-orbit interaction in the scattering of 147-220 MeV nucleons by light nuclei

The polarizations and differential cross sections in the elastic scattering of 147-220 MeV nucleons by He⁴, Li⁷, C¹² and Al²⁷ are examined using the optical model. The usual form of the nuclear potential. ν(r) = -(V+iW)g(r)+(γ+iδ)r^-( dg dr)σ·L, where g(r) is a Woods-Saxon form factor, is found to be inadequate for a detailed description of the observations especially for light nuclei. Taking a spin-orbit potential of the form. γ′+iδ′){r^-3( d²g dr²)+ε′r^-( dg dr)}σ·L gives substantially better agreement with the data. It is shown how this modification of the Thomas-Fermi spin-orbit interaction may be related to higher order terms in the optical model expansion obtained in Born approximation from nucleon-nucleon scattering amplitudes.