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

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The polarizations and differential cross sections in the elastic scattering of 147–220 MeV nucleons by He 4, Li 7, C 12 and Al 27 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( d 2g dr 2 )+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.