The Spin-Spin Interaction in Nucleon-Nucleus Scattering

Abstract

The existence of spin-spin terms in the optical potential for nucleons scattered on targets with non-zero spin has been the subject of investigation for many years. The presence of spin-spin and tensor terms in the nucleon-nucleon interaction leads one to suspect that these forces may still reveal themselves in the scattering on odd mass targets in the form of an interaction that couples the projectile and target spins. It was Feshbach¹) who first suggested that such terms may be present in the optical model potential. Two of the possible invariant forms that may appear in the potential are: a spherical spin-spin term

$${U_{SS}}\left( r \right) = - {V_{SS}}{F_0}\left( r \right)\vec \sigma \cdot \vec I$$

(1)

and a tensor term

$${U_{ST}}\left( r \right) = - \frac{1}{2}{V_{ST}}{F_T}\left( r \right)\left[ {3\left( {\vec \sigma \cdot \hat r} \right)\left( {\vec I \cdot \hat r} \right) - \vec \sigma \cdot \vec I} \right]$$

(2)

where $\vec \sigma$ is the Pauli spin operator for the scattered nucleon and $\vec I$ is the spin operator of the target nucleus. V_SS and V_ST are the strengths of the spherical and tensor terms, respectively.

Supported in part by the Atomic Energy Control Board of Canada