Shell-Model Form Factors for theZr90(p,p′)Reaction

The application of the shell model to the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(p,p^{\prime })$ reaction is described. The nuclear matrix elements, and particularly the radial form factors, are discussed. Interactions of Gaussian and Yukawa form between projectile and target nucleons are used. They are assumed to be central, but spin and isospin dependence is included. The shell-model orbitals are calculated for a potential of the Woods-Saxon shape. The effects of parameter variations and of corrections such as may be due to nonlocality of the potentials are studied in some detail. It is shown how the data for the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}(p,p^{\prime })$ reaction favor a Yukawa interaction with a range of about 1 F.