Calculation of Elastic and Inelastic Proton Scattering with a Generalized Optical Model

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Abstract
An extension of the optical model is considered in which a state of quadrupole collective motion is strongly coupled to the nuclear ground state. The calculations include a spin-orbit potential and the simultaneous coupled differential equations of the problem are solved numerically on a high-speed computer. Experimental data on the scattering of medium energy protons from Ti, Cr, Fe, Ni, and Zn are analyzed. A good average optical potential is determined and conclusions are drawn about the energy dependence of the parameters. Evidence is presented for the validity of the collective model. Nuclear deformabilities derived by fitting the inelastic differential cross sections are in good agreement with those determined by electro-magnetic methods. Various limitations and ambiguities of the model are discussed and possible improvements are indicated.