Analysis of Proton Scattering and Reactions with the Generalized Optical Model

Abstract

Isobaric analog resonances in proton scattering experiments are analyzed using a set of coupled optical equations which include both elastic and inelastic channels as well as other channels which can couple to these via the charge-exchange operator ($\overrightarrow{\tau }·\overrightarrow{\mathrm{T}}$). The method has been applied to the particular case of ${\mathrm{Sr}}^{88}+p$, in which only the $p_0\left(0_1^{+}\right)$ and $p_1\left(2_1^{+}\right)$ proton channels are dominant and mixing of the ($j\times 0_1^{+}$) and ($j^{\prime }\times 2_1^{+}$) configurations describes the primary fragmentation of the $2d_{\frac{5}{2}}$, $3s_{\frac{1}{2}}$, $2d_{\frac{3}{2}}$, and $j^{\prime }\times 2_1^{+}$ neutron states in the parent nucleus ${\mathrm{Sr}}^{89}$. Our purpose in this investigation was to see whether or not one could obtain a consistent match to both the level structure of the bound parent analog system and the analog resonance data in the various open channels with a general expression for the effective nucleon-nucleus interaction. Restricting as many parameters and potential terms as possible using independent sources of data, we obtained a detailed fit to the level structure of ${\mathrm{Sr}}^{89}$ and the resonant ${\mathrm{Sr}}^{88}(p,p_0)$ and ($p,p_1^{\prime }$) excitation functions, the resonant ${\mathrm{Sr}}^{88}\mathrm{}(p,n)\mathrm{}$ total cross-section data, and the elastic polarization functions for an incident proton energy from $E_p=4.8\mathrm{} \mathrm{to} 8.2$ MeV. The predicted on-resonance $p^{\prime }\left(2_1^{+}\right)$ angular distributions follow the main features of the data but not the finer details. It was found that the interference between the resonance and the direct inelastic background depends mostly on the nuclear rather than the Coulomb core excitation, and that direct inelastic charge-exchange does not affect the results. Our ability to fit all of the data in a consistent manner is interpreted as a confirmation of the main features of the generalized potential model assumed.