Neutron Spectroscopic Factors from Isobaric Analog States

Abstract

The spectroscopic factors $S_n$ of bound neutron states are usually found from ($d,p$) stripping reactions. An alternative method of finding $S_n$ for medium-to-heavy nuclei is to analyze isobaric analog resonances observed in ($p,p$) scattering from these nuclei. The present analysis uses a modified $R$-matrix theory in which boundary matching is done within the optical-model potential region rather than directly onto the Coulomb potential region. A resonance mixing phase and an optical penetrability are introduced. Both single- and multilevel resonances are treated. The effects of compound elastic scattering and the energy dependence of the level shift are investigated. Formulas for the spreading width are obtained. The variation of $S_n$ with the value of the matching radius and the best choice of this radius are discussed. As examples of the method, analyses of the $s$-wave resonance in ${}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}\mathrm{}(p,p)\mathrm{}{}_{}{}^{92}{}_{}{}^{}\mathrm{Zr}$ near 6.0-MeV bombarding energy and of $s$- and $d$-wave resonances in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}\mathrm{}(p,p)\mathrm{}{}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ near 5.8 and 6.8 MeV are presented. The values of $S_n$ obtained are compared with those from ($d,p$) experiments, and the reliability of the two methods is discussed.