Quantitative Studies of Nuclear Structure Through Isobaric Analog Resonances

Isobaric analog resonances (IAR) observed in the elastic scattering of protons from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ are analyzed in the framework of the shell-model theory of reactions. Parametrization of the energy-averaged $S$ matrix elements given by the shell-model theory is discussed, and the dependence of the spectroscopic factors upon the various optical-model parameters is exhibited. The resonance mixing phases for most of the IAR analyzed here cannot be distinguished from zero. Damping of the single-particle wave functions arising from the nonlocality of the optical potentials is consistently incorporated. The nonlocality length of 0.85 F employed in this analysis leads to an attenuation of the single-particle wave functions by about 15% inside the nucleus. Neutron spectroscopic factors obtained here compare favorably with corresponding results from the study of ($d,p$) and ($t,d$) reactions.