Quantitative Studies of Nuclear Structure Through Isobaric Analog Resonances

Abstract

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.