Study of Inelastic Scattering of Protons from ${\mathrm{Sn}}^{116}$, ${\mathrm{Sn}}^{122}$, and ${\mathrm{Sn}}^{124}$ at Isobaric Analog Resonances

Inelastic scattering of protons from targets of ${\mathrm{Sn}}^{116}$, ${\mathrm{Sn}}^{122}$, and ${\mathrm{Sn}}^{124}$ was studied with solid-state detectors at the resonances which are isobaric analog states of the $s_{\frac{1}{2}}$ and $d_{\frac{3}{2}}$ single-quasiparticle states of ${\mathrm{Sn}}^{117}$, ${\mathrm{Sn}}^{123}$, and ${\mathrm{Sn}}^{125}$, respectively. Angular distributions were measured on and off the resonances. Sums of inelastic partial widths $\Sigma {\Gamma }_{p^{\prime }}$ are extracted from the data and compared with theoretical predictions from the shell-model calculations of Baranger, Baranger, and Kuo; the over-all agreement is quite good. In particular, the strong transitions observed to excited states at approximately 2.5-MeV excitation in the target nucleus are predicted by the theory. The transition to the collective $3^{-}$ state does not show resonances.