Effect of inelastic coupling on0+analog transitions

A comparison is made between experimental cross sections for the ($p,n$) reaction to the ground-state analogs of the isotopes ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{98}{}_{}{}^{}\mathrm{Mo}$, ${}_{}{}^{100}{}_{}{}^{}\mathrm{Mo}$, and coupled-channel calculations including coupling to the $2^{+}$ and $3^{-}$ inelastic states and their analogs. When the coupling is included, very good fits are obtained for the ($p,n$) $0^{+}$ analog differential cross section using uniform optical parameters for all three isotopes. Experimentally observed variations of about 50% in $\frac{\sigma }{\mathrm{}(N-Z)\mathrm{}}$, which in distorted-wave Born approximation changes by only 10%, are explained by the coupling. A crude third-order distorted-wave Born approximation model is developed which shows that the three-step amplitudes $0^{+}$ → $2^{+}$ → $2^{+}$ analog → $0^{+}$ analog, $0^{+}$ → $2^{+}$ → $0^{+}$ → $0^{+}$ analog, and $0^{+}$ → $0^{+}$ analog → $2^{+}$ analog → $0^{+}$ analog are all in phase and are destructive to the dominant one-step $0^{+}$ → $0^{+}$ analog amplitude.