Phase relation for a common doorway state inV47

The ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$($p$,$p^{\prime }\gamma$),${}_{}{}^{46}{}_{}{}^{}\mathrm{Ti}$ reaction has been studied from $E_p=2.25\mathrm{} \mathrm{to} 3.10$ MeV with an overall energy resolution of about 350 eV. The magnitudes and relative signs of inelastic decay amplitudes were determined for the fine-structure resonances of a $\frac{3}{2^{-}}$ analog state in ${}_{}{}^{47}{}_{}{}^{}\mathrm{V}$. The relative sign of the decay amplitudes is constant for the fine-structure states, in agreement with both the theoretical prediction and the one previous measurement.