Role of dynamical particle-vibration coupling in reconciliation of the d_3/2 puzzle for spherical proton emitters

It has been observed that the decay rate for proton emission from d_3/2 single particle state is systematically quenched compared with the prediction of a one-dimensional potential model although the same model successfully accounts for measured decay rates from s_1/2 and h_11/2 states. We reconcile this discrepancy by solving coupled-channels equations, taking into account couplings between the proton motion and vibrational excitations of a daughter nucleus. We apply the formalism to proton emitting nuclei ^160,161Re to show that there is a certain range of parameter set of the excitation energy and the dynamical deformation parameter for the quadrupole phonon excitation which reproduces simultaneously the experimental decay rates from the 2d_3/2, 3s _1/2, and 1 h _11/2 states in these nuclei.