  It has been observed that 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
$^{160,161}$Re 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 2$d_{3/2}$, 3$s_{1/2}$ and 1$h_{11/2}$ states in these nuclei.
