Gamow and R -matrix approach to proton emitting nuclei

Proton emission from deformed nuclei is described within the nonadiabatic weak coupling model which takes into account the coupling to $\ensuremath{\gamma}$ vibrations around the axially symmetric shape. The coupled equations are derived within the Gamow state formalism. A new method, based on the combination of the $R$-matrix theory and the oscillator expansion technique, is introduced that allows for a substantial increase of the number of coupled channels. As an example, we study the deformed proton emitter $^{141}\mathrm{Ho}$.