Gamow and R-matrix Approach to Proton Emitting Nuclei

Proton emission from deformed nuclei is described within the non-adiabatic weak coupling model which takes into account the coupling to $\gamma$-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 $^{141}$Ho.