Multipolar model of bremsstrahlung accompanying proton-decay of nuclei

Emission of bremsstrahlung photons accompanying proton decay of nuclei is studied. The new improved multipolar model describing such a process is presented. The angular formalism of calculations of the matrix elements is stated in details. The bremsstrahlung probabilities for the $^{157}{\rm Ta}$, $^{161}{\rm Re}$, $^{167}{\rm Ir}$ and $^{185}{\rm Bi}$ nuclei decaying from the $2s_{1/2}$ state, the $^{109}_{53}{\rm I}_{56}$ and $^{112}_{55}{\rm Cs}_{57}$ nuclei decaying from the $1d_{5/2}$ state, the $^{146}_{69}{\rm Tm}_{77}$ and $^{151}_{71}{\rm Lu}_{80}$ nuclei decaying from the $0h_{11/2}$ state are predicted. Such spectra have orders of values similar to the experimental data for the bremsstrahlung photons emitted during the $\alpha$-decay. This indicates on real possibility to study bremsstrahlung photons during proton decay experimentally and perform further measurements.