Angular analysis of bremsstrahlung in alpha decay

A quantum mechanical approach to calculation of bremsstrahlung spectra in $\alpha$-decay of heavy nuclei with taking into account an angle between directions of $\alpha$-particle propagation and photon emission is presented. The spectrum dependence on the angle is obtained in the explicit analytical form. Probability, intensity and energy of the bremsstrahlung during tunneling of the $\alpha$-particle through a barrier for the needed angle are determined. An acceleration of the $\alpha$-particle during its propagation above the barrier and its tunneling under the barrier with taking into account the bremsstrahlung is found.