  In this paper the improved multipolar model of bremsstrahlung accompanied the
$\alpha$-decay is presented. The angular formalism of calculations of the
matrix elements, being enough complicated component of the model, is stated in
details. A new definition of the angular (differential) probability of the
photon emission in the $\alpha$-decay is proposed where direction of motion of
the $\alpha$-particle outside (with its tunneling inside barrier) is defined on
the basis of angular distribution of its spacial wave function. In such
approach, the model gives values of the angular probability of the photons
emission in absolute scale, without its normalization on experimental data.
Effectiveness of the proposed definition and accuracy of the spectra
calculations of the bremsstrahlung spectra are analyzed in their comparison
with experimental data for the $^{210}{\rm Po}$, $^{214}{\rm Po}$, $^{226}{\rm
Ra}$ and $^{244}{\rm Cm}$ nuclei, and for some other nuclei predictions are
performed (in absolute scale). With a purpose to find characteristics taking
influence on the bremsstrahlung probability strongly, a dependence of the
bremsstrahlung probability on effective charge of the decaying system is
analyzed. As a natural result, as supposed type of decaying system the emission
of proton from nucleus is studied, for which the effective charge is
essentially larger in a comparison with $\alpha$-decay. For some proton
emitters estimations of the bremsstrahlung probability are obtained (at first
time, in fully quantum approach). Also the bremsstrahlung in fission of the
$^{252}{\rm Cf}$ nucleus is analyzed.
