A fully quantum model describing the angular distribution of the bremsstrahlung photon emission accompanying the alpha-decay of a deformed nucleus is presented for the first time. An analytical dependence of the bremsstrahlung probability on the quadrupole deformation parameter beta(2) of the decaying nucleus has been found. Such a model and the detailed formalism allow us to calculate the stable spectra of the bremsstrahlung emission probability for different values of the angle between the direction of the alpha-particle motion and the symmetry axis of the decaying nucleus. We present the results of this new model by the calculation of the photon emission probability accompanying the alpha-decay of the (226)Ra nucleus which has the nuclear deformation parameter beta(2) = 0.151. The results show by a clear way the role and the influence of the nuclear deformation of the decaying nucleus on the bremsstrahlung photon Spectrum.
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