We investigate emission of bremsstrahlung photons during scattering of $alpha$-particles off nuclei. For that, we construct bremsstrahlung model for $alpha$-nucleus scattering, where a new formalism for coherent and incoherent bremsstrahlung emissions in elastic scattering and mechanisms in inelastic scattering is added. Basing of this approach, we analyze experimental bremsstrahlung cross-sections in the scattering of $alpha$-particles off the isotope[59]{Co}, isotope[116]{Sn}, isotope[rm nat]{Ag} and isotope[197]{Au} nuclei at 50 MeV of $alpha$-particles beam measured at the Variable Energy Cyclotron Centre, Calcutta. We observe oscillations in the calculated spectra for elastic scattering for each nucleus. But, for isotope[59]{Co}, isotope[116]{Sn} and isotope[rm nat]{Ag} we obtain good agreement between calculated coherent spectrum with incoherent contribution for elastic scattering with experimental data in the full photon energy region. For heavy nucleus isotope[197]{Au} we find that (1) Oscillating behavior of the calculated spectrum of coherent emission in elastic scattering is in disagreement with experimental data, (2) Inclusion of incoherent emission improves description of the data, but summarized spectrum is in satisfactory agreement with the experimental data. To understand unknown modification of wave function for scattering, we add new mechanisms of inelastic scattering to calculations and extract information about unknown new amplitude of such mechanisms from experimental data analysis. This amplitude has maxima at some energies, that characterizes existence of states of the most compact structures (clusters) in nucleus-target. We explain origin of oscillations in the bremsstrahlung spectra for elastic scattering (at first time). New information about coherent and incoherent contributions is extracted for studied reactions.
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