Shaulskyi K. Quantum relativistic methods of description of nuclear processes in compact stars

The dissertation is devoted to the development of theoretical models for studying various nuclear processes: pycnonuclear reactions (fusion reactions of atomic nuclei at low temperatures) in the crystalline lattices of compact stars; bremsstrahlung accompanying proton-deuteron scattering reactions and nucleon scattering on atomic nuclei in the environments of compact stars. To investigate pycnonuclear reactions, a model based on the method of multiple internal reflections was developed, which was applied to nuclei in the crystalline lattices of white dwarfs and neutron stars. Based on this model, the rates of pycnonuclear reactions were calculated, which turned out to be approximately 1.893 times smaller compared to previously calculated rates based on quasіclassical methods. This difference can be explained by the fact that the method of multiple internal reflections has no application limitations, unlike the WKB-approximation. Using the developed model, the probabilities of compound nucleus formation, which is an intermediate stage before the complete fusion of two nuclei, were calculated. The calculations showed that the probability of this process is much higher than the direct fusion, which was previously studied using the Zel'dovich method (based on zero-point energy). In the study of the proton-deuteron scattering process, models based on the cluster approach were developed. Analyzing the bremsstrahlung in laboratories provides an opportunity to refine the deuteron model based on the obtained experimental data. The bremsstrahlung spectra calculated using the developed model describe the available experimental data well, which were obtained by scattering a deuteron beam on a proton target at an energy of 145 MeV. At these energies, the influence of the model parameters on the calculated spectra is minimal. According to the calculations, at scattering beam energies up to 1.5 GeV, the influence of the parameters on the cross-sections becomes more significant. In the study of the properties of atomic nuclei in the dense environment of compact stars, a microscopic model of the nucleus was constructed based on the model of deformed oscillator shells. The model was improved for application in compact stars using the polytropic equation of state for stellar matter. The calculations using the model showed that lighter atomic nuclei can exist in neutron stars at greater depths than heavier ones (the binding energy of the nucleus becomes positive). The bremsstrahlung spectra from proton and neutron scattering on atomic nuclei in the environment of compact stars were calculated. There is a significant effect on the calculated spectra in the environment of neutron stars.