Omelchenko V. D. Coherent and incoherent effects in the scattering of highenergy particles in thin targets. – Qualifying scientific paper, manuscript copyright.
Thesis for the scientific degree of Doctor of Philosophy: specialty 104 – «Physics and Astronomy». – Akhiezer Institute for Theoretical Physics, National Scientific Center «Kharkiv Institute of Physics and Technology» NAS of Ukraine, Kharkiv, 2024.
The thesis is devoted to the analytical description of the scattering process of relativistic charged particles on stationary and moving targets in the Born and eikonal approximations of quantum electrodynamics, obtaining the corresponding differential scattering cross-sections and investigating coherent and incoherent effects in scattering.
Section 1 is devoted to the literature review on the thesis topic. Based on the researched sources, the thesis tasks were formulated.
In Section 2, the differential cross-sections of relativistic charged particles scattering on different configurations of atoms in the target are obtained in the first Born approximation based on consideration of the Laue-Bragg interference factor.
The split of the obtained differential scattering cross-sections into coherent and incoherent scattering cross-sections is demonstrated. The limit transition from the differential scattering cross-section on a set of ordered parallel atomic strings to the scattering cross-section on a set of parallel crystal atomic planes in the model of uniform distribution of atoms in each plane is shown.
In Section 3, in the eikonal approximation, the differential cross section of relativistic charged particles scattering on the atomic plane in the model of the uniform distribution of atoms is obtained. In the eikonal approximation in this thesis, corrections proportional to negative powers of the momentum are not taken into account. It is shown that the expression for the differential cross-section in the eikonal approximation turns into the corresponding expression in the Born approximation in the limiting case of a sufficiently thin target. Calculations of the differential crosssection in the eikonal approximation were carried out, including with the help of the stationary phase method and the Laplace method.
In Section 4, in the eikonal approximation, the process of rainbow scattering of relativistic charged particles on the atomic plane in the model of uniform distribution of atoms is investigated. The differential scattering cross-section, in this case, was also calculated when the transferred momentum is far from the rainbow point, taking into account the interference of the scattering amplitudes, which correspond to the single-valued branches of the dependence of the impact parameter on the transferred momentum. Approximate and numerical methods were used to obtain the expression for the scattering cross-section.
Section 5 is devoted to obtaining the wave function in the eikonal approximation for the scattering of an ultrarelativistic particle in the time-dependent four-potential of a beam of ultrarelativistic charged particles. The first correction to the phase of the wave function in the eikonal approximation, the differential crosssection of the scattering of ultrarelativistic particles by a beam of ultrarelativistic particles in the eikonal approximation in this case were obtained. Also fulfillment of the energy conservation law was checked for this case. The case of a flat beam is considered. In this paper, a flat beam is a beam that, in the plane transverse to the movement direction, has a Gaussian distribution of particles along one of the axes and a zero thickness along the other axis. The phase of the wave function for a particle scattered at the flat target beam is obtained. Using numerical methods and the stationary phase method, the differential cross-sections of the scattering of ultrarelativistic charged particles on a flat beam of ultrarelativistic particles for various numbers of particles in the beam were obtained.
The practical use of the results of this thesis involves the application of these theoretical results for describing the scattering process, which is a component of modern experiments at existing and future accelerators of elementary particles, such as SuperKEKB (Japan), the Large Hadron Collider (CERN), ILC, FCC, and others.
The analysis of the rainbow scattering cross-sections can help to investigate the form of the interatomic potential of targets. The expressions for the differential scattering cross-sections obtained in this work can be used both for designing experiments for the study of quantum phenomena in the scattering of relativistic charged particles on oriented crystals and for a theoretical description of the radiation process, which is determined by the characteristics of scattering.
