Accurate eigenvalues and eigenfunctions of a two-level system interacting with a one-mode quantum field are calculated numerically. A special iteration procedure based on the operator method permits one to consider the solution within a wide range of the Hamiltonian parameters and to find the uniformly approximating analytical formula for the eigenvalues. Characteristic features of the model are considered, such as the level intersections, the population of the field states and the chaotization in the system through the doubling of the frequencies.

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A new mechanism of the instability of an electron (positron) beam under conditions of the parametric X-rays is discovered. Equations, which define the amplitude increment of the instability and the starting current, are obtained. It is shown that a considerable part of the particle energy transforms into coherent X-ray energy due to this parametric instability.

Resume. 2014 Dans cet article on présente les calculs numériques de la distribution spectrale et angulaire des rayons X paramétriques pour différents cristaux. On analyse leurs variations en fonction de l'énergie des particules. Abstract 2014 The numerical calculation of the parametric X-ray spectral and angular distributions for different crystals is performed. Their dependence on the particle energy is discussed.

To cite this version:V.G. Baryshevsky, I.D. Feranchuk. Parametric X-rays from ultrarelativistic electrons in a crystal : theory and possibilities of practical utilization. Journal de Physique, 1983, 44 (8) Abstract. 2014 The detailed theory of parametric X-rays from charged particles in a crystal is considered. It is shown that this radiation is due to the diffraction of the particle's electromagnetic field. Some features of the parametric X-rays allow us to separate this radiation from other radiation types. Methods of the experimental investigation and uses of parametric X-rays are discussed.J. Physique 44 (1983)

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Exact solutions of the Schrödinger equation for the Coulomb potential are used in the scope of both stationary and time-dependent scattering theories in order to find the parameters which define regularization of the Rutherford cross-section when the scattering angle tends to zero but the distance r from the center remains fixed. Angular distribution of the particles scattered in the Coulomb field is investigated on the rather large but finite distance r from the center. It is shown that the standard asymptotic representation of the wave functions is not available in the case when small scattering angles are considered. Unitary property of the scattering matrix is analyzed and the "optical" theorem for this case is discussed. The total and transport cross-sections for scattering of the particle by the Coulomb center proved to be finite values and are calculated in the analytical form. It is shown that the considered effects can be essential for the observed characteristics of the transport processes in semiconductors which are defined by the electron and hole scattering in the fields of the charged impurity centers.

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