Regularization of the Coulomb scattering problem

Abstract

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.

Parametric x-ray radiation along the velocity of relativistic electron in a Bragg scattering geometry

“…From the second equation of the system (3) follows an expression relating the diffracted and incident fields in a crystal 2 ( , ) ( )cr ( )cr…”

“…The theory of parametric X-ray radiation (PXR) of a relativistic particle in a crystal predicts radiation not only in the Bragg scattering direction but also along the velocity of a radiating particle (FPXR) [1][2][3]. Due to extensive experimental attempts made to study FPXR [4][5][6], a theoretical description of its mechanism appears to be urgent.…”

Diffracted transition radiation of a relativistic electron in a three-layer structure

“…It should be noted that compact X-ray sources being developed on the basis o f transition radiation from relativistic electrons in amorphous media [2,3], parametric X-ray radiation emitted by relativistic elec trons in crystals [4,5], as well as radiation emitted upon channeling of electrons in crystals [6], were con sidered most suitable for applications [7]. However, calculations and experimental data revealed that all these sources are not very effective because o f the low intensities o f the beams of emitted X-ray photons even for strong electron currents.…”

Coherent X-ray radiation from a relativistic electron in a combined medium

“…When a charged particle crosses the sur face o f a crystal plate, the transition radiation arising at the boundary is diffracted by a system o f parallel atomic planes in the crystal to produce diffracted tran sition radiation (DTR) [10][11][12][13] whose photons move in the Bragg scattering direction in a narrow spectral range. When a fast charged particle crosses a single crystal, its Coulomb field is scattered by a system of parallel atomic planes in the crystal to generate para metric X-ray radiation (PXR) [14][15][16] whose photons together with the DTR photons move in the Bragg scattering direction. At present, there are two approaches to describe the PXR process: kinematic [17,18] and dynamic [15,16,19].…”

“…When a fast charged particle crosses a single crystal, its Coulomb field is scattered by a system of parallel atomic planes in the crystal to generate para metric X-ray radiation (PXR) [14][15][16] whose photons together with the DTR photons move in the Bragg scattering direction. At present, there are two approaches to describe the PXR process: kinematic [17,18] and dynamic [15,16,19]. It should be noted that the diffracted transition radiation by itself is a dynamic effect, namely the dynamic diffraction effect.…”