Regularization of the Coulomb scattering problem

Journal Article · Mon Nov 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.052701· OSTI ID:20646215

Baryshevskii, V G; Feranchuk, I D; Kats, P B ^[1]

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1. Byelorussian State University, 4, F. Skariny Av., 220050, Minsk (Belarus)

The exact solution of the Schroedinger equation for the Coulomb potential is used within the scope of both stationary and time-dependent scattering theories in order to find the parameters which determine the regularization of the Rutherford cross section when the scattering angle tends to zero but the distance r from the center remains finite. The angular distribution of the particles scattered in the Coulomb field is studied on rather a large but finite distance r from the center. It is shown that the standard asymptotic representation of the wave functions is inapplicable in the case when small scattering angles are considered. The 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 the particle by the Coulomb center proved to be finite values and are calculated in the analytical form. It is shown that the effects under consideration can be important for the observed characteristics of the transport processes in semiconductors which are determined by the electron and hole scattering by the field of charged impurity centers.

• OSTI ID: 20646215
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR DISTRIBUTION
COULOMB FIELD
COULOMB SCATTERING
CROSS SECTIONS
DISTANCE
ELECTRON MOBILITY
ELECTRONS
EXACT SOLUTIONS
HOLE MOBILITY
HOLES
OPTICAL THEOREM
POTENTIAL ENERGY
RENORMALIZATION
S MATRIX
SCHROEDINGER EQUATION
SEMICONDUCTOR MATERIALS
TIME DEPENDENCE
WAVE FUNCTIONS