2 research outputs found
Regularization of the Coulomb scattering problem
Exact solutions of the Schr\"odinger 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.Comment: 20 pages, 6 figure