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2. Discussion of theories
All of the theories discussed here are theories of bremsstrahlung
accompanying electron scattering from a static central potential.
That is, they are all theories within the independent particle
approximation (IPA). We will be comparing ``exact'' predictions of
such a theory (in a partial wave and multipole decomposition
numerically summed to convergence) with simpler approximations to such
a theory. We will identify circumstances in which the more exact
treatment matters. In this work we will only consider scattering from
neutral atoms (although each of the theories may also be applied to
ionic species). Within the IPA, except for the screening of the
nuclear charge, effects of the bound atomic electrons are ignored.
The potentials used here are the relativistic self-consistent field
(Dirac-Slater) potentials discussed by Liberman
[5], but without a Latter tail [6].
We utilize a coordinate system in which the photon momentum defines the z axis, and the x-z plane contains the initial
electron momentum
and .
For convenience we define
as the angle between
and the initial electron
momentum ,
as the angle between
and the
final electron momentum ,
and
as the angle between
the plane containing
and
and the plane containing
and .
This coordinate system is shown in Figure
6.1. We define the energies of the initial and
final electron and the photon as E1,E2 and k, respectively. We
also define the momentum transfered to the nucleus
.
The quantity of interest in our discussion is
the triply differential cross section
for radiation in
scattering of an unpolarized electron from a neutral atom of atomic
number Z, where the polarization properties of the radiated photon
and scattering electron are not observed. Here ()
is the finite solid angle subtended by the photon
momentum (outgoing electron momentum). (Some discussion of the
polarization correlations associated with the triply differential
cross section was given in [4].)
Next: 2.1 Bethe-Heitler approximation
Up: Comparison of relativistic partial
Previous: 1. Introduction
Eoin Carney
1999-06-14