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In the Elwert-Haug formulation, the interaction of the scattering
electron with the static Coulomb field of the nucleus is included in
the unperturbed Hamiltonian. However the exact wave functions in the
Coulomb field are replaced by the approximate wavefunctions of
Sommerfeld and Maue [9]. Bethe and Maximon
[10] showed that these wavefunctions correctly represent
all partial waves with
in the exact (Darwin)
solution. Using the Sommerfeld-Maue wavefunctions and making some
further approximation, Elwert and Haug obtained an analytic but rather
complicated expression for the triply differential cross section,
involving hypergeometric functions, as a function of Z, the momentum
vectors and energies. (In a recent paper [11] Haug
has also derived an expression for the polarization correlation
*C*_{200}). We have found it more convenient in our calculations of
the predictions of this theory to work from Elwert and Haug's results
for the *matrix element*, computing the hypergeometric functions
numerically. The Elwert-Haug result is expected to be valid in the
point Coulomb potential for
at all energies, or for
all
at small scattering angles and sufficiently high
incident and outgoing electron energy ,
and in suitable
intermediate situations. In the case of the neutral atom, screening
by the bound electrons is treated by taking the product of the form
factor *F*(*q*), calculated as above, with the Elwert-Haug result for
the matrix element, thus making an additional approximation reducing
the region of validity.

** Next:** 2.3 The exact partial
** Up:** 2. Discussion of theories
** Previous:** 2.1 Bethe-Heitler approximation
*Eoin Carney*

*1999-06-14*