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Description of the Average Approximation
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The Average Approximation (AA) is a method of calculating cross sections
for excitation or ionization of atomic ions, described in the reference
J.M. Peek and J.B. Mann, Phys. Rev. A, Vol. 16, page 2315 (1977).
Peek and Mann developed a computer code to carry out the AA calculations
for the Coulomb case.
Recently Peek has extended the calculations to the DWA
case. During a visit to the Atomic and Molecular Data Unit he
brought a version of that computer code and installed it at the
Unit.
The current version of the AA is operational for electron impact excitation
only. There are plans to extend it to ionization cross sections and to
allow the impact particle to be either an electron or proton.
The AA code uses target state wave functions from the Hartree-Fock
atomic structure code of R.D. Cowan (Theory of Atomic Structure and
Spectra, R.D. Cowan, University of California Press, Berkeley California).
The atomic structure code can be downloaded from Los Alamos
National Laboratory
Group T-4 web page.
The link to the codes can be found under the heading "T-4 Computer Codes
and Data" with the topic "Cowan Atomic Structure Codes". In the current
application, the rcn.f code is used to generate the radial wave functions
for the requested configurations.
The current AA code operates in configuration average mode only,
although it is possible
that in the future angular coupling will be incorporated so that
transitions for fine structure levels could be calculated and target
state mixing could also be incorporated.
For high impact electron energies, the
cross sections fail to converge unless a large number of partial waves
are included. To obtain closure with a small number of partial waves,
we have added the plane wave Born (PWB) calculation. The method used
is to calculate the total PWB from the generalized oscillator strength
and to also calculate the PWB in the partial wave expansion. This
allows a calculation of the portion of the PWB total that comes from
the high partial waves. Since at high energy the DWA approaches the
PWB, and especially so at large partial waves, this quantity is added to
the DWA to arrive at an estimate of the total DWA. This addition
is performed only for energies above three times the excitation energy.
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