Description of the Average Approximation

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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