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Manuscript Title: Born total ionisation cross sections: an algebraic computing program using Maple.
Authors: P.L. Bartlett, A.T. Stelbovics
Program title: BIX
Catalogue identifier: ADRZ_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 154(2003)159
Programming language: Maple V Release 5.1, Fortran.
Computer: DEC Alpha.
Operating system: Unix, Windows NT 4.0/XP Professional Ed.
RAM: 256M words
Keywords: Born approximation, Electron-impact ionisation cross-section, Maple, Hartree-Fock, Atomic physics, Scattering.
Classification: 2.4.

Nature of problem:
Calculates the total electron impact ionisation cross-section for neutral and ionised atomic species using the first-Born approximation. The scattered electron is modelled by a plane wave, and the ejected electron is modelled by a hydrogenic Coulomb wave, which is made orthogonal to all occupied atomic orbitals, and the atomic orbitals are approximated by Hartree-Fock Slater functions.

Solution method:
An analytic form of the matrix element is evaluated using the Maple algebraic computing software. The total ionisation cross-section is then calculated using a three-dimensional Clenshaw-Curtis numerical integration algorithm.

There is no theoretical limit on the quantum state of the target orbital that can be solved with this methodolgy, subject to the availability of Hartree-Fock coefficients. However, computing resource limitations will place a practical limit to, approximately, n<=7 and l<=4. The precision of results close to the ionisation threshold of larger atoms (<1eV for Z>48) is limited to ~5%.

Unusual features:
To reduce calculation time, FORTRAN source code is generated and compiled automatically by the Maple procedures, based upon the analytic form of the matrix element. Numerical evaluation is then passed to the FORTRAN executable and the results are retrieved automatically.

Running time:
5 to 40 minutes for initial calculation for an atomic orbital, then 5 to 300 seconds for subsequent energies of the same orbital.