Born total ionisation cross sections: an algebraic computing program using Maple. P.L. Bartlett, A.T. Stelbovics.

PROGRAM SUMMARY
Title of program: BIX
Catalogue identifier: ADRZ
Ref. in CPC: 154(2003)159
Distribution format: tar gzip file
Operating system: Unix, Windows NT 4.0 and XP Professional Ed
High speed store required: 256MK words
Number of lines in distributed program, including test data, etc: 2824
Keywords: Born approximation, Electron-impact ionisation cross-section, Maple, Hartree-Fock, Atomic physics, Scattering.
Programming language used: Maple V Release 5.1, Fortran
Computer: DEC Alpha .

Nature of physical 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.

Method of solution:
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.

Restrictions:
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%.

Typical 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.

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.