Born total ionisation cross sections: An algebraic computing program using Maple Original Research Article

The software described in this paper uses the Maple algebraic computing environment to calculate an analytic form for the matrix element of the plane-wave Born approximation of the electron-impact ionisation of an atomic orbital, with arbitrary orbital and angular momentum quantum numbers. The atomic orbitals are approximated by Hartree–Fock Slater functions, and the ejected electron is modelled by a hydrogenic Coulomb wave, made orthogonal to all occupied orbitals of the target atom. Clenshaw–Curtis integration techniques are then used to calculate the total ionisation cross-section. For improved performance, the numerical integrations are performed using FORTRAN by automatically converting the analytic matrix element for each orbital into a FORTRAN subroutine. The results compare favourably with experimental data for a wide range of elements, including the transition metals, with excellent convergence at high energies.