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. Program summary Title of program: BIX Catalogue identifier:ADRZ Program summary URL: http://www.cpc.cs.qub.ac.uk/cpc/summaries/ADRZ Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computers: Platform independent Operating systems: Tested on DEC Alpha Unix, Windows NT 4.0 and Windows XP Professional Edition Programming language used: Maple V Release 5.1 and FORTRAN 90 Memory required: 256 MB No. of processors used: 1 No. of bytes in distributed program, including test data, etc.:61754 Distributed format:tar gzip file Keywords: Born approximation, electron-impact ionisation cross-section, Maple, Hartree–Fock 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 on the complexity of the problem: There is no theoretical limit on the quantum state of the target orbital that can be solved with this methodology, 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 (< 1 eV 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 of the program: 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.