Convergence of the two-centre atomic orbital (TCAO) close-coupling method in ion - atom collisions is carefully examined within the semiclassical impact parameter approximation. Calculations were carried out for protons colliding with H(1s) in the impact energy range 15 - 1000 keV. It is shown that the spurious oscillatory structures in previous large scale TCAO close-coupling calculations are due to the simultaneous use of the short-ranged pseudo-continuum states on both collision centres. By including a large number of pseudo-continuum states only at one centre in the TCAO expansion, we demonstrate that the resulting cross sections for excitation, capture and ionization for p + H(1s) collisions vary smoothly with collision energy and are in better agreement with the experimental data.

Convergence of the two-centre atomic orbital (TCAO) close-coupling calculations for the excitation and ionization of atomic hydrogen by keV proton impact is carefully examined using various large basis sets on each centre. It is shown that reliable cross sections for the weak channels can only be obtained with a large number of basis states on the target and a limited number of bound states on the projectile. Cross sections for excitation to , , and states and for ionization are presented and compared to available experimental data and to other theoretical calculations.

Our recently developed two-centre atomic orbital (TCAO) close-coupling method is applied to He 2+-H(1s) collisions in the impact energy range from 20-400 keV amu −1. Convergent cross sections are obtained for this system by using a large number of bound and pseudostate basis functions on the target and a limited number of bound states on the projectile. Cross sections for electron transfer to 1s, 2 , 3 , 4 and 5 , for excitation to 2 , 3 , 4 and 5 and for ionization are presented and compared with available experimental data and other theoretical calculations. The accuracy of the previous TCAO close-coupling calculations is challenged and the reliability of some experimental data for this system is questioned.

We have performed a close-coupling calculation for the He++H collision in the energy range 2.5-25 keV amu-1 using the two-centre atomic orbital expansion method. The collision system was approximated in a one-electron model with proper accounting for the Pauli exclusion principle. From the calculated excitation cross sections, cross sections for Lyman-alpha and Balmer-alpha emission were determined and compared with available measurements. Detailed comparison is also made with the most recent theoretical results reported by Ermolaev et al. (1994). The overall better agreement between our calculation and the measurement is observed. On the other hand, the calculated total electron capture cross sections, which are much larger than the excitation cross sections, agree well with the results of Ermolaev et al., but differ from the measured values reported in Olson et al. (1977) by 30-50%. We suspect the reliability of the latter experimental results.

Multi-centre molecular integrals over spherical Gaussian-type orbitals modified with plane-wave phase factors, which arise in the close-coupling treatment of ion-atom collisions as well as in some molecular structure calculations, are evaluated analytically in closed form by means of the Fourier transform and the addition theorem of harmonic polynomials. The resulting integral formulae for spherical Gaussian orbitals, consisting of vector-coupling coefficients and well known functions, are more compact than those for their counterparts, Cartesian Gaussian orbitals. Practical techniques are suggested for the efficient implementation of the present formulae.