Alignment effects in charge transfer and excitation for H + and He 2 + collisions with H 2 +

The study of ion-atom collisions has a long history for both experimental and theoretical techniques. There has been much less effort for ion-molecule collisions. Computationally, the ion-molecule collisions are much more difficult than ion-atom collisions. This is partly due to the multicenter nature of the problem instead of the two centers for ion-atom collisions. Perhaps more importantly, the cross sections may depend on several other coordinates. Thus, there is a dramatic increase in the number of calculations needed to explore the physically relevant parameters. There is also the possibility that interference due to the extended size of the electron orbitals will cause the results to depend sensitively on the accuracy of the calculation. Finally, molecules have a larger number of low-lying excited states compared to similar atoms which may sensitively affect the outcome of collisions. To see where some of the difficulties lie, we examine what is needed for ions scattering from a diatomic molecule that has no initial angular momentum about the internuclear axis. We simplify the picture further by assuming the ion may be treated as a classical particle traveling in a straight line and the nuclei in the molecule may be treated as fixed in space during the collision. In the comparable case for ionatom collisions, one only needs to calculate the probability for a process as a function of the impact parameter. For the ion-molecule collision, the probability for a process needs to be calculated as a function of the impact parameter in a plane i.e., two dimensions, as a function of the separation of the nuclei, and as a function of the angle between the ion’s velocity and the internuclear axis. Thus, we have gone from one parameter to four; assuming we need 5–10 examples of each parameter for an adequate exploration of ion-molecule collision we find there are approximately 100–1000 times more trajectories that are needed for ion-molecule calculations than for a comparable ion-atom calculation. The simplest ion-molecule system is when there is only one electron present. References 1,2 studied the collision of He 2+ with the D 2 + molecular ion. Reference 1 measured the total charge transfer cross section and compared the results to calculations using a model for the electronic orbital for the molecule. The model used a linear combination of atomic orbitals and the transition amplitudes are approximated as a linear superposition of the amplitudes for each atomic orbital 3. The calculated and measured total charge transfer cross sections were in good agreement. Reference 2 measured the dependence of the total charge transfer cross section on the angle between the velocity of the atomic ion and the internuclear axis and compared the measurement to the results of a model calculation again based on Ref. 3. Although the agreement was not as good, the general trends were the same: the cross section is much larger for perpendicular geometry than when the velocity is parallel to the internuclear axis. At velocity 0.4 a.u., the measurement gives a cross section 3–4 times larger at 90° than at 0° while the calculation gives a factor of 7–8. At velocity 0.5 a.u., the measurement gives a cross section 3–6 times larger at 90° compared to 1.5–2 for the calculation. Reference 4 presents calculations for total charge transfer for this system using both classical methods and a 2+1 -center close-coupling approximation. The total charge transfer cross section was 20–30 % lower than the previous measurement and calculation. In this paper, we present the results of calculations for charge transfer from the H 2 + molecular ion to He 2+ ions and to H + ions. Because the protons of the molecular ion are fixed during the collision, our results apply equally well to D2 + . The focus of this paper is the dependence of the cross section on the angle between the ion’s velocity vector and the internuclear axis and the dependence on the internuclear separation. Our method of calculation consists of direct numerical solution of Schrodinger’s equation on a grid of points; grid methods can be thought of as a basis set method with the number of basis functions equal to the number of grid points 10 7 in our case but with a momentum cutoff roughly equal to the inverse of the separation of grid points.