The role of the potential saddle in He2+ + H impact ionization

We compute the full three-dimensional momentum space distribution of ejected electrons resulting from alpha particle impact ionization of hydrogen. At low impact velocities the transverse momentum distributions are shown to exhibit strong oscillations with energy. For the longitudinal component, the momentum distribution peaks near the target at high energies, shifts towards the projectile centre at intermediate energies and then back towards the target at low energies. The shift of the longitudinal momentum distribution towards the target at low energies gives the experimental signature of the importance of potential saddle for impact ionization at low energies. The saddle point mechanism (Winter and Lin 1984, Sidky et al 2000) for single ionization by ion impact has attracted much attention because of its potential to give a universal explanation for electron ejection in low energy ion–atom collisions. Briefly, the idea states that the active electron in an ion–atom collision can find itself balanced on the internuclear potential saddle during the collision. As the nuclei recede from each other the electron will remain at that point since the Coulomb forces from both nuclei balance at the saddle point, and the electron will be promoted up to the continuum as the saddle is pushed upward. Not only is this a simple explanation of an otherwise complicated three-body break-up process, but this mechanism can also explain single ionization of multi-electron atoms since the saddle point is far from the influence of any structure in either target or projectile ionic core. Moreover, this mechanism was thought to provide a unique signature in the distribution of ejected electrons; namely, the ejected electrons should move with the saddle velocity in the lab frame of reference. On the face of it the saddle point mechanism for ion impact ionization seems to be a well-defined, easily verifiable concept. But after its introduction in the early 80s, this mechanism has been the centre of much controversy (Stohlterfoht et al 1997). Theoretically, it is clear that the saddle point promotion must occur, but the disagreement in the literature has centred on what range of impact velocities the saddle point mechanism 3 To whom correspondence should be addressed. 0953-4075/01/060163+10$30.00 © 2001 IOP Publishing Ltd Printed in the UK L163 L164 Letter to the Editor is important. More critically, is it possible to make a semi-quantitative estimation for its importance? Olson and co-workers have been promoting the idea that the saddle point mechanism is most important for intermediate energy ion–atom collisions, where the total ionization cross section is the largest (Olson 1983, 1986, Olson et al 1987). Their identification of saddle point electrons was based on examining the longitudinal momentum distribution from classical calculations. They found that the distribution peaked at v/2, half the projectile velocity, coinciding with the potential saddle point velocity. It is not clear, however, that a v/2 peak uniquely identifies the saddle point mechanism, since the centre of charge and the saddle point coincide for singly charged ions impacting on neutral targets. Indeed, Sidky et al (2000) showed, using a combined quantum and classical analysis, that the saddle point mechanism is a low energy phenomenon and that the v/2 peak does not necessarily indicate that saddle point ionization is significant. This conclusion leads to the question of what happens in a system of asymmetric collisions such as α-particles impacting on a hydrogen atom, where the saddle point and centre of charge do not coincide. Earlier classical work by Illescas et al (1998) explored the asymmetric α–H collision system. They concluded that the saddle point mechanism is important only at low impact energies. In this letter we explore theα–H system with both the quantum two-centre momentum space discretization (TCMSD) and classical trajectory Monte Carlo (CTMC) method, and we show quantitatively what the role of the saddle point mechanism is for ionization. Furthermore, we examine the longitudinal distribution and show that for this asymmetric system a shift, at low impact velocity, of the electron’s longitudinal momentum distribution towards the saddle velocity does indicate saddle point ionization. Another motivation for exploring ionization in α–H collisions stems from recent experimental results by cold target recoil ion momentum spectroscopy (Dörner et al 1996, Abdallah et al 1998a, b, 2000). Such experiments have measured the ejected electron momentum distribution (EEMD) for many ion–atom collision systems. An interesting feature that appears to be common to many ion–atom collision systems is the ‘ubiquity of π structure’ in the continuum (Abdallah et al 1998a). The asymmetry or symmetry of the transverse momentum distribution, however, varies greatly from system to system. For example, the transverse momentum distributions turned out to have strong energy dependence for some systems, e.g. p + He collisions, and little energy dependence for other systems, such as He+ on He. In this letter we explore ionization for an asymmetric, one-electron system, namely alpha particles on hydrogen. After a brief review of the TCMSD theory we will begin this letter by examining the EEMDs for α on H collisions and their energy dependence. We then outline the role of the saddle point mechanism for the α on H system, and finally derive a general scaling law for the range of saddle point ionization for arbitrary ion–atom collision systems. Our study of the He2+ + H system focuses primarily on impact velocity dependence of the transverse and longitudinal momentum distributions of the ejected electrons, and the dynamics of the ejected electron cloud are studied both quantum mechanically and classically. We select an impact parameter of two atomic units, since it is near the maximum of ionization probability and a previous CTMC study, with which we compare, concentrated on the impact parameter b = 2 au (Illescas et al 1998). In the TCMSD theory, the electron wavefunction in the ion–atom collision is represented by a two-centre expansion in momentum space: