Electron-impact ionization of H_2^+ using a time-dependent close-coupling method

The first application of the time-dependent close-coupling method to electron– molecule scattering is used to calculate electron-impact ionization cross sections for H2. The time-dependent Schrödinger equation for the sixdimensional wavefunction is reduced to a set of close-coupled equations on a four-dimensional numerical lattice in (r1, θ1, r2, θ2) centre-of-mass spherical polar coordinates. When the non-perturbative close-coupling results for low lM angular momenta are combined with perturbative distorted-wave results for high lM angular momenta, the resulting ab initio ionization cross sections are found to be in excellent agreement with experimental measurements in the intermediate energy range. Accurate knowledge of the strength of electron-impact ionization processes for molecules and their ions is important in many different areas of physics and chemistry, with a number of applications in laboratory and astrophysical plasma science. In particular, electron ionization of simple molecules containing one or more H atoms is important in understanding edge plasma dynamics in controlled fusion experiments [1]. In the past a number of ab initio theoretical methods have been developed to treat electron-impact excitation of molecules and their ions at low energies [2]. Although semi-empirical methods based on binary encounter theory have been extended from atoms [3] to molecules [4, 5], only a limited number of ab initio theoretical methods have been developed to treat electron-impact ionization of molecules at energies near the peak of their cross sections; the so-called intermediate energy regime. Recently, perturbative distorted-wave methods [6, 7] have been applied to the electron ionization of H2, while a non-perturbative R-matrix with pseudo-states method [8, 9] has been applied to the electron ionization of H2 and H3. In this letter, we present a time-dependent close-coupling method which is used to calculate the electron-impact ionization cross section for H2. The time-dependent Schrödinger equation for the six-dimensional wavefunction of a two-electron molecular system is reduced to a set of close-coupled equations on a four-dimensional numerical lattice in (r1, θ1, r2, θ2) centre-of-mass spherical polar coordinates. In our calculation for H2, we employ the fixednuclei approximation. The molecular time-dependent close-coupling method has previously 0953-4075/05/170285+06$30.00 © 2005 IOP Publishing Ltd Printed in the UK L285 L286 Letter to the Editor been used to calculate the double photoionization cross section for H2 at a fixed internuclear distance [10]. Unless otherwise stated, all quantities are given in atomic units. Due to the reduced symmetry of molecules, the time-dependent wavefunction for a given MS symmetry is expanded in products of rotation functions: