Electron-impact double ionization of H−

Electron-impact double ionization cross sections for H− are calculated using a non-perturbative time-dependent close-coupling theory. The total wavefunction for the three-electron system is represented by a coupled channels expansion involving simple products of three-dimensional radial lattices and six-dimensional coupled spherical harmonics. Following time evolution of the total wavefunction according to the Schrödinger equation, collision probabilities are found by projection of the total wavefunction onto fully antisymmetric products of spatial and spin functions representing three outgoing Coulomb waves. The completely ab initio double ionization cross section results for H− are found to be more than a factor of 5 below the experimental measurements of Peart et al (1971 J. Phys. B: At. Mol. Phys. 4 88) and in excellent agreement with the experimental measurements of Yu et al (1992 J. Phys. B: At. Mol. Opt. Phys. 25 4593). In the last couple of years, a time-dependent close-coupling method has been developed to treat three continuum electrons moving in the field of a charged core, that is Coulomb fourbody breakup. This non-perturbative method has produced ab initio cross sections for the triple photoionization of Li [1] that are in excellent agreement with synchrotron light source experiments [2] and for the electron-impact double ionization of He [3] that are in excellent agreement with crossed-beams experiments [4]. The time-dependent close-coupling method has also been used to predict double photoionization with excitation and triple photoionization cross sections for Li and Be [5], as well as to investigate the double autoionization of triply excited hollow atom states of Li [6]. In this letter, we apply the time-dependent close-coupling method developed for Coulomb four-body breakup to the electron-impact double ionization of H− in an attempt to resolve a long-standing disagreement between experimental measurements. The early crossed-beams experimental measurements of Peart et al [7] for the double ionization cross section of H− peaked at 50 Mb (1.0 Mb = 1.0 × 10−18 cm2) around 50 eV incident electron energy. Subsequent perturbative Born calculations [8] found a peak cross section of about 35 Mb. Two 0953-4075/06/060127+05$30.00 © 2006 IOP Publishing Ltd Printed in the UK L127 L128 Letter to the Editor decades later the crossed-beams experimental measurements of Yu et al [9] for the double ionization of H− found a peak cross section of about 10 Mb. More recent perturbative Born calculations [10] report peak cross sections substantially below the Yu et al [9] experimental measurements. Depending on the description of the final state, the recent Born results vary from 0.01 Mb to 0.50 Mb at the peak of the cross section. In the ensuing paragraphs, we first review the time-dependent close-coupling (TDCC) theory, then compare the theoretical cross sections with the experiments and then conclude with a brief summary. Unless otherwise stated, all quantities are given in atomic units. The fully correlated wavefunction, , for the ground state of a two-electron target atom is obtained by relaxation of the time-dependent Schrödinger equation in imaginary time (τ = it): − ( r1, r2, τ ) ∂τ = Htarget ( r1, r2, τ ), (1) where the non-relativistic Hamiltonian is given by