Electron-impact single and double ionization of helium

Abstract

Electron-impact ionization cross sections for helium are calculated using time-dependent close-coupling theory. The total wave function for the three electron system is expanded in nine dimensions, where three dimensions are represented on a radial lattice and a coupled channels expansion is used to represent the other six dimensions. Collision cross sections are obtained by t → ϱ projection onto fully antisymmetric spatial and spin functions, with care as to orthogonality of different representations. Cross sections are also obtained using time-independent first-and second-order perturbative distorted-wave theory. Total cross sections are calculated at incident energies above the double ionization threshold for electron-impact single ionization leaving He + in the 1s, 2s, and 2p states and for electron-impact double ionization. Both the single ionization cross section, leaving He + in the 1s ground state, and the double ionization cross section are in excellent agreement with previous absolute experimental measurements.

Pentuple energy and angle differential cross sections for the electron-impact double ionization of helium

“…For the triple photoionization of the Li atom, TDCC total cross sections [1] are in good agreement with synchrotron experiments [2], while for the triple photoionization of the Be atom, TDCC total cross sections [3] are about a factor of 3 lower than double shakeoff model calculations [4]. For the electron-impact double ionization of He, TDCC total cross sections [5,6] are in good agreement with crossed-beams experiments [7], while for the electron-impact double ionization of H − , TDCC total cross sections [8] are in good agreement with the more recent of two sets of crossed-beams experiments [9,10].…”

“…The time-dependent close-coupling theory for the electronimpact single and double ionization of an atom has been set forth in our original work on helium [5]. For electron-impact ionization of an atom with two active electrons, the angular reduction of the time-dependent Schrödinger equation in nine spatial dimensions yields an l 1 l 2 Ll 3 set of time-dependent coupled partial differential equations given by…”

Electron-heliumS-wave model benchmark calculations. I. Single ionization and single excitation

“…To date, TDCC is the only nonperturbative ab initio fourbody technique that has been used to successfully calculate total double-ionization cross sections for helium at low energies [7]. Recent TDCC calculations [8] also give energyand angle-differential results for double ionization but they disagree markedly with measurements, while their shape is in general agreement for some kinematic arrangements.…”

Electron-heliumS-wave model benchmark calculations. II. Double ionization, single ionization with excitation, and double excitation

“…Hybrid methods that combine CCC or RMPS with distorted-wave techniques, or indeed full distorted-wave methods, have made some progress in this regard [1,3] though large discrepancies remain, especially with low-energy collisions. Presently, TDCC is the only ab initio method that has been applied to electron-impact double ionization of helium, and while it is in reasonable agreement with measurements of the total cross sections [7], angular-differential calculations differ markedly from measurement [8]. There is, therefore, a growing need for accurate theoretical modeling of four-body processes.…”