Wave-packet evolution approach to ionization of the hydrogen molecular ion by fast electrons

Abstract

The multifold differential cross section of the ionization of hydrogen molecular ion by fast-electron impact is calculated by a direct approach, which involves the reduction of the initial six-dimensional ͑6D͒ Schrödinger equation to a 3D evolution problem followed by the numerical modeling of the wave-packet dynamics. This approach avoids the use of stationary Coulomb two-center functions of the continuous spectrum of the ejected electron that demands cumbersome calculations. The results obtained, after verification of the procedure in the case of atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.

Time scaling with efficient time-propagation techniques for atoms and molecules in pulsed radiation fields

“…In atomic and molecular physics, Solov'ev and Vinitsky [18] and later on, Ovchinnikov et al [19] treated the Coulomb three-body problem, in particular ion-atom and atom-atom collisions, within a proper adiabatic representation by timescaling the internuclear distance. More recently, the TSC method has been used by Sidky and Esry [20] and Derbov et al [21] to treat the interaction of a model atom and molecule with an electromagnetic pulse, and by Serov et al [22,23] to study electron-impact single and double ionization of helium and later double photoionization of two-electron atomic systems [24]. The TSC method is an extension of a self-similarity analysis which has been introduced recently in astrophysics [25].…”

“…Furthermore, it has been shown [21,22,28] that a long time after the end of the interaction of the atom or the molecule with the pulse, the energy spectrum of the ejected electrons is simply proportional to the squared modulus of this scaled wave packet. The confinement of the scaled wave packet is due to three factors: the presence of a harmonic potential, the narrowing of the atomic potential, and the increase of the effective mass of the electrons with time.…”

Hybrid surface-flux method for extraction of the ionization amplitude from the calculated wave function

“…Secondly, for the different gauges one has the distinct forms of the operatorD entering the flux definition (8). Namely, the operatorD is represented correspondingly in the length, velocity, and acceleration gauge as follows:…”

“…Among them one should mention those rest upon the evaluation of the projection to the approximate continuum wave function [1,2], the space Fourier transform of the wavefunction asymptotic part [3], the temporal Fourier transform (tFT) of the wavefunction [4,5] or the autocorrelation function [6]. The latter approach has also the refined version, namely the technique built upon the tFT of the probability amplitude flux through a certain closed surface [7][8][9][10][11][12] (following [10], hereinafter we will refer to this method as the t-SURFF). Finally, McCurdy et al have suggested an approach rest upon the evaluation of the flux of the probability amplitude for the scattering function derived by the Green's function operator action to the wavefunction after the end of the pulse [13,14] (in what follows we will refer to this method as the E-SURFF).…”

Modified two-centre continuum wavefunction: application to the dissociative double ionization of H2by electron impact

“…where 1 F 1 (a, b, x) is the Kummer confluent hypergeometric function, α i = −Z/k i is the Sommerfeld parameter and ε i is the small real parameter. The term υ is the repulsive Gamow factor: Integrating over the position of the fast incident electron R using the Bethe transformation dR |R − r| exp(ıKR) = 4π exp(ıKr) K 2 (13) and substituting the functions defined in equations (7) and (9) into equation 4, and using the Fourier transform for one of the centres for each electron, we get…”