Time-dependent Close-coupling Method Research Articles

Time-dependent and time-independent close-coupling methods for the electron-impact ionization of Be^{+}

The electron-impact ionization cross section of Be{sup +} is calculated using both a time-dependent and a time-independent close-coupling method. The time-dependent method is based on the propagation of wave packets constructed using excited-state orbitals calculated in a core pseudopotential. The time-independent method is an R-matrix solution based on a total wave function constructed using antisymmetrized products of Laguerre pseudo-orbitals and zero-derivative box orbitals. In both methods, low partial-wave close-coupling results are added to high partial-wave distorted-wave results to yield ionization cross sections for Be{sup +} substantially below the experimental crossed-beam measurements of Falk and Dunn [Phys. Rev. A {bold 27}, 754 (1983)] and in agreement with the recent time-independent close-coupling calculations of Bartschat and Bray [J. Phys. B {bold 30}, L109 (1997)]. {copyright} {ital 1997} {ital The American Physical Society}

Total ionization cross section for electron-hydrogen scattering using a time-dependent close-coupling method.

A time-dependent close-coupling method is combined with a time-independent distorted-wave method to calculate the electron ionization cross section for hydrogen. A second-order differencing of the time propagator for the close-coupled equations is found to be very efficient. Low partial-wave close-coupling results are added to high partial-wave distorted-wave results to yield total ionization cross sections in excellent agreement with experiment between 30- and 50-eV incident electron energy. The distorted-wave method found most suitable for the high partial waves is based on a mixture of ${\mathit{V}}^{\mathit{N}}$ and ${\mathit{V}}^{\mathit{N}\mathrm{\ensuremath{-}}1}$ scattering potentials. \textcopyright{} 1996 The American Physical Society.

Time-dependent close-coupling method for electron-impact ionization of hydrogen.

Electron-impact ionization of atomic hydrogen is studied by direct solution of a set of time-dependent close-coupled partial differential equations. The close-coupled equations describe the propagation of a time-evolving wave packet on a two-dimensional radial lattice. Following the collision, the wave packet is projected onto stationary states of the target to obtain probabilities for elastic and inelastic scattering processes. Ionization cross sections are calculated for various {ital LS} partial waves and compared with previous theoretical methods. {copyright} {ital 1996 The American Physical Society.}

Unstable periodic orbits, recurrences, and diffuse vibrational structures in the photodissociation of water near 128 nm

The photodissociation of H2O in the second absorption band (X̃→B̃) is investigated in a completely time-dependent approach. The Schrödinger equation is solved by a time-dependent close-coupling method expanding the two-dimensional wave packet in terms of free rotor states. The vibrational degree of freedom of the OH fragment is fixed and only motion on the B̃-state potential-energy surface is considered. The calculated absorption spectrum exhibits a long progression of diffuse structures, ΔE∼0.1 eV, in very good agreement with the experimental spectrum. The structure is readily explained in terms of a recurrence of the autocorrelation function after about 40 fs. The recurrence, in turn, is attributed to special indirect trajectories which on the average perform one oscillation within the deep potential well before they dissociate into products H+OH. These trajections are ‘‘guided’’ by so-called unstable periodic orbits which persist to energies high above the H+OH(2 Σ) threshold. The existence of unstable periodic orbits leading to a recurrence of the autocorrelation function gives, for the first time, a consistent explanation of the diffuse structure in the absorption spectrum of H2 O in the second band.

Electron scattering from atoms in the presence of a laser field

The formal development of the problem of electron-atom scattering in the presence of a laser field is considered. A time-dependent close-coupling method and a time-dependent optical-potential method are presented. With hydrogen as an example, and a weak laser tuned near the $1S\ensuremath{-}2P$ resonance, the effective long-range potentials are explicitly obtained. These potentials are time dependent, noncentral, and fall off as ${r}^{\ensuremath{-}n}$, where we limit ourselves to terms with $n=2, 3, \mathrm{and} 4$. They are then used to find the elastic, inelastic, and superelastic cross sections for small momentum transfer.