C. Bottcher

Basis-Spline collocation method for the lattice solution of boundary value problems

Abstract We study a particular utilization of the basis-spline collocation method (BSCM) for the lattice solution of boundary value problems. We demonstrate the implementation of a general set of boundary conditions. Among the selected problems are the Schrodinger equation in radial coordinates, the Poisson, and the generalized Helmholtz equations in radial and three-dimensional Cartesian coordinates.

Dissociative electron attachment to the metastable c 3 Pi u state of molecular hydrogen

The H2- 2 Pi u resonance is used in an estimation of the cross section for dissociative electron attachment (DA) to the metastable c3 Pi u state of molecular hydrogen. The cross section is found to be substantially larger than that for DA to the low vibrational levels of the ground electronic state X1 Sigma g+. It appears that DA to c3 Pi u could play an important role in the production of the relatively high densities of negative ions in low-density hydrogenic plasma.

Dissociative recombination of large molecular ions

The theory of indirect dissociative recombination (which occurs through the excitation of rotational or vibrational degrees of freedom in the molecular ion) is developed in order to explain the very large rates measured for the recombination of polyatomic molecular ions. Theoretical upper bounds on the rates are established. The formulation simplifies considerably for loosely-bound aggregates, and it is thus possible to explain the dependence upon n of the observed rates for H3O+(H2O)n.

Numerical calculations on electron-impact ionization

Publisher Summary This chapter discusses numerical calculations on the electron impact ionization of single-electron systems at energies near threshold. The wave packet method is simply a numerical experiment whose advantage is that because the wave packet is ever confined to a finite region of position space; no boundary conditions are required on the wave function. The procedure is particularly suited to breakup problems where the asymptotic boundary conditions are uncertain. Another method, the finite element procedure include its ability to handle the Coulomb singularity, the capability of using grids with variable spacing, for example, taking larger steps at large r 1 than near r 1 = 0), great flexibility in treating different metrics and coordinate systems and above all, its inherent stability.

Excitation-autoionisation of Ti3+, Zr3+and Hf3+in the distorted-wave approximation with exchange

Full distorted-wave calculations have been carried out on np6 to np5nd2 transitions to test the formalism for complex atomic configurations, and to provide a more meaningful comparison with experiment than was possible from earlier calculations. Agreement with experiment is certainly improved, but some discrepancies remain.

Numerical solution of the Peterkop-Rabik Temkin-Hahn model of electron impact ionisation

Finite-element integration of the Schrodinger equation for the time evolution of a wavepacket is used to solve the two-dimensional model of electron impact ionisation proposed by Temkin and Hahn (1974), and Peterkop and Rabik (1972), as a test bench for mathematical and numerical techniques. The quantitative features of Wanniers transition state theory (1953) are reproduced, not only at threshold, but at much higher energies. Ionisation probabilities and ejected electron spectra are presented from threshold up to initial energies nine times the threshold energy.

Strong-field laser ionization of alkali atoms using two-dimensional cylindrical and three-dimensional Cartesian time-dependent Hartree–Fock theory

The time-dependent Schrodinger equation is solved directly for an alkali atom subject to an arbitrarily strong electromagnetic field. Two methods are compared. A tridiagonal finite-difference method is used to solve Schrodinger’s equation on a two-dimensional (2D) cylindrical coordinate lattice, while a finite-element method using odd-order B splines is used to solve Schrodinger’s equation on a three-dimensional (3D) Cartesian coordinate lattice. Multiphoton ionization cross sections are extracted from 2D cylindrical calculations for hydrogen and lithium and then compared with previous perturbation theory results. Single-photon ionization probabilities are compared from 2D cylindrical and 3D Cartesian calculations for hydrogen.

Electron impact ionization data for the iron isonuclear sequence

Atomic data for the electron impact ionization of ions in the iron isonuclear sequence are reviewed. The best available data are identified. Comments are made on current research activities leading to future data for iron ions.

Coherent Higgs and W± pair production

Cross sections for the coherent electromagnetic production of the intermediate vector bosons and the Higgs boson in ultrarelativistic heavy-ion collisions are calculated from standard electroweak theory. The distributions of the resulting decay products are also considered. Particular attention is given to the energy regime of the Superconducting Supercollider and the CERN Large Hadron Collider.

Numerical studies on the electron impact ionisation of hydrogen near threshold

Electron impact ionisation of atomic hydrogen is calculated in the energy range 13.6-27 eV by numerically following the time evolution of a wavepacket. All dynamical degrees of freedom are included and total angular momenta L<or=2 have been considered. Plots of differential probability against ejection energy and the angle theta between the outgoing electrons reveal a strong influence of the interelectronic repulsion. Although angles theta approximately 180 degrees are favoured, another more isotropic mechanism can be distinguished. The slope of the total cross section near threshold has been extracted and found to agree with experiment.