N. Grün

neutralization in collisions with fast highly charged ions

The neutralization of negative hydrogen ions in collisions with fast (including relativistic velocities) highly charged projectiles is considered by using a simple approach resulting in analytical cross sections for the range of parameters where the Born approximation is invalid. A formula has been derived for the cross section of neutralization.

Numerical treatment of the time-dependent Schrodinger equation in rotating coordinates

The Schrodinger equation for an electron in the time-dependent field of two nuclei is solved numerically in a rotating coordinate system. Two space dimensions are treated by discretisation and the third by an analytical expansion in magnetic substates. Finite difference techniques together with the implicit Crank-Nicolson method for the time evolution are used to treat the resulting system of coupled equations. The method is applied to p+H scattering Elab=2 keV. Comparisons with experimental data and calculations using analytical expansions are made.

Classical trajectory calculations for H+-H collisions with the Wigner function as initial phase space distribution

For classical trajectory Monte-Carlo calculations the authors propose the use of the Wigner function for the initial distribution of the coordinates and momenta of the electron instead of the microcanonical phase space distribution. For physical reasons they restrict the Wigner function in energy space. The allowed energy interval is determined by a cut-off parameter Emax which is fitted to the experimental data. The calculated total cross sections for ionisation and charge transfer in H+-H collisions reproduce the experimental data in the range of incident proton energies Elab=25-200 keV. In addition they present the probabilities of ionisation and charge transfer as functions of the impact parameter and angular distributions of the ionised electron.

Finite element formulation of the Dirac equation and the problem of fermion doubling

Abstract We apply the method of finite elements to the one-dimensional Dirac equation. The dispersion relation of the finite element formulation shows that the method leads to a problem known as “fermion doubling”. Investigating the propagation of a Gaussian wave packet on a finite element mesh we demonstrate that fermion doubling has unphysical consequences such as wave packets moving with velocities greater than the speed of light.

Auger rates for dielectronic recombination cross sections with highly charged relativistic heavy ions

Abstract Relativistic wave functions and corrections to the Coulomb interaction between two electrons are used to calculate Auger rates and the cross section for dielectronic recombination (DR). Results are given for hydrogen-like Pb ions. The cross section of the DR is compared with an estimate of the cross section of the direct radiative electron capture.

Pair production with inner-shell capture

The production of electron-positron pairs with simultaneous capture of the electron into bound states of the target is studied for relativistic heavy-ion collisions in the range of energies 1<or=Elab<or=100 GeV amu-1. Impact-parameter-dependent probabilities and cross sections are calculated in the semiclassical approximation by using time-dependent perturbation theory in first order and Coulomb-Dirac wavefunctions for the electron and positron states. The authors predict a cross section of about 70 b for the capture of electrons into the target K shell in U92++U92+ collisions at Elab=100 GeV amu-1.

K-shell ionisation in relativistic heavy-ion collisions

For relativistic heavy-ion collisions K-shell ionisation probabilities are calculated in the semiclassical approximation (SCA) and first-order perturbation theory. Most of the results are obtained for a uranium target and show the increasing importance of the spin-dependent interaction potential for relativistic relative velocities nu /c>0.5. Interesting structures arising in certain partial differential ionisation probabilities are discussed.

Solution of the time-dependent Schrödinger equation with a trajectory method and application to H+-H scattering

Abstract The Schrodinger equation for the scattering of H+ on H(1s) is solved with a method which is based on an interpretation of this equation in terms of fluid mechanics. Results for the ionization and charge exchange probability are presented.

Solution of the time-dependent Dirac equation by the finite difference method and application for Ca20++U91+

The Dirac equation for an electron moving in time-dependent electromagnetic fields is solved by the method of finite differences. For simplicity the solution is restricted to problems with a rotational symmetry about an axis. The method is applied to the scattering of Cs20+ on a hydrogen-like U91+ ion at relativistic incident energies. Excitation and ionisation probabilities and the K-shell vacancy production probability are calculated.

Trajectory method for the solution of the time-dependent Schrodinger equation in atomic physics and application to H+-H scattering

A trajectory method has been developed for the solution of the one-electron Schrodinger equation in atomic scattering problems. The method is based on the fluid dynamical interpretation of the quantum mechanical probability density and current. The time evolution is described by trajectories of particles, which represent the probability distribution. The trajectories are calculated by solving classical equations of motion with forces depending on the probability density. Results are obtained for the differential and total ionisation and charge exchange cross sections for the scattering of H+ on H.