H J Ludde

Comment on inclusive cross sections

The authors indicate a simple scheme for the evaluation of inclusive transition probabilities in atomic collision problems. Assuming that the time development of the orbitals can be represented in terms of an effective one-particle picture (as, for example, the time-dependent Hartree-Fock picture), inclusive probabilities are readily expressed in terms of one-particle density matrix elements.

The basis generator method: optimized dynamical representation of the solution of time-dependent quantum problems

The theoretical investigation of time-dependent quantum systems requires the solution of the time-dependent Schrodinger (Dirac) equation. The basis generator method presented here allows a systematic construction of dynamically adapted wavefunctions based on a decomposition of the Hilbert space into a hierarchical structure of finite subspaces. For the class of interactions obeying an inverse integer power law, e.g., Coulomb and polarization interactions, an explicit representation of the dynamically optimized basis set is given.

TDHF calculations for two-electron systems

TDHF calculations using a two-centre basis expansion technique are carried out for two-electron systems in the energy range of 5 to 40 keV/nucleon. Cross sections are calculated for one-electron capture of p+He(1s2) and for one- and two-electron capture of He2+ and Li3+ from He(1s2) and compared with other theoretical and experimental results. The influence of the exchange potential is briefly traced by considering the collision systems He+(2s)+He+(2s) and He+(2s)+H(1s) for the spin-singlet and spin-triplet cases.

Method for the calculation of global probabilities for many-electron systems

The question of extracting global transfer cross sections from determinantal wavefunctions as encountered in the impact parameter treatment of many-electron atomic collision systems is investigated. The authors demonstrate in particular a relation between two-electron and one-electron capture in the two-electron system He2++He and indicate the extension to N-electron situations.

Inner- and outer-shell electron dynamics in proton collisions with sodium atoms

p+Na collisions have been investigated theoretically and experimentally at impact energies in the keV regime. We present results for capture and ionization processes, and, in particular, analyse the role of initial inner-shell electrons, whose active participation is identified in the experiments through the analysis of recoil-ion momentum spectra. Quantum-mechanical calculations within the independent particle model have been carried out for all active electrons. A very good overall agreement between the theoretical and experimental results is found. The calculations support the observation that capture from inner shells is an important reaction channel even at relatively low impact energies, and dominates total capture above 40 keV.

Calculation of inclusive probabilities from single-particle amplitudes

Abstract On the basis of the independent particle model, used to describe collisions between ions and atoms involving many electrons, the formalism of inclusive probabilities allows the computation of many-electron transition probabilities from single-particle amplitudes. The method presented can answer practically any experimental question formulated in terms of a certain number of vacancies and occupancies as can be measured in a typical ion-atom collision experiment. It is specialised to calculate many-particle probabilities with respect to a minimum number of vacancies or occupancies in one or more subshells as obtained e.g. in KLL- or KLM-Auger spectra.

Direct and capture processes in proton-hydrogen scattering. II. Total cross sections for bombarding energies of 1 to 50 keV

The authors present total cross sections for direct and transfer processes in p-H scattering in the energy range between 1 and 50 keV. The results were obtained (as those of a previous pilot study at 2 and 8 keV) by numerical solution of the time-dependent Schrodinger equation in the impact parameter approximation by expansion in a pseudobasis set of the Hylleraas type. The authors discuss, in some detail, the properties of the coupled-channel equations involved and compare the calculated cross sections with the available experimental data.

Density Functional Approach to Molecular Structure and Atomic Scattering

We discuss density functional methods as alternatives to stationary two-center Hartree Fock (HF) and time dependent HF (TDHF) calculations.

Optimized dynamical representation of the solution of time-dependent quantum problems

The theoretical investigation of time-dependent quantum systems requires the solution of the time-dependent Schrodinger (Dirac) equation. We present a formalism which enables the generation of an optimized set of pseudostates based on a decomposition of the Hilbert space into a hierarchical structure of finite subspaces. To illustrate the method we present results for a simple interatomic collision problem.

Optical potentials in time-dependent quantum systems

The authors present a Feshbach projector formalism for the solution of the time-dependent Schrodinger equation leading to a finite set of coupled-channel equations with complex potentials. The derivation of non-perturbative optical potentials is based on the assumption that successive interactions occur instantaneously rather than with a time delay. This so-called local approximation is investigated in some detail on three successive levels, with special emphasis on the tractability of the matrix elements involved.