Theoretical evidence for quasi-molecular structure at small internuclear distances in elastic ion-atom scattering

The potential energy curve of the system Ne-Ne is calculated for small internuclear distances from 0.005 to 3.0 au using a newly developed relativistic molecular Dirac-Fock-Slater code. A significant structure in the potential energy curve is found which leads to a nearly complete agreement with experimental differential elastic scattering cross sections. This demonstrates the presence of quasi-molecular effects in elastic ion-atom collisions at keV energies.

Many-electron relativistic calculation and interpretation of atomic processes in time dependent heavy-ion scattering

The time dependence of a heavy-ion-atom collision system is solved via a set of coupled channel equations using energy eigenvalues and matrix elements from a self-consistent field relativistic molecular many-electron Dirac-Fock-Slater calculation. Within this independent particle model we give a full many-particle interpretation by performing a small number of single-particle calculations. First results for the P(b) curves for the Ne K-hole excitation for the systems F{^8+} - Ne and F{^6+} - Ne as examples are discussed.

Inclusive probabilities for the scattering system 16 MeV-S{^16+} on Ar

We performed ab initio calculations of many particle inclusive probabilities for the scattering system 16 MeV-S{^16+} on Ar. The solution of the time-dependent DIRAC-FOCK-SLATER-equation is achieved via a set of coupled-channel equations with energy eigenvalues and matrix elements which are given by static SCF molecular many electron calculations.

Realistic many electron coupled channel calculations in heavy ion scattering

The time dependent Dirac equation which describes a heavy ion-atom collision system is solved via a set of coupled channel equations with energy eigenvalues and matrix elements which are given by a selfconsistent field many electron calculation. After a brief discussion of the theoretical approximations and the connection of the many particle with the one particle interpretation we discuss first results for the systems F{^8+} - Ne and F{^6+} - Ne. The resulting P(b) curves for the creation of a Ne K-hole are in good agreement with the experimental results.

Quasi-Interpolation von Funktionen und Anwendungen auf Potentialprobleme

Ausgangspunkt der Dissertation ist ein von V. Maz'ya entwickeltes Verfahren, eine gegebene Funktion f : Rn ! R durch eine Linearkombination fh radialer glatter exponentiell fallender Basisfunktionen zu approximieren, die im Gegensatz zu den Splines lediglich eine näherungsweise Zerlegung der Eins bilden und somit ein für h ! 0 nicht konvergentes Verfahren definieren. Dieses Verfahren wurde unter dem Namen Approximate Approximations bekannt. Es zeigt sich jedoch, dass diese fehlende Konvergenz für die Praxis nicht relevant ist, da der Fehler zwischen f und der Approximation fh über gewisse Parameter unterhalb der Maschinengenauigkeit heutiger Rechner eingestellt werden kann. Darüber hinaus besitzt das Verfahren große Vorteile bei der numerischen Lösung von Cauchy-Problemen der Form Lu = f mit einem geeigneten linearen partiellen Differentialoperator L im Rn. Approximiert man die rechte Seite f durch fh, so lassen sich in vielen Fällen explizite Formeln für die entsprechenden approximativen Volumenpotentiale uh angeben, die nur noch eine eindimensionale Integration (z.B. die Errorfunktion) enthalten. Zur numerischen Lösung von Randwertproblemen ist das von Maz'ya entwickelte Verfahren bisher noch nicht genutzt worden, mit Ausnahme heuristischer bzw. experimenteller Betrachtungen zur sogenannten Randpunktmethode. Hier setzt die Dissertation ein. Auf der Grundlage radialer Basisfunktionen wird ein neues Approximationsverfahren entwickelt, welches die Vorzüge der von Maz'ya für Cauchy-Probleme entwickelten Methode auf die numerische Lösung von Randwertproblemen überträgt. Dabei werden stellvertretend das innere Dirichlet-Problem für die Laplace-Gleichung und für die Stokes-Gleichungen im R2 behandelt, wobei für jeden der einzelnen Approximationsschritte Konvergenzuntersuchungen durchgeführt und Fehlerabschätzungen angegeben werden.

The Navier-Stokes Equations with Particle Methods

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0

X-Ray spectra of superheavy and quasi-superheavy elements

We discuss the possibility of identifying superheavy elements from the observation of their M-shell x-ray spectra, which might occur during the collision of a superheavy element with a heavy target. The same question is discussed for the possible observation of the x-rays from the quasimolecule (quasi-superheavy element) which is formed during such a heavy-ion collision. It is shown that it is very difficult, if not impossible, to determine any information about the interesting quantum electrodynamical effects from the M-shell x-ray spectra of these quasimolecules.

Influence of the electronic shell structure on the elastic scattering of heavy ions

The interatomic potential of the system I - I at intermediate and small distances is calculated from atomic DFS electron densities within a statistical model. Structures in the potential, due to the electronic shells, are investigated. Calculations of the elastic differential scattering cross section for small angles and several keV impact energies show a detailed peak pattern which can be correlated to individual electronic shell interaction.

Total differential scattering cross section of {Ar^+}-Ar at 15 to 400 keV

We report on the measurement of the total differential scattering cross section of {Ar^+}-Ar at laboratory energies between 15 and 400 keV. Using an ab initio relativistic molecular program which calculates the interatomic potential energy curve with high accuracy, we are able to reproduce the detailed structure found in the experiment.

Influence of occupation number of single particle levels on K - K charge transfer in collisions of 90 keV - Ne{^9+} on Ne

The influence of the occupation of the single particle levels on the impact parameter dependent K - K charge transfer occuring in collisions of 90 keV Ne{^9+} on Ne was studied using coupled channel calculations. The energy eigenvalues and matrixelements for the single particle levels were taken from ab initio self consistent MO-LCAO-DIRAC-FOCK-SLATER calculations with occupation numbers corresponding to the single particle amplitudes given by the coupled channel calculations.

Evidence for an additional coupling of the innermost shells in very heavy quasi-molecular ion-atom collisions

Due to the tremendous spin-orbit splitting of quasi-molecular levels in superheavy collision systems (Z = Z_1 + Z_2 {\ge\approx} 137) bombarding energy 0.5-6 MeV N{^-1}, unusual couplings may occur around Z \simeq 165. Experimental evidence for such a theoretically predicted coupling is discussed.

New calculations of P(b) curves for 1s_\sigma excitation in low-Z (Z\le10) ion-atom scattering

Ab initio fully relativistic SCF molecular calculations of energy eigenvalues as well as coupling-matrix elements are used to calculate the 1s_\sigma excitation differential cross section for Ne-Ne and Ne-O in ion-atom collisions. A relativistic perturbation treatment which allows a direct comparison with analogous non-relativistic calculations is also performed.

Multiple vacancy inclusive probabilities for the scattering system 16 MeV S{^16+} on Ar

To evaluate single and double K-shell inclusive charge transfer probabilities in ion-atom collisions we solve the time-dependent Dirac equation. By expanding the timedependent wavefunction in a set of molecular basis states the time-dependent equation reduces to a set of coupled-channel equations. The energy eigenvalues and matrix elements are taken from self-consistent relativistic molecular many-electron Dirac-Fock-Slater calculations. We present many-electron inclusive probabilities for different final configurations as a function of impact parameter for single and double K-shell vacancy production in collisions of bare S on Ar.

Interatomic potential structures in highly ionized scattering systems

The interatomic potential of the ion-atom scattering system I^N+-I at small intermediate internuclear distances is calculated for different charge states N from atomic Dirac-Focker-Slater (DFS) electron densities within a statistical model. The behaviour of the potential structures, due to ionized electronic shells, is studied by calculations of classical elastic differential scattering cross-sections.