# Hannover 2010 – wissenschaftliches Programm

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# A: Fachverband Atomphysik

## A 26: Electron Scattering and Recombination / Interaction of Matter with Ions (with MO)

### A 26.3: Vortrag

### Freitag, 12. März 2010, 11:30–11:45, B 302

**Finite basis set approach to the two--center Dirac problem** — •Anton Artemyev and Andrey Surzhykov — Universität Heidelberg and GSI Helmholtzzentrum für Schwerionenforschung

Owing to the recent experimental advances in ion accelerator and storage ring techniques, more possibilities arise to study formation of quasi--molecules in (relatively) slow collisions of highly--charged, heavy ions. Extremely strong electromagnetic fields produced in these collisions are expected to cause a ``decay'' of unstable physical vacuum and a spontaneous creation of electron-positron pairs. Theoretical understanding of such an overcritical--field phenomenon requires, in general, solution of the two--center time--dependent Dirac equation. For low velocities of colliding ions this equation may still be treated adiabatically and, hence, can be traced back to the static (two--center) problem. In our work we developed an efficient method for dealing with this problem by utilizing finite basis sets constructed from B--splines. We argue that B--spline analysis can be performed most naturally in Cassini coordinates that are very efficient for the description of two--center Coulomb potential [1, 2]. To underline the advantages of the present approach, detailed calculations will be presented for quasi--molecular energy spectra obtained for slow symmetric (Z1 = Z2) as well as asymmetric (Z1 > Z2) ion--ion collisions.

[1] P. Schlüter, K.-H. Wietschorke, and W. Greiner, J. Phys. A v. 16, 1999, (1983).

[2] K.-H. Wietschorke, P. Schlüter, and W. Greiner, J. Phys. A v. 16, 2017, (1983).