# Bonn 2010 – wissenschaftliches Programm

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# HK: Fachverband Physik der Hadronen und Kerne

## HK 18: Anwendungen kernphysikalischer Methoden

### HK 18.5: Vortrag

### Dienstag, 16. März 2010, 15:00–15:15, HG V

**Spectrum of particles with short-ranged interactions in a harmonic potential** — •Simon Tölle, Hans-Werner Hammer, and Bernard Metsch — Helmholtz-Institut für Strahlen- und Kernphysik (Theorie), Universität Bonn

The possibility to control short-ranged interactions of cold gases in optical traps by Feshbach-resonances makes these systems ideal candidates to study universal scale properties and Efimov physics. For *A* particles with equal mass *m* the energy spectrum in a trap, idealised by an harmonic potential, in the zero-range limit in leading order is determined by the Hamiltonian
H=∑_{i=1}^{A}(|p^→_i|^2/2m+1/2mω^2|x_i|^2)+∑_{i<j}^{A}V_ij+∑_{i<j<k}^{A}W_ijk ,
where ω is the trapping frequency and *V*_{ij} and *W*_{ijk} are 2- and 3-particle contact interactions. In Jacobi-coordinates the centre-of-mass motion is separated. The Hamiltonian is regularised by restricting the coupled oscillator basis with a cutoff *N*. For a given *N* the corresponding Hamilton matrix is diagonalised numerically. The effective coupling constants are renormalised by the requirement that for each *N* the ground state energies of the 2- and 3-body sector match the exact results. The excitation spectrum can in general be extrapolated reliably for *N*→∞. Appropriate symmetries for identical bosons and fermions can be considered. Results for 2-, 3- and 4-particle systems will presented. First applications to physical systems like ^{6}Li will be discussed.