Exact computation of the scattering length

Jochen Pade

M. Marinescu

A simple and easily implemented highly accurate method to compute the scattering length and effective range for a diatomic potential is presented. It combines the numerical solution for small internuclear distances R with analytical corrections for large R. The method provides upper and lower limits to the exact values, to any desired precision. A numerical example and discussion are given for the case of the Cs-Cs ground-state interaction.

Michael J. Jamieson, Henni Ouerdane

Eric L. Bolda, Eite Tiesinga, Paul S. Julienne

We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering phase shift for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single-channel s-wave scattering of ${}^{23}\mathrm{Na}$ atoms in an isotropic harmonic trap, even when outside the Wigner threshold regime. Our model works also for multichannel scattering, where the scattering length can be made large due to a magnetically tunable Feshbach resonance.

Th. Sexl