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Dresden 2011 – wissenschaftliches Programm

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A: Fachverband Atomphysik

A 2: Ultra-cold atoms, ions and BEC I (with Q)

A 2.2: Vortrag

Montag, 14. März 2011, 10:45–11:00, BAR 106

Universality of s-wave scattering phase shifts beyond the effective-range expansion — •Alexander Kaiser, Tim-Oliver Müller, and Harald Friedrich — Physik Department, TU München, Germany

The properties of scattering states at low energies in deep potentials with a homogeneous attractive tail V(r) = −ℏ2 βαα−2 / (2µ rα) with α>2 are strongly related to the location of the bound states just below the dissociation threshold. It has been shown that the noninteger part Δth of the threshold quantum number determines the scattering length [1] as well as the semiclassical behaviour [2] of the scattering phase shift at intermediate energies. With a new method we derived a formula for the scattering phase shift, accurately describing the whole energy range from threshold to the semiclassical regime, tan(δ0)=As/Ac sin(φs−φsr)/cos(φs−φsr), where As/Ac, φs and φc are universal functions of energy, which depend on the potential tail (i.e. α) alone and φsr contains a single parameter Δ th, accounting for all short range effects. The bound states below threshold are given by the quantization function [3], Ftail(En)=nthn, so that the whole energy spectrum around the dissociation threshold is determined by the scattering length.

[1] G. Gribakin and V. Flambaum, Phys. Rev. A 48, 546 (1993).

[2] G. Gribakin et al., Phys. Rev. A 59, 1998 (1999).

[3] P. Raab and H. Friedrich, Phys. Rev. A 78, 022707 (2008).

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