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Q: Fachverband Quantenoptik und Photonik

Q 4: Ultra-cold atoms, ions and BEC I

Q 4.2: 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 β_α^α−2 / (2µ r^α) 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 Δ_th 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)=A_s/A_c sin(φ_s−φ_sr)/cos(φ_s−φ_sr), where A_s/A_c, φ_s and φ_c are universal functions of energy, which depend on the potential tail (i.e. α) alone and φ_sr contains a single parameter Δ _th, accounting for all short range effects. The bound states below threshold are given by the quantization function [3], F_tail(E_n)=n_th−n, 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).