Efimov physics and the three-body parameter within a two-channel framework

Abstract

We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. We find corrections to the universal scaling laws for large binding energies. For narrow resonances we find a distinct nonmonotonic behavior of the threshold at which the lowest Efimov trimer merges with the threebody continuum. The origin of the three-body parameter is related to the two-body atom-atom interactions in a physically clear model. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down the relation of two-and three-body physics in atomic systems.

Physical origin of the universal three-body parameter in atomic Efimov physics

“…Unlike what is stated in Ref. [36], this shape does not guarantee that configurations at larger hyperradius are not suppressed by the two-body suppression (i.e. that "no regions with infinite potentials are sampled" in the hard-core potential picture), because some configurations with elongated shapes are clearly suppressed at larger hyperradii, as can be seen in Fig.…”

“…The particular case of the linear shape (α = π/2) considered in Ref. [36] gives a suppression hyperradius R = 2r vdW . Unlike what is stated in Ref.…”

“…In Ref. [36], it is argued that the repulsion results from the interatomic two-body hard-core repulsion. Let us first note that this statement is not general enough, since the three-body repulsion also occurs for purely attractive potentials with no hard-core repulsion, as shown in Ref.…”

“…[36] then proceeds by noticing that the three-body configurations for which two particles are within the van der Waals length must have near zero probability because of the two-body probability suppression [48]. Therefore, for small enough hyperradius, all three-body configurations are trivially suppressed since there are always at least two particles within the suppression radius, no matter what the shape of the three-body system is.…”

Three-body parameter for Efimov states inLi6

“…However, in atomic systems it has been found experimentally [13,27] that the 3BP is nearly constant when expressed in terms of the van der Waals length r vdW [6], which quantifies the dispersion interaction between two neutral atoms. We refer to this feature of Efimov physics as van der Waals universality of the 3BP, and it has been the subject of a number of theoretical investigations [28][29][30][31][32][33].…”