Efimov effect in the Born-Oppenheimer picture

TL;DR

This paper investigates the Efimov effect in a mass-imbalanced three-particle system using the Born-Oppenheimer approximation, revealing that the Efimov spectrum depends only on mass ratio and particle statistics in the unitary limit.

Contribution

It extends previous work by analyzing all angular momenta and shows the Efimov spectrum's dependence on mass ratio and statistics without a three-body parameter.

Findings

Efimov spectrum depends only on mass ratio and particle statistics at unitarity.

Spatial size of near-threshold bound states is about 2.8 times the scattering length.

Derived a sharper Bargmann bound for the number of bound states.

Abstract

In this work, we study the Efimov effect in a mass-imbalanced system consisting of two heavy particles and one light particle within the Born-Oppenheimer approximation. The result obtained in R. Figari, H. Saberbaghi, and A. Teta, J. Phys. A: Math. Theor. 57(5), 2024, for zero angular momentum is recovered here as a special case, and the analysis is extended to all angular momenta. In this setting, the resonant heavy-light interactions are modeled as point interactions, under the assumption of either exchange symmetry or antisymmetry with respect to the positions of the delta centers. Within this framework, we prove that in the unitary limit the Efimov spectrum depends solely on the mass ratio and particle statistics; that is, the so-called three-body parameter is absent. We also provide a condition ensuring that the spectrum contains no nonEfimov eigenvalues. Furthermore, we study the system away from the unitary limit and show that the spatial size of the weakest bound state near the threshold is approximately 2.8 times the two-body scattering length, in contrast to the common assumption that these two scales coincide. Finally, we compute Bargmann bound for the number of bound states and obtain a sharper estimate than the results in the literature.