Single-Particle Momentum Distributions of Efimov States in Mixed-Species Systems

TL;DR

This paper analytically and numerically investigates Efimov states in mass-imbalanced three-body systems, deriving formulas for the Efimov spectrum scaling, analyzing momentum distributions, and exploring the mass ratio dependence of the three-body contact parameter.

Contribution

It provides new analytical formulas for Efimov spectrum scaling and the three-body contact parameter in mixed-species systems with zero-range interactions.

Findings

Derived formulas for Efimov spectrum scaling factor.

Analyzed the momentum distribution tail and three-body contact.

Showed the dependence of the contact term on mass ratio.

Abstract

We solve the three-body bound state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero-range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyse the tail of the momentum distribution to obtain the three-body contact parameter. Our finding demonstrate that the functional form of the three-body contact term depends on the mass ratio and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of Lithium with either two Caesium or Rubium atoms which are systems of current experimental interest.