Crossover trimers connecting continuous and discrete scaling regimes

TL;DR

This paper introduces crossover trimers that bridge the gap between Efimov and Kartavtsev-Malykh trimers, revealing a universal third type of three-body bound states with unique scaling properties.

Contribution

It identifies and characterizes crossover trimers that connect discrete and continuous scaling regimes across different mass ratios and scattering lengths.

Findings

Crossover trimers exist universally regardless of potential details.

They connect Efimov and Kartavtsev-Malykh trimers as parameters vary.

Regions for different trimer types are mapped as functions of mass ratio and scattering length.

Abstract

For a system of two identical fermions and one distinguishable particle interacting via a short-range potential with a large s-wave scattering length, the Efimov trimers and Kartavtsev-Malykh trimers exist in different regimes of the mass ratio. The Efimov trimers are known to exhibit a discrete scaling invariance, while the Kartavtsev-Malykh trimers feature a continuous scaling invariance. We point out that a third type of trimers, "crossover trimers", exist universally regardless of short-range details of the potential. These crossover trimers have neither the discrete nor continuous scaling invariance. We show that the crossover trimers continuously connect the discrete and continuous scaling regimes as the mass ratio and the scattering length are varied. We identify the regions for the Kartavtsev-Malykh trimers, Efimov trimers, crossover trimers, and non-universal trimers as a function of the mass ratio and the s-wave scattering length by investigating the scaling property and model-independence of the trimers.