# Two-body and three-body contacts for three bosons in the unitary regime: Analytic expressions and limiting forms

## TL;DR

This paper derives analytic expressions for two- and three-body contacts in a trapped three-boson system at unitarity, linking few-body physics to thermodynamics and providing insights into universal relations in strongly interacting Bose gases.

## Contribution

It provides the first analytic formulas for two- and three-body contacts in a trapped three-boson system at unitarity, extending understanding of universal relations in such regimes.

## Key findings

- Derived explicit analytic expressions for contacts at unitarity.
- Compared new formulas with existing limiting cases and numerical results.
- Enhanced understanding of universal relations in strongly interacting Bose systems.

## Abstract

The two and three-body contacts are central to a set of univeral relations between microscopic few-body physics within an ultracold Bose gas and its thermodynamical properties. They may also be defined in trapped few-particle systems, which is the subject of this work. In this work, we focus on the unitary three-body problem in a trap, where interactions are as strong as allowed by quantum mechanics. We derive analytic results for the two and three-body contacts in this regime and compare with existing limiting expressions and previous numerical studies.