Three body problem in a dilute Bose-Einstein condensate

TL;DR

This paper derives an explicit three-body contact potential for dilute Bose-Einstein condensates, linking microscopic collision amplitudes to the stability of condensates with attractive interactions.

Contribution

It provides a new explicit form of the three-body coupling constant derived from microscopic theory, enabling quantitative analysis of condensate stability.

Findings

Coupling constant matches Wu's predicted form

Expressed in terms of two and three body collision amplitudes

Facilitates studies on condensate stability with attractive forces

Abstract

We derive the explicit three body contact potential for a dilute condensed Bose gas from microscopic theory. The three body coupling constant exhibits the general form predicted by T.T. Wu [Phys. Rev. 113, 1390 (1959)] and is determined in terms of the amplitudes of two and three body collisions in vacuum. In the present form the coupling constant becomes accessible to quantitative studies which should provide the crucial link between few body collisions and the stability of condensates with attractive two body forces.