Bose-Einstein condensation of positronium: modification of the s-wave scattering length below the critical temperature

TL;DR

This paper investigates how the presence of a positronium Bose-Einstein condensate alters the effective s-wave scattering length, providing a theoretical framework for understanding low-temperature positronium interactions.

Contribution

It introduces a simplified model using Bogoliubov theory to describe many-body positronium collisions and derives an effective scattering length modified by the condensate.

Findings

Effective scattering length depends on a single dimensionless parameter.

The model applies broadly to different bosonic species.

Modification of collision processes below the critical temperature.

Abstract

The production of a Bose-Einstein condensate made of positronium may be feasible in the near future. Below the condensation temperature, the positronium collision process is modified by the presence of the condensate. This makes the theoretical description of the positronium kinetics at low temperature challenging. Based on the quasi-particle Bogoliubov theory, we describe the many-body particle-particle collision in a simple manner. We find that, in a good approximation, the full positronium-positronium interaction can be described by an effective scattering length. Our results are general and apply to different species of bosons. The correction to the bare scattering length is expressed in terms of a single dimensionless parameter that completely characterizes the condensate.