S-wave Scattering Length from Effective Positronium-Positronium Interaction for Bose-Einstein Condensates

TL;DR

This paper estimates the s-wave scattering length for positronium interactions, enabling the modeling of positronium Bose-Einstein condensates and analyzing their static properties and phase transition behavior.

Contribution

It provides a semi-phenomenological estimate of the positronium-positronium scattering length and applies it to study properties of Ps BEC using the Gross-Pitaevskii equation.

Findings

Scattering length estimated as ~0.44 nm

Gross-Pitaevskii equation applied to Ps BEC

Phase transition temperature shift evaluated

Abstract

The s-wave scattering length for the Positronium-Positronium interaction is estimated semi-phenomenologically with the long-range van der Waals force and the short-range repulsive potential that represents the hard core between two positronium. The obtained value of the scattering length is $a \sim 0.44{\rm nm}$, and its stability is also checked for different parametrizations. Using this value, the Gross-Pitaevskii equation can be fixed for the Positronium Bose-Einstein condensates (Ps BEC). The static properties of Ps BEC are studied from the solutions of that equation. The phase-transition temperature shift of the Ps BEC due to the Ps-Ps interaction is also evaluated with the mean-field approximation.