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

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

1999-11-29

arxiv.org/abs/cond-mat/9911456v1

Physics

Condensed Matter

7 pages, 6 figures, submitted to Phys. Rev. A

Scientific paper

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.

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