S-wave scattering parameters for positronium-positronium interaction and positronium Bose-Einstein condensates

The s-wave scattering parameters for the Positronium-Positronium (Ps-Ps) interaction are estimated semi-phenomenologically with the long-range van der Waals force and the short-range repulsive potential. The obtained values of the scattering length and the effective range are a similar to 0.44 nm, and r(0) similar to 0.2 nm for the symmetric channel. Stability of them is also checked with two kinds of potential with different parametrizations. Spin coupling schemes for the Ps-Ps system are discussed and the formulae of scattering length fur each spin channel are derived. Using this value of the scattering length, the Gross-Pitaevskii equation call be fixed for the Positronium Bose-Einstein condensates (Ps BEG). The static properties of Ps BEC are discussed using the solutions of that equation. The critical temperature shift of the phase-transition due to the Ps-Ps interaction is also evaluated in the mean-field approximation.