  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.

Condensed Matter