Positronium-positronium interaction: Resonance, scattering length, and Bose-Einstein condensation

The low-energy scattering of ortho positronium (Ps) by ortho Ps has been studied in a full quantum mechanical coupled-channel approach. In the singlet channel (total spin $s_T=0$) we find S- and P-wave resonances at 3.35 eV (width 0.02 eV) and 5.05 eV (width 0.04 eV), respectively and a binding of 0.44 eV of Ps$_2$. The scattering length for $s_T=0$ is 3.95 \AA and for $s_T=2$ is 0.83 \AA . The small $s_T=2$ scattering length makes the spin-polarized ortho Ps atoms an almost noninteracting ideal gas which may undergo Bose-Einstein condensation.