Towards a hyperspherical description of positronium-positronium scattering

The interest in the scattering properties of the positronium (Ps) has grown with the possibility of creating a Bose-Einstein condensate of matter-antimatter. Such an experimental realization would not only permit an exploration of quantum effects at macroscopic temperatures, but it would also contribute to our understanding of the relationship between the Ps$_2$ molecule and more conventional molecules like H$_2$. A deep understanding of positronium's collisional properties is crucial for cooling techniques and for the realization of a Bose-Einstein condensate. A hyperspherical analysis of this four-body system with two electrons and two positrons allow us not only to benchmark calculations of the Ps-Ps scattering length which have been previously studied (see e.g. Ref. [1]) but also to analyze recombination processes such as Ps+e+e$^+$ $\to$ Ps+Ps or Ps$^-$ + e$^+$, etc... We extend previous implementations of the correlated Gaussian hyperspherical method [2] to describe four-body systems with Coulomb interactions. The results from this hyperspherical analysis are compared with previous studies and correlated Gaussian calculations. \\[4pt] [1] I. A. Ivanov, J. Mitroy, and K. Varga. Phys. Rev. A 65, 022704 (2002)\\[0pt] [2] J. von Stecher and C.H. Greene. Phys. Rev. A 80, 22504(2009)