Variational Calculations of the Ps-Ps System

Knowing the value of the o-Ps--o-Ps scattering length has enabled it to be shown that it is possible to create a Ps Bose-Einstein Condensate [1,2]. We intend to use the Kohn and inverse Kohn variational methods to calculate accurately the scattering length and phase shifts for o-Ps--o-Ps scattering, which is a four-body scattering system made entirely of leptons. These two methods, with flexible trial functions, have provided accurate results for other four-body scattering systems, such as Ps-H scattering [3]. We have determined the ground-state energy and binding energy of Ps$_2$ using the Rayleigh-Ritz variational method with a short-range interaction trial wave function [4]. We plan to investigate the variation of the energies with different trial wave functions. \begin{enumerate} \item E. P. Liang, C. D. Demer, Opt. Commun. {\bf 65}, 419 (1998) \item P. M. Platzman, A. P. Mills, Jr., Phys. Rev. B {\bf 49}, 454 (1994) \item D. Woods, S. J. Ward, P. Van Reeth, Phys. Rev. A {\bf 92}, 022713 (2015) \item Y. K. Ho, Phys. Rev. A {\bf 33}, 3584 (1986) \end{enumerate}