Variational calculations of the bound-state energy of Ps$_2$

We have accurately computed the bound-state energy of Ps$_2$ using the Rayleigh-Ritz variational method with a highly correlated Hylleraas-type trial function

that includes all six interparticle distances \cite{[1]}. We considered both electron and positron exchange.

We also computed the bound-state energy of Ps$_2$ using the the same trial functions that Ho used which include only the direct and electron-exchange terms \cite{[2]}.

The energies we obtained using these trial functions are in excellent agreement with Ho's earlier results \cite{[2]}.

Interestingly, we found that a bound-state of the Ps-Ps system is obtained when we considered only the direct term in a highly correlated Hylleraas-type trial function.

\begin{thebibliography}{References}

\bibitem{[1]} Gabriel Medrano, S. J. Ward and P. Van Reeth, {\it in preparation}.

\bibitem{[2]} Y. K. Ho, Phys.~Rev.~A {\bf 33}, 3584 (1986).

\end{thebibliography}

We are thankful for discussions with Drs. G. W. F. Drake and J. W. Humberston.

The North Texas Scientific Computing (NTSC), a division under the office of the CIO at University of North Texas, is acknowledged for providing Talon computational resources.