Variational treatment of positronium molecules

A variational treatment for obtaining the binding energies, wavefunctions and internal distances of the positronium molecule (Ps₂) is presented. For this purpose, very modern Hylleraas-type trial wavefunctions, as well as different envelope functions (upsilon^m6e^{- γv} where m₆=0, 1, 2, 3 and upsilon is the distance between the two positrons), are employed. The resulting binding energies show excellent convergence when the number of components of the wavefunction considered is increased. Our results at m₆=2 show that only 22 components of our wavefunction are sufficient for obtaining the binding energy omega P(s₂)=-0.03 Ryd (=-0.41 eV) which is identical to the binding energy calculated by Ho via 400 components of his trial wavefunctions. The best convergence, however, has been achieved via 22 components of our wavefunctions at m₆=1. In this case, omega P(s₂)=-0.042 Ryd (=-0.573 eV). Comparison with the very recent value of omega P(s₂)(=-0.435 eV) determined by Kinghorn and Poshusta (1993) and Kozlowski and Adamowicz (1993), using 300 components of their trial wavefunctions, supports the opinion that the exact binding energy of Ps₂ is less than-0.41 eV. Our average values for the internal distances of Ps₂ agree quite well with those determined by previous authors and emphasize the argument that the size of the molecule is decreased when the binding energy is lowered.