VARIATIONAL TREATMENT OF POSITRONIUM MOLECULES

A variational treatment for obtaining the binding energies, wavefuncti ons and internal distances of the positronium molecule (Ps(2)) is pres ented. For this purpose, very modern Hylleraas-type trial wavefunction s, as well as different envelope functions (nu(m6)e(-gamma nu) where m (6) = 0, 1, 2, 3 and nu is the distance between the two positrons), ar e employed. The resulting binding energies show excellent convergence when the number of components of the wavefunction considered is increa sed. Our results at m(6) = 2 show that only 22 components of our wavef unction are sufficient for obtaining the binding energy omega(Ps2) = - 0.03 Ryd (= -0.41 eV) which is identical to the binding energy calcula ted by Ho via 40D components of his trial wavefunctions. The best conv ergence, however, has been achieved via 22 components of our wavefunct ions at m(6) = 1. In this case, omega(Ps2) = -0.042 Ryd (= -0.573 eV). Comparison with the very recent value of omega(Ps2) (= -0.435 eV) det ermined by Kinghorn and Poshusta and Kozlowski and Adamowicz, using 30 0 components of their trial wavefunctions, supports the opinion that t he exact binding energy of Ps(2) is less than -0.41 eV. Our average va lues for the internal distances of Pst agree quite well with those det ermined by previous authors and emphasize the argument that the size o f the molecule is decreased when the binding energy is lowered.