Precise nonvariational calculation of the positronium negative ion

The three-body Schrödinger equation is solved directly for the ground state of the positronium negative ion by using a rapidly convergent correlation function hyperspherical harmonic method, which involves no adjustable parameters. The inclusion of 169 hyperspherical functions yields the ground-state energy 0.262 004 86 a.u., which is converged to an error in the seventh significant figure. Expectation values of different functions of interparticle distances as well as the two-photon annihilation rate are calculated and compared with those obtained by variational calculations.