Some calculations on the ground 1S state of the positronium negative ion

The series solution method used by H. Cox, S. J. Smith and B. T. Sutcliffe (1994, Phys. Rev. A, 49, 4520, 4533) to obtain extremely accurate eigenvalues and eigenvectors for the lowest singlet and triplet states of low Z helium-like systems has been applied to the ground 1S state of the positronium negative ion. Secular determinatnts of up to size 2847 × 2847 have been solved to give a ground state energy of 0·262 005 070 231 742 au. This agrees to 12 decimal places with the most accurate literature value reported by Y. K. Ho (1993, Phys. Rev. A, 48, 4780). Various expectation values involving the interparticle distances have also been evaluated. We estimate the positron-electron annihilation rate Г as 2·086 1223 ns-1. This is in agreement with the most accurate literature value of 2·086 1222 ± 5 × 10-7 (Ho, 1993, Phys. Rev. A, 48, 4780) and the experimental value of 2·09 ± 9 × 10-2 (Mills, 1983, Phys. Rev. Lett., 50, 671).