Precise nonvariational calculation of the two-photon annihilation rate of the positronium negative ion.

Abstract

A direct (nonvariational) solution of the Schr\"odinger equation for the ground state of the positronium negative ion is obtained with the correlation-function hyperspherical-harmonic (CFHH) method. Given the proper correlation function chosen from physical considerations, the CFHH method generates wave functions accurate in the whole range of interparticle distances that lead, in turn, to precise estimates of the expectation values of the Hamiltonian and of different functions of interparticle distances. The correlation function used was chosen to have proper electron-positron and electron-electron cusps as well as asymptotic behavior. The inclusion of 225 hyperspherical functions yields the nonextrapolated ground-state energy value of 0.262 005 058 atomic units, which is lower than the nonextrapolated energy values 0.262 004 895 and 0.262 005 056 calculated in works of Ho [J. Phys. B 16, 1503 (1983)] and Bhatia and Drachman [Phys. Rev. A 28, 2523 (1983)] but higher than the best variational value 0.262 005 069 obtained by Petenlenz and Smith [Phys. Rev. A 36, 5125 (1987)]. The accuracy of our value of 2.086 10 \ifmmode\pm\else\textpm\fi{}0.000 06 ${\mathrm{nsec}}^{\mathrm{\ensuremath{-}}1}$ for the two-photon annihilation rate is higher by an order of magnitude than obtained in the previous literature.