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

Abstract

A direct (nonvariational) solution of the Schrodinger equation for the ground state of the positronium negative ion is obtained with the correlation-function hyperspherical-harmonic (CFHH) method. Cxiven 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 0.262005 058 atomic units, which is lower than the nonextrapolated energy values 0.262004 895 and 0.262005 056 calculated in works of Ho [J. Phys. B 16, 1503Phys. B 16, (1983] and Bhatia and Drachman [Phys. Rev. A 28, 2523] but higher than the best variational value 0.262005069 obtained by Petenlenz and Smith [Phys. Rev. A 36, 5125 (1987)]. The accuracy of our value of 2.08610+0.00006 nsec for the two-photon annihilation rate is higher by an order of magnitude than obtained in the previous literature.

Lifetime of Positronium Molecule. Study with Boys' Explicitly Correlated Gaussians

“…22 The theoretical study of the two-photon annihilation rate of Ps -was performed by Ho, 19 by Bhatia and Drachman, 20 and most recently by Krivec, Haftel, and Mandelzweig. 23 All the most recent theoretical estimates remain in good agreement with their experimental value.…”

Positronium-Ion Decay

“…Together, this led to the theoretical prediction for the Ps ÿ decay width [7], ÿ 1983 th 2:0866 ns ÿ1 ; (2) where the size of the O corrections was used to estimate the uncertainty [10] (see also Refs. [11][12][13]). Recent measurement [10] agrees with this prediction and approaches its precision, ÿ exp 2:08915 ns ÿ1 .…”

“…(15) such that the divergences appear only in the coefficient of one operator, namely 3 r 12 . To this end, we rewrite [24] the delta-function as 4 d r 12 4 d r 12 H 0 ÿ E; 1…”

New description of orbital motion with arbitrary angular momenta

“…The results for the positronium negative ion are compared to other calculations [22][23][24][25][26][27] in Table II. The energy obtained at the dimension K is also shown. The trial function of case (i) does not produce good result, which is not surprising because the interparticle correlation is poorly represented in this case.…”