Anomalous magnetic moment of the positronium ion

Abstract

We determine the gyromagnetic factor of the positronium ion, a three-body system consisting of two electrons and a positron, including first relativistic corrections. We find that the g-factor is modified by a term α − ( ) 0.51 1 2 , exceeding 15 times the α 2 correction for a free electron. We compare this effect with analogous results found previously in atomic positronium and in hydrogenlike ions.

Electromagnetic moments of the bound system of charged particles

“…Table I presents expectation value of operators in the ground state of Ps − calculated numerically, where the uncertainty for our total g-factor g Ps − is estimated by 2 α 4 δg. Our value for δg is in agreement with the one obtained in [10] −0.51(1), but is significantly more accurate and includes the leading QED effects. Surprisingly we do not agree with the corresponding formula obtained in [10], which is much different and not equivalent to that of ours in Eq.…”

Magnetic moment of the positronium ion and virial relations

“…In addition to revealing the equivalence of the two published results [3,4], it allows us to eliminate one of the three expectation values and thus present a new expression, simpler and more precise, for the magnetic moment of Ps-.…”

“…The values of A and B agree with the more precise evaluations by Frolov [7], The results for Abound found recently in Refs. [3,4] are (for now neglecting self-interaction corrections, taking gfree -»• 2), respectively,…”

“…Equation (13) is but one example of hypervirial relations that can be used to check the accuracy of variational calculations. This is a welcome development, now that Pshas become more accessible to precise measurements [14], where we have included the actual value of the free-positron g factor, using the result of [4] (rather than approximating 8free 2 as in [3]). Taking the recently measured gtree of the electron [10] and the values of A and B from [7], we confirm and improve the result of [4], as well as the less precise result [3], Abound --0.510551 028 187 6(6)a2 + 0 ( a 4).…”

“…The two electrons in Ps form a spin singlet, so the entire magnetic interaction is due to the positron, whose gyromagnetic ratio is, however, slightly modified by the binding. This binding effect, of the order of the fine-structure constant squared, a 2, has recently been determined using two different approaches [3,4], with the latter one being more precise. The result is the expectation value of a combination of three operators, involving the kinetic and the potential energies of the positron, and a correlation of position vectors of the three particles.…”