We report on recent improvements to our non-perturbative calculation of the positronium spectrum. Our Hamiltonian is a two-body effective interaction which incorporates one-photon exchange terms, but neglects fermion self-energy effects. This effective Hamiltonian is diagonalized numerically in a harmonic oscillator basis at strong coupling (α=0.3) to obtain the mass eigenvalues. We find that the mass spectrum compares favorably to the Bohr spectrum of non-relativistic quantum mechanics evaluated at this unphysical coupling.
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