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We report on recent improvements to our non-perturbative calculation of thepositronium spectrum. Our Hamiltonian is a two-body effective interaction whichincorporates one-photon exchange terms, but neglects fermion self-energyeffects. This effective Hamiltonian is diagonalized numerically in a harmonicoscillator basis at strong coupling ($\alpha=0.3$) to obtain the masseigenvalues. We find that the mass spectrum compares favorably to the Bohrspectrum of non-relativistic quantum mechanics evaluated at this unphysicalcoupling.

Non-perturbative Calculation of the Positronium Mass Spectrum in Basis Light-Front Quantization