is the Hamiltonian for atomic hydrogen and is the interaction between the positron and the atom. In (3) to (5), rp (re) is the position vector of the positron (electron) relative to the nucleus. However, when positronium is formed it is more natural to use the "positronium coordinates"
where R is the position vector of the Ps centre of mass relative to the nucleus and t is the Ps internal coordinate. In terms of (6) the Hamiltonian (3) may be alternatively written where
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