Abstract
Explicit calculations were performed to verify that a previously derived relativistic three-fermion equation [Phys. Lett. A 158 (1991) 361] contains the complete O(α 4) physics. Perturbative solutions of the ground state eigenenergy, to O(α 4), are presented for equal mass systems, such as Ps -, as well as for helium-like systems. Results for the helium-like system agree with those obtained from the Breit equation in the Pauli approximation. The relativistic corrections to the Ps - energy are very small.
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