TTP99-40 CPT-invariant two-fermion Dirac equation with extended hyperfine operator

TTP99-40 CPT-invariant two-fermion Dirac equation with extended hyperfine operator

TTP99-40 CPT-invariant two-fermion Dirac equation with extended hyperfine operator

For the S-states of muonium and positronium, the hyperfine shifts to the order $\alpha^6$ of a recently derived two-fermion equation with explicit $\cal CPT$-invariance are checked against the results of a nonrelativistic reduction, and the leading $\alpha^8$ shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for $r\to 0$ of the Dirac hyperfine operator, such that the resulting extended operator can be used nonperturbatively. The binding correction to magnetic moments is mentioned.

 V. Hund and H. Pilkuhn J. Phys. B33 1617 2000 PDF PostScript arXiv