Two-body $P$-state energies at ${\alpha }^6$ order

Abstract

We present an analytical calculation of the complete ${\alpha }^6$ correction to energies of $nP$-levels of two-body systems consisting of the spin-$0$ or $1/2$ extended-size particles with arbitrary masses and magnetic moments. The obtained results apply to a wide class of two-body systems such as hydrogen, positronium, muonium, and pionic or aniprotonic helium ion. We found an additional ${\alpha }^6$ correction for $nP$-levels of positronium, which was previously overlooked. Our results are also relevant for light muonic atoms, whose accurate theoretical predictions are required for extracting the nuclear charge radii.

arXiv comment14 pages, 1 figure, corrected the second-order iteration of the Breit Hamiltonian, final results for positronium P-states agree now with former calculations

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Cited by in corpus (1)

• Stability conditions for bound states in antiprotonic atoms