English

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

Atomic Physics 2026-02-19 v3

Abstract

We present an analytical calculation of the complete α6\alpha^6 correction to energies of nPnP-levels of two-body systems consisting of the spin-00 or 1/21/2 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 α6\alpha^6 correction for nPnP-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.

Keywords

Cite

@article{arxiv.2401.05922,
  title  = {Two-body $P$-state energies at $\alpha^6$ order},
  author = {Vojtěch Patkóš and Vladimir A. Yerokhin and Krzysztof Pachucki},
  journal= {arXiv preprint arXiv:2401.05922},
  year   = {2026}
}

Comments

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