Expansion of bound-state energies in powers ofm/Mand(1−m/M)

2001/12/19 by Ian Blokland, Andrzej Czarnecki, Kirill Melnikov · 2 citations
Engineering · Physics and Astronomy · #Atomic and Molecular Physics #Muon and positron interactions and applications #Particle accelerators and beam dynamics #hep-ph

paper · pdf · doi:10.1103/physrevd.65.073015

published as Phys.Rev.D65:073015,2002 · 9 pages, revtex

arxiv created 2001/12/19 · openalex publication_date 2002/03/19 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Elaborating on a previous Letter [A. Czarnecki and K. Melnikov, Phys. Rev. Lett. 87, 013001 (2001)], we use a new approach to compute energy levels of a nonrelativistic bound state of two constituents, with masses m and M, by systematic expansions---one in powers of m/M and another in powers of (1\ensuremath-m/M). Technical aspects of the calculations are described in detail. Theoretical predictions are given for O(\ensuremathα(Z\ensuremathα)⁵) radiative recoil and O((Z\ensuremathα)⁶) pure recoil corrections to the average energy shift and hyperfine splitting relevant for hydrogen, muonic hydrogen, and muonium.

Citations

• Effective Hamiltonian approach to the bound state: Positronium hyperfine structure
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• Theory of Light Hydrogenlike Atoms

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