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        "description": "The result is exact in the mass ratio within the specified perturbative order and point-particle model. It is not an all-orders atomic spectrum, a calculation of every radiative or annihilation contribution, or a treatment of proton structure. States with nonzero orbital angular momentum are addressed through other cited work. The authors report checks against earlier numerical and equal-mass results; the complete integral reduction and numerical implementation have not been independently reproduced here. Extension to order (Zα)^7 is proposed rather than completed.",
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      "statement": "# Analytic arbitrary-mass pure-recoil corrections for two-fermion atomic S states\n\nAdkins, Gomprecht, Li and Shinn obtained analytic pure-recoil energy corrections at order (Zα)^6 for Coulombic S states of two spin-1/2 particles, retaining the full dependence on their mass ratio. Their calculation combines nonrelativistic-QED contributions with relativistic matching integrals expressed through harmonic polylogarithms, and gives both spin-averaged and hyperfine corrections. The result connects unequal-mass systems such as muonium to the equal-mass positronium limit and identifies corrections to earlier mass-ratio expansions.\n\n## Scientific scope\n\nThe result is exact in the mass ratio within the specified perturbative order and point-particle model. It is not an all-orders atomic spectrum, a calculation of every radiative or annihilation contribution, or a treatment of proton structure. States with nonzero orbital angular momentum are addressed through other cited work. The authors report checks against earlier numerical and equal-mass results; the complete integral reduction and numerical implementation have not been independently reproduced here. Extension to order (Zα)^7 is proposed rather than completed.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nGregory S. Adkins; Jonathan Gomprecht; Yanxi Li; Evan Shinn\n\nThese are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.\n\n\n\n## Original sources\n\n- [Recoil Corrections to the Energy Levels of Hydrogenic Atoms (Physical Review Letters130,023004)](https://scoap3-prod-backend.s3.cern.ch/media/files/75036/10.1103/PhysRevLett.130.023004.pdf)\n",
      "summary": "Adkins, Gomprecht, Li and Shinn obtained analytic pure-recoil energy corrections at order (Zα)^6 for Coulombic S states of two spin-1/2 particles, retaining the full dependence on their mass ratio. Their calculation combines nonrelativistic-QED contributions with relativistic matching integrals expressed through harmonic polylogarithms, and gives both spin-averaged and hyperfine corrections. The result connects unequal-mass systems such as muonium to the equal-mass positronium limit and identifies corrections to earlier mass-ratio expansions.",
      "title": "Analytic arbitrary-mass pure-recoil corrections for two-fermion atomic S states"
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