Hydrogen and hydrogen-like-ion bound states and hyperfine splittings: finite nuclear size effects

2023/02/13 by Igor Kuzmenko, Kuzmenko, Igor, Tetyana Kuzmenko +5
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #Atomic and Molecular Physics #FOS: Physical sciences #Nuclear physics research studies #Quantum Physics (quant-ph) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.2302.06288

openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

Using the Dirac equation, we study corrections to electron binding energies and hyperfine splittings of atomic hydrogen and hydrogen-like ions due to finite nuclear size (FNS) effects, relativistic QED radiative corrections and nuclear recoil corrections. Three models for the charge distribution and the magnetic moment distribution within the nucleus are considered. Calculations are carried for light atoms (H, He and K) and heavy atoms (Rb, Cs, Pb, Bi, U). The FNS corrections to the ground-state energy are shown to be smaller than the electron-nucleus reduced mass corrections, and comparable to the relativistic QED radiative corrections for the light nuclei, but much larger than both these corrections for heavy nuclei. Comparison is made with an experiment on the 1s-2s transition frequency for hydrogen. FNS corrections to the ground state hyperfine splitting are comparable in size to the relativistic QED radiative corrections for light nuclei, but are larger for heavy nuclei.

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