2022/11/10 by Kuzmenko, Igor, Kuzmenko, Tetyana, Avishai, Y. +1
#Atomic Physics (physics.atom-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2211.05411
Using the Dirac equation, radiative corrections and finite nuclear size and mass corrections, we calculate the 1s-2s quantum transition frequency f1s,2s of hydrogen and its uncertainty due to the uncertainties δme, δmp, δα, δrp, δR∞ of the electron mass me, proton mass mp, fine structure constant α, proton root mean squared charge radius rp, and the Rydberg constant R∞. We use the 2018 CODATA [E. Tiesinga, P. J. Mohr, D. B. Newell, B. N. Taylor, Rev. Mod. Phys. \bf 93, 025010 (2021)] procedure for the calculation of f1s,2s, and the fundamental constants given therein. We find that the value of the experimental frequency lies outside the theoretical uncertainty (the discrepancy between the theoretical and the experimental frequency is Δf1s,2s(2018) = -23.948~kHz). But, by fitting rp we obtain a vanishing discrepancy between the calculated and experimental frequencies and a 6.4 kHz theoretical uncertainty, with rp = 0.830734~fm (and a theoretical uncertainty of δrp = 0.0022 fm), consistent with a recent measurement~[W. Xiong, \itet al., Nature (London) \bf 575, 147 (2019)].