Proton size from precision experiments on hydrogen and muonic hydrogen atoms

Abstract

The "proton radius puzzle" was recently solved by reducing the four-standard deviation discrepancy between the results for electronic hydrogen (H) and muonic hydrogen (µH) atoms to 3.3 value. The value of the root-mean-square radius of the proton (rp), extracted from experiments on measuring the one-photon 2s − 4p transition and the Lamb shift in hydrogen, is now 0.8335(95) fm, that is in good agreement with the muonic hydrogen experiments, 0.84087(39) fm. Even so, these values deviate significantly from the CODATA value, which is determined as the average using the results for various spectral lines including two-photon transitions in the hydrogen atom. The solution of the proton radius puzzle was realized by taking into account the influence of interference effect in one-photon scattering processes. The importance of interfering effects in atomic frequencies measurements gives an impetus to the study of experiments based on two-photon spectroscopy with the suchlike thoroughness. It is shown here that the effect of interfering pathways for two-photon 2s − nd transitions in a hydrogen atom is also significant in determining the proton charge radius and Rydberg constant.

Angular correlations in two-photon spectroscopy of hydrogen

“…It is important to note that numerical values of NR corrections given by Eqs. ( 33)-( 36) are turned out several times less than the same NR corrections calculated recently in [13] for the other type of experiment monitoring the rate of 2s state quenching [8,9]. The difference with present results actually arises due to the rejected transiton matrix element of the emitted photon in the amplitude of scattering process used in [13].…”

“…( 33)-( 36) are turned out several times less than the same NR corrections calculated recently in [13] for the other type of experiment monitoring the rate of 2s state quenching [8,9]. The difference with present results actually arises due to the rejected transiton matrix element of the emitted photon in the amplitude of scattering process used in [13]. It can be concluded that the detection of the excited ns/nd fraction of atoms via its fluorescence has a considerably higher potential accuracy than the experiments monitoring the rate of metastable state quenching [10].…”

“…In [10] it was shown that the detection of the excited ns/nd fraction of atoms via its fluorescence has a considerably higher potential accuracy than the experiments monitoring the rate of metastable state quenching [8,9], which were limited by a large background of unexcited 2s atoms. Recently, in [13] it was shown that nonresonant (NR) correction to the 2s F =1 1/2 − nd F =2 3/2(5/2) transition frequencies measured in the experiments of the type [8,9] reaches the level of several kHz, making it significant in determining the proton charge radius r p and Rydberg constant R ∞ . In particular, taking into account for NR correction the averaged values of r p were found as coinciding with the resuts reported in [1].…”

Thermal corrections for positronium

“…The excellent agreement of theoretical and experimental results up to this level is in some cases violated [13][14][15][16], which directs scientific attention to the verification of fundamental interactions, which, in turn, pursues the goal of eliminating such contradictions [17][18][19]. In such cases, a critical analysis of theoretical calculations of energies, fine structure, isotope shifts, etc is required for states in various atomic systems, revealing unresolved discrepancies with experiment, to determine fundamental constants or interactions [20], to set constraints to dark matter [21].…”

Analysis of nonresonant effects in the two-photon spectroscopy of helium

“…transition frequencies in hydrogen [23], the correction equation ( 11) also does not depend on the angles between any pair of the vectors ν 3 , e 1 and e 2 . Therefore, the asymmetry of observed line profile cannot be eliminated by choosing 'magic' angles or experimental geometry as in [1,2].…”