Nonresonant corrections to the1s−2stwo-photon resonance for the hydrogen atom

Abstract

The nonresonant (NR) corrections are estimated for the most accurately measured two-photon transition 1s-2s in the hydrogen atom. These corrections depend on the measurement process and set a limit for the accuracy of atomic frequency measurements. With the measurement process adopted in the modern experiments the NR contribution for 1s-2s transition energy can reach 10 −3 Hz while the experimental inaccuracy is quoted to be ± 46 Hz. PACS numbers: 31.30.Jv, 12.20.Ds, 0620Jr., 31.15.-p Nonresonant (NR) corrections have been first introduced in Ref.[1] where the modern QED theory of the natural line profile in atomic physics has been formulated. The NR corrections indicate the limit up to which the concept of the energy of an excited atomic state has a physical meaning -that is the resonance approximation. In the resonance approximation the line profile is described by the two parameters: energy E and width Γ .Beyond this approximation the specific role of E and Γ should be replaced by the complete evaluation of the line profile for the particular process. If the distortion of the Lorentz profile is small one can still consider the NR correction as an additional energy shift. Unlike all other energy corrections, this correction depends on the particular process which has been employed for the measurement of the energy difference. Quite independent of the accuracy 1 of theoretical calculations of the "traditional" energy corrections which can be much poorer than the experimental accuracy, NR corrections define the principal limit for the latter.One can state that nonresonant corrections set the limit for the accuracy of all the atomic frequency standards.Nonresonant corrections have been evaluated for H-like ions of phosphorus (Z=15) and uranium (Z=92) in Refs. [2,3]. While for uranium the NR correction turned out to be negligible, its value was comparable with the experimental error bars in case of phosphorus.Recently the NR correction has been evaluated for the Lyman-α 1s-2p transition in hydrogen [4]. In [4] the process of the resonance photon scattering was considered as a standard procedure for the determination of the energy levels. According to [1] the parametric estimate of the NR correction to the total cross-section is (in relativistic units):

Proton size from precision experiments on hydrogen and muonic hydrogen atoms

“…Then, later, in [12,13], the importance of nonresonant corrections for the Lamb shift measurements and the process of radiative electron capture in highly charged hydrogen-like ions was demonstrated. In further NR corrections were evaluated for the hydrogen atom in [14][15][16][17][18], whereas the most essential NR contribution was found in [19]. It is the nonresonant correction including the fine structure splitting of atomic levels [16,19] represents a special interest in further investigations, see, for example, [20][21][22][23][24][25][26].…”

“…In further NR corrections were evaluated for the hydrogen atom in [14][15][16][17][18], whereas the most essential NR contribution was found in [19]. It is the nonresonant correction including the fine structure splitting of atomic levels [16,19] represents a special interest in further investigations, see, for example, [20][21][22][23][24][25][26]. Recently a theoretical analysis of the experiment [5] was presented in [27], where it was shown that QIE effects should be carefully studied with each specific spectroscopic measurement.…”

“…There is still the problem of calculating the proton charge radius taking into account transitions to higher excited states in the hydrogen atom, the measurements of which are carried out using two-photon spectroscopy. The first attempts to calculate NR corrections to them were made in [16,19], where the negligibly small contributions for the 1s−2s transition frequency with respect to the current level of experimental accuracy were found. Theoretical analysis of such experiments is complicated by the presence of an external electric field acting on the excited atom with a time delay, see [17,18,33].…”

Enhancement of Blackbody Friction due to the Finite Lifetime of Atomic Levels

“…On the other hand, in Ref. [7], the authors explain in the text after Eq. ( 2) that "the velocity [gauge] form follows originally from the [fully relativistic] QED description" and should therefore be used off resonance, for the obvious reason that the nonrelativistic limit of the Dirac matrix vector α, which enters the relativistic expression for the self-energy [17] is the momentum operator p/(mc).…”

Angular correlations in two-photon spectroscopy of hydrogen

“…( 12) we have to take into account all neighboring terms in the sum over n. Then in case of only two neighboring states, only terms in Eq. ( 12) with n = a (leading resonant term to which we introduce NR correction) and n = b (closest by energy to the resonant term) need to be considered [19][20][21][22][23].…”