Relativistic recoil

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

The term AEcorr contains relativistic, relativistic recoil, Lamb shift, and finite nuclear size... 

The contributions that have been considered in order to obtain precise theoretical expressions for hydrogenic energy levels are as follows the Dirac eigenvalue with reduced mass, relativistic recoil, nuclear polarization, self energy, vacuum polarization, two-photon corrections, three-photon corrections, finite nuclear size, nuclear size correction to self energy and vacuum polarization, radiative-recoil corrections, and nucleus self energy. 

In contrast to normal atoms this calculation is not accurate enough because of essential recoil effects. The leading relativistic recoil term for the Is state is of order (Za)2m/M and it depends on the nuclear structure. The difference is free of nuclear influence and the result is [16]... 

Relativistic Recoil Corrections to the Atomic Energy Levels... 

Abstract. The quantum electrodynamic theory of the nuclear recoil effect in atoms to all orders in aZ and to first order in m/M is considered. The complete aZ-dependence formulas for the relativistic recoil corrections to the atomic energy levels are derived in a simple way. The results of numerical calculations of the recoil effect to all orders in aZ are presented for hydrogenlike and lithiumlike atoms. These results are compared with analytical results obtained to lowest orders in aZ. It is shown that even for hydrogen the numerical calculations to all orders in aZ provide most precise theoretical predictions for the relativistic recoil correction of first order in m/M. 

It is known that to the lowest order in aZ the relativistic recoil correction to the energy levels can be derived from the Breit equation. Such a derivation was made by Breit and Brown in 1948 [1] (see also [2]). They found that the relativistic recoil correction to the lowest order in aZ consists of two terms. The first term... 

First attempts to derive formulas for the relativistic recoil corrections to all orders in aZ were undertaken in [11,12]. As a result of these attempts, only a part of the desired expressions was found in [12] (see Ref. [13] for details). The complete aZ-dependence formula for the relativistic recoil effect in the case of a hydrogenlike atom was derived in [14]. The derivation of [14] was based on using a quasipotential equation in which the heavy particle is put on the mass shell [15,16]. According to [14], the relativistic recoil correction to the energy of a state a is the sum of a lower-order term ALL and a higher-order term A Eh ... 

As was shown in [13], to include the relativistic recoil corrections in calculations of the energy levels, we must add to the standard Hamiltonian of the electron-positron field interacting with the quantized electromagnetic field and with the Coulomb field of the nucleus Vc an additional term. In the Coulomb gauge, this term is given by... 

Table 2. The values of the relativistic recoil correction to hydrogen energy levels beyond the Salpeter contribution, in kHz. The values given in the second and third rows include the (aZ)6m2/M contribution and all the contributions of higher orders in aZ. In the last row the sum of the (otZ f m2/M and (otZ)7 og2 (aZ)m2/M contributions is given...

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