Recoil correction nuclear

The experimental value is in agreement with the present result of the theoretical calculation as quoted in section 2. It confirms the QED calculations of the order a/V on the 1 % level. It is also sensitive to the nuclear recoil correction. 

The complete aZ-dependence formulas for the nuclear recoil corrections in high Z few-electron atoms were derived in Ref. [21]. As it follows from these formulas, within the (aZ)4m2/M approximation the nuclear recoil corrections can be obtained by averaging the operator... 

Let as apply this formalism to the case of a single level a in a one-electron atom. To find the Coulomb nuclear recoil correction we have to calculate the contribution of the diagram shown in Fig. 1. A simple calculation of this diagram... 

The one-transverse-photon nuclear recoil correction corresponds to the diagrams shown in Fig. 2. One easily obtains... 

The two-transverse-photon nuclear recoil correction is defined by the diagram shown in Fig. 3. We find... 

The nuclear recoil correction is the sum of the one-electron and two-electron contributions. The one-electron contribution is the sum of the expressions (15) for the a and b states. The two-electron contributions are defined by the diagrams shown in Figs. 4-6. A simple calculation of these diagrams yields... 

One of the main goals of the calculations of Refs. [25,26,33] was to evaluate the nuclear recoil correction for highly charged ions. In the case of the ground state of hydrogenlike uranium these calculations yield -0.51 eV for the point nucleus case [25] and -0.46 eV for the extended nucleus case [33], This correction... 

For low Z, in addition to the corrections considered here, the Coulomb inter-electronic interaction effect on the non-relativistic nuclear recoil correction must be taken into account. It contributes on the level of order (1 /Z)(aZ)2m2/M. 

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. 

Unlike the proton, the deuteron is a weakly bound system so one cannot simply use the results for the hydrogen recoil and structure corrections for deuterium. What is needed in the case of deuterium is a completely new consideration. Only one minor nuclear structure correction [72, 73, 74, 75] was discussed in the literature for many years, but it was by far too small to explain the difference between the experimental result in (12.25) and the sum of nonrecoil corrections in (12.28)... 

The book is organized as follows. In the introductory part we briefly discuss the main theoretical approaches to the physics of weakly bound two-particle systems. A detailed discussion then follows of the nuclear spin independent corrections to the energy levels. First, we discuss corrections which can be calculated in the external field approximation. Second, we turn to the essentially two-particle recoil and radiative-recoil corrections. Consideration of the spin-independent corrections is completed with discussion of the nuclear size and structure contributions. A special section is devoted to the spin-independent... 

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. 

There have been a number of recent reviews of hydrogenic systems and QED [9]-[12] these proceedings contain the most extensive and recent information. To calculate transition frequencies in hydrogen to an accuracy comparable with the experimental precision which has been achieved [3], it is necessary to take into account a large number of corrections to the values obtained using the Dirac equation. These include quantum electrodynamic (QED) corrections, pure and radiative recoil corrections arising from the finite nuclear mass, and a correction due to the non-zero volume of the nucleus. The evaluation of these corrections is an extremely challenging task. 

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. 

As it follows from Ref. [13], the formulas (3)- (5) will incorporate partially the nuclear size corrections to the recoil effect if Vib(r) is taken to be the potential of an extended nucleus. In particular, this replacement allows one to account for the nuclear size corrections to the Coulomb part of the recoil effect. In Ref. [33], where the calculations of the recoil effect for extended nuclei were performed, it was found that, in the case of hydrogen, the leading relativistic nuclear size correction to the Coulomb low-order part is comparable with the total value of the (aZ)em2/M correction but is cancelled by the nuclear size correction to the Coulomb higher-order part. 

In 1S-2S spectra of hydrogen and deuterium, recorded by C. WIEMAN [16] in this way, the observed linewidth remained as large as 100 MHz. Nonetheless, the isotope shift could be measured well enough to yield first experimental evidence for a relativistic correction to the nuclear recoil effect This correction was known theoretically, but was considered too small to be observable. 

Electron affinity of Hydrogen, Deuterium and Tritium. The term AEcorr contains relativistic, relativistic recoil, Lamb shift and finite nuclear size corrections... 

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