Recoil term

An important consideration is the relative importance of the two processes that supply radionuclides to the dissolved and adsorbed inventories from within the host rock minerals. The recoil term in Equation (1), bsiA,pPR, can be compared to the weathering... 

Leading recoil corrections in Za (of order (Za) (m/M)") still may be taken into account with the help of the effective Dirac equation in the external field since these corrections are induced by the one-photon exchange. This is impossible for the higher order recoil terms which reflect the truly relativistic two-body nature of the bound state problem. Technically, respective contributions are induced by the Bethe-Salpeter kernels with at least two-photon exchanges and the whole machinery of relativistic QFT is necessary for their calculation. Calculation of the recoil corrections is simplified by the absence of ultraviolet divergences, connected with the purely radiative loops. 

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]... 

Rydberg constant, where c is the speed of light and h the Planck constant. QED corrections for radiative effects e ad are of order a due to the lepton magnetic anomalies, recoil contributions e ec are of order ame/rtin and combined radiative and recoil terms Brad-rec start at The strong interaction adds... 

Table 4.1 summarizes the various contributions to the energy, expressed as a double expansion in powers of a 1/137.036 and the electron reduced mass ratio ji./M 10 . Since all the lower-order terms can now be calculated to very high accuracy, including the QED terms of order Ry, the dominant source of uncertainty comes from the QED corrections of order Ry or higher. The comparison between theory and experiment is therefore sensitive to these terms. For the isotope shift, the QED terms independent of /x/M cancel out, and so it is only the radiative recoil terms of order a fx/M 10 Ry ( 10 kHz) that contribute to the uncertainty. Since this is much less than the finite nuclear size correction of about 1 MHz, the comparison between theory and experiment clearly provides a means to determine the nuclear size. 

The velocities of very cold atoms are very small, i.e., the linear and the quadratic Doppler effects both become small and the recoil term becomes significant. It turns out that for cold Ca atoms at T = 10 pK, the recoil effect leads to large asymmetries in the Lamb dips of absorption spectra taken with short pulses [1119]. These are not found in experiments performed at room temperature, where the broad Doppler background masks these asymmetries, and they are based on the fundamental asymmetry between absorption and stimulated emission with short pulses. 

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