Photon recoil shift

In addition to the Rydberg constant a number of different quantities, all based on intrinsically accurate frequency measurements, are needed. Experiments are under way in Stanford in S. Chu s group to measure the photon recoil shift free = fmh/2mcs( of the cesium Di line [48]. Together with the proton-electron mass ratio mp/me, that is known to 2 x 10-9 [49] and even more precise measurements of the cesium to proton mass ratio mcs/mp in Penning traps, that have been reported recently [50], our measurement has already yielded a new value of a [45]. 

In the near future a small improvement in 1 can be expected from ongoing determinations of fr/me in measurements of the photon recoil in Cs atom spectroscopy and a Cs atomic mass measurement [29], The present limitation for accuracy of aj1 arises mainly from the muon mass uncertainty. Therefore any better determination of the muon mass, e.g. through a precise measurement of the reduced mass shift in Z zvls2s, will result in an improvement of 1. 

A study of the electron mass is now of interest also because of determination of the fine structure constant a from the photon-recoil-spectroscopy [22,23], A measurement of the recoil frequency shift... 

The corresponding peaks in the population distribution NkiVz) of molecules in the upper level A ) are shifted due to photon recoil (Fig. 9.2a). They show up, according to (9.5), at the velocity components... 

Since the Doppler broadening is large compared to the recoil shift and the homogeneous linewidth, the probability that the emitted photon is absorbed by any atom is PtoM = n R a = 1. 

The first term wq = (Eg -Ej )/h represents the eigen frequency of the atom in rest if recoil is neglected. The second term is the linear (first-order) Doppler effect, describing the well-known Doppler shift Aw =J< in the absorption frequency of a moving atom. The third term represents the second-order Doppler effect. Note that this term is independent of the direction of V and cannot be eliminated by the methods, discussed in Chap.10, which only overcome the first-order Doppler effect. The last term in (13.14) describes the photon recoil effect, where has been approximated by wq. 

The recoil effect causes an energy shift of the emission line from Eq to smaller energies by an amount r, whereby the y-photon carries an energy of only Ey = Eq — Ep. However, a recoil effect also occurs in the absorption process so that the photon, in order to be absorbed by a nucleus, requires the total energy Ey = Eq+ r to make up for the transition from the ground to the excited state and the recoil effect (for which and Py will have the same direction). 

Non-occurrence of the inverse event was explained by Mossbauer in terms of the energy loss because of atomic recoil, during emission of the 7-ray photon. A simple calculation shows that a photon of frequency 1018 Hz has sufficient momentum to cause an Fe atom to recoil at a velocity of 102 ms-1. Alternatively, the photon is Doppler shifted because of the recoil by an amount... 

Let us start systematic discussion of such corrections with the recoil corrections to the leading contribution to the Lamb shift. The most important observation here is that the mass dependence of all corrections of order a." Za.Y obtained above is exact, as was proved in [1, 2], and there is no additional mass dependence beyond the one already present in (3.7)-(3.24). This conclusion resembles the similar conclusion about the exact mass dependence of the contributions to the energy levels of order (Za) m discussed above, and it is valid essentially for the same reason. The high frequency part of these corrections is generated only by the one photon exchanges, for which we know the exact mass dependence, and the only mass scale in the low frequency part, which depends also on multiphoton exchanges, is the reduced mass. 

The radiative-recoil correction to the Lamb shift induced by the polarization insertions in the exchanged photons was also calculated in [9]. The result of that work contradicts the results in [8, 4]. The calculations in [9] are made in the same way as the calculation of the recoil correction of order (Za) (m/M)m in [10], and lead to a wrong result for the same reason. 

As can be seen from Table 1, the CH result for the transition, 2787.997 eV, is consistent with all other potentials within 0.01 eV. Adding in small three-photon and recoil corrections of -0.033 eV gives a final theoretical prediction of 2787.964 eV for the CH potential. As this disagrees with experiment, new physics must be present. The source of this physics is well known from the hydrogen Lamb shift, where two-loop effects are known to be quite important, and in fact are at present the dominant source of uncertainty, with the only other major unknown in the calculation being the precise size of the proton. We infer, then,... 

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