Frequency shift, 0 electrodynamics

Furthermore, as mentioned above the screening of the dipole field by the conduction electrons can be represented by an image dipole inside the metal. This complex of the chemisorbed molecule and its image has a vibration frequency different from that of the free molecule. The electrodynamic interaction between a dipole and its image has been discussed in many works. The theoretical problem is that the calculated frequency shift is extremely sensitive to the position of the image plane (Fig. 3a). One can with reasonable parameter values obtain a downward frequency shift of the order of 5-50 cm S but the latest work indicates that the shift due to this interaction is rather small. 

Leung, P. T, and Hider, M. H. (1993] Nonlocal electrodynamic modeling of frequency shifts for molecules at rough surfaces,/ Chem. Phys., 98, 5019-5022. 

Equation (2.98) describes the frequency shift of a classical harmonic oscillator, 5E , located above a surface at distances much less than the wavelength of its oscillations (Chance et al. 1975b). A rigorous quantum-electrodynamical treatment of the problem (Wylie and Sipe 1984, 1985) predicts, besides this classical term, a correction term arising from the van der Waals interaction between atom and surface. The total shift of the electronic energy level a can be written as... 

By comparison of one quarter of the IS1 — 25 transition frequency with the 25 — 45 and 25 — 4D transition frequency, the main energy contributions described by the simple Rydberg formula are eliminated. The remaining difference frequency (about 5 GHz) is determined by well known relativistic contributions, the hyperfine interaction, and a combination of Lamb shifts. Since quantum electrodynamic contributions scale roughly as 1/n3 with the principal quantum number, the Lamb shift of the 15 level is the largest. 

The discovery of the 25 — 2P Lamb shift has led to the development of the theory of quantum electrodynamics. Today, radio frequency measurements of this splitting have reached the uncertainty limits imposed by the 100 MHz natural linewidth of the 2P state. The considerably sharper optical two-photon resonances used in optical experiments leave significant room for future improvements. 

A dimensionless frequency ratio, such as f(lS-2S)/f(2S-nS), on the other hand, is independent of the Rydberg constant. Its measurement can serve as a sensitive test of quantum electrodynamic level shifts and as a means to determine the size of the proton or deuteron, provided QED is correct. 

The possibilities of Doppler-free two-photon spectroscopy for metrology and fundamental physics has been impressively demonstrated by precision measurements of the 1S-2S transition in atomic hydrogen [260-263]. Precise measurements of this one-photon forbidden transition with a very narrow natural linewidth of 1.3 Hz yield accurate values of fundamental constants and can provide stringent tests of quantum electrodynamic theory (Sect. 9.7). A comparison of the 1S-2S transition frequency with the 2S-3P frequency allows the precise determination of the Lamb shift of the 15 ground state [261], whereas the 2S Lamb shift was already measured long ago by the famous Lamb-Rutherford experiments where the RF transition between 25 1/2 and 2P /2 were observed. Because of the isotope shift the 15-25 transitions of and differ by... 

Since the measurements on RBC exhibit such beautiful quantitative agreement with theory one has concluded that the electrodynamic part of the basic equations needs improvement. This was the motivation for introducing the WEM (Section 13.2). The linear stability calculations for the conductive mode have been carried out within this model [48, 49] using the same approximations which led to the analytic threshold formulas within the SM [12-15]. It is found that there is an upward shift in the threshold, which may be quite small, and, more importantly, a Hopf bifurcation with critical frequency... 

We end this section by remarking that neglecting Etmg in the absorption does not allow to predict an interesting effects of the electrodynamics coupling between molecule and plasmon excitations the shifts of the absorption frequencies, of both the molecule and the plasmonics nanoparticle. 

With the envisioned higher resolution, it should be possible to determine a better value of the electron/proton mass ratio from a precise measurement of the isotope shift. And a measurement of the absolute frequency or wavelength should provide a new value of the Rydberg constant with an accuracy up to 1 part in 10, as limited by uncertainties in the fine structure constant and the mean square radius of the proton charge distribution. A comparison with one of the Balmer transitions, or with a transition to or between Rydberg states could provide a value for the IS Lamb shift that exceeds the accuracy of the best radiofrequency measurements of the n=2 Lamb shift. Such experiments can clearly provide very stringent tests of quantum electrodynamic calculations, and when pushed to their limits, they may well lead to some surprising fundamental discovery. 

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