Second-order Doppler shift using

The recoil-free fraction depends on the oxidation state, the spin state, and the elastic bonds of the Mossbauer atom. Therefore, a temperature-dependent transition of the valence state, a spin transition, or a phase change of a particular compound or material may be easily detected as a change in the slope, a kink, or a step in the temperature dependence of In f T). However, in fits of experimental Mossbauer intensities, the values of 0 and Meff are often strongly covariant, as one may expect from a comparison of the traces shown in Fig. 2.5b. In this situation, valuable constraints can be obtained from corresponding fits of the temperature dependence of the second-order-Doppler shift of the Mossbauer spectra, which can be described by using a similar approach. The formalism is given in Sect. 4.2.3 on the temperature dependence of the isomer shift. 

Fig. 4.2 Temperature dependence of the isomer shift due to the second-order Doppler shift, sod- The curves are calculated for different Mossbauer temperatures 0m by using the Debye model whereby the isomer shift was set to (5 = 0.4 mm s and the effective mass to Meff =100 Da, except for the dashed curve with Meff = 57 Da...

With an appropriate choice of B the compensation is effective for all atomic velocities. As the velocity of the thermal beam of hydrogen atoms at 300 K is not well known, the magnetic field will be used to measure precisely the velocity distribution, and so the second order Doppler shift. 

The method of symmetric points was used to determine the center of the interference curve. Extensive calculations showed that the line profile should be symmetric about the center frequency. The line center was then corrected for the second order Doppler shift, The Bloch-Siegert and rf Stark shifts, coupling between the rf plates, the residual F=1 hyperfine component, and distortion due to off axis electric fields. A small residual asymmetry in the average quench curve was attributed to a residual variation of the rf electric field across the line and corrected for on the assumption this was the correct explanation. Table 1 shows the measured interval and the corrections for one of the 8 data sets used to determine the final result. 

First order Doppler broadening can be eliminated by using a standing wave geometry (i.e. oppositely running waves) to excite the two-photon transition. The fractional second order Doppler shift, v1 c2, is less than 2 x 10-16 at a temperature of 1 mK. 

Values from ref. 125 have been corrected for the zero-point motion in the second-order Doppler shift by up to 0-006 mm s . Data from ref. 126 were quoted relative to Ba/CaFj and have been converted using CsCl as the reference, but the errors quoted are the original values. 

Abstract. This paper deals with high resolution spectroscopy of hydrogen and deuterium atoms. The 1S-3S and 2S-6S/D transitions have been used to determine the ground state Lamb shift with an accuracy of 46 kHz. The aim of the present experiment is to make an absolute frequency measurement of the 1S-3S transition. We present in this paper the improvement on the experiment and the developpment of a new method to compensate the second order Doppler effect by the application of a magnetic field. 

Mossbauer Spectroscopy. Mdssbauer spectroscopy has been used as a powerful technique to probe the electronic structure of the five- and six-coordinate ferrous nitrosyl porphyrins. The isomer shifts of both types of complexes (5 0.35 mm s ) are similar and show temperature dependences that are consistent with a second-order Doppler effect, but are slightly smaller than those of most other iron(II) porphyrin complexes (5 0.45 mm Unlike the isomer... 

The velocity of a fast accelerated atom is typically 1 mm/ns compared to an average thermal velocity of lO mm/s. Thus the kinematics becomes important the first-order Doppler shift can be as large as 100 A and the second-order shift several GHz. Thus resonant three-level spectroscopy, using only one laser field can be carried out by Doppler tuning the energy levels appropriate. A simplified three-level system is shown in Fig.2. The excited velocity classes determined by... 

An experimental realization of the controlled frequency chirp uses amplitude modulation of the laser with the modulation frequency 2l. The sideband at

atomic transition and can be matched to the time-dependent Doppler shift by changing k2i(t) in time. In order to compensate for optical pumping into other levels than F" = 2 by overlap of the laser with other hfs components, the transition F" = I F = 2 is simultaneously pumped (Fig. 9.5). This can be achieved if the pump laser is additionally modulated at the second frequency 22, where the sideband >l -I- matches the transition F" = 1 F = 2 [1123, 1126]. 



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