Doppler shift

The scattering techniques, dynamic light scattering or photon correlation spectroscopy involve measurement of the fluctuations in light intensity due to density fluctuations in the sample, in this case from the capillary wave motion. The light scattered from thermal capillary waves contains two observables. The Doppler-shifted peak propagates at a rate such that its frequency follows Eq. IV-28 and... 

The atom will therefore experience a net restoring force pushing it back to the origin. If the light beams are red detuned F, then the Doppler shift of the atomic motion will introduce a velocity-dependent tenn to the restoring force such that, for small displacements and velocities, the total restoring force can be expressed as the sum of a tenn linear in velocity and a tenn linear in displacement. 

Elementary physies elasses express the so-ealled Doppler shift of a wave s frequeney indueed by movement either of the light souree or of the moleeule (Einstein tells us these two points of view must give identieal results) as follows ... 

For all of the eases eonsidered earlier, a C(t) funetion is subjeeted to Fourier transformation to obtain a speetral lineshape funetion I(co), whieh then provides the essential ingredient for eomputing the net rate of photon absorption. In this Fourier transform proeess, the variable co is assumed to be the frequeney of the eleetromagnetie field experienced by the molecules. The above considerations of Doppler shifting then leads one to realize that the correct functional form to use in converting C(t) to I(co) is ... 

This result, when substituted into the expressions for C(t), yields expressions identieal to those given for the three eases treated above with one modifieation. The translational motion average need no longer be eonsidered in eaeh C(t) instead, the earlier expressions for C(t) must eaeh be multiplied by a faetor exp(- co2t2kT/(2me2)) that embodies the translationally averaged Doppler shift. The speetral line shape funetion I(co) ean then be obtained for eaeh C(t) by simply Fourier transforming ... 

The reaction path shows how Xe and Clj react with electrons initially to form Xe cations. These react with Clj or Cl- to give electronically excited-state molecules XeCl, which emit light to return to ground-state XeCI. The latter are not stable and immediately dissociate to give xenon and chlorine. In such gas lasers, translational motion of the excited-state XeCl gives rise to some Doppler shifting in the laser light, so the emission line is not as sharp as it is in solid-state lasers. 

A method which competes with interferometric distance measurement is laser Doppler displacement. In this approach the Doppler shift of the beam reflected from a target is measured and integrated to obtain displacement. This method also is best suited to use indoors at distances no more than a few hundred meters. Table 2 compares some of the characteristics of these laser-based methods of distance measurement. 

Elastic scattering is also the basis for Hdar, in which a laser pulse is propagated into a telescope s field of view, and the return signal is collected for detection and in some cases spectral analysis (14,196). The azimuth and elevation of the scatterers (from the orientation of the telescope), their column density (from the intensity), range (from the temporal delay), and velocity (from Doppler shifts) can be deterrnined. Such accurate, rapid three-dimensional spatial information about target species is useful in monitoring air mass movements and plume transport, and for tracking aerosols and pollutants (197). 

Multiphoton Absorption and Ionization. High laser powers can induce the simultaneous absorption of two or more photons that together provide the energy necessary to excite a transition this transition may be one that is forbidden as a single-photon process (8,297). Such absorption can be made Doppler-free by propagating two laser beams of frequency V in opposite directions, so the Doppler shifts cancel and a two-photon transition occurs at 2v for any absorber velocity. The signal is strong because aU absorbers contribute, and peak ampHtudes are enhanced by, which may... 

The advent of lasers allowed optical interferometry to become a useful and accurate technique to determine surface motion in shocked materials. The two most commonly used interferometric systems are the VISAR (Barker and Hollenbach, 1972) and the Fabry-Perot velocity interferometer (Johnson and Burgess, 1968 Durand et al., 1977). Both systems produce interference fringe shifts which are proportional to the Doppler shift of the laser light reflected from the moving specimen surface. Both can accommodate a speci-... 

The binary pulsar PSR1913+16. In 1974 Russell Hulse and Joseph Taylor discovered a very special pulsar PSR1916+13. A striking feature that was revealed just after its discovery was a large shift of the pulses rate with a period of a few hours. This was explained by Doppler shift, so PSR1916-H13 is in fact a binary system in which a pulsar orbits about the center of mass of the system. Thanks to the presence of this very stable local clock, Hulse and Taylor were able to obtain all the orbital parameters of this system. By studying the variations of those parameters over nearly twenty years, they... 

Ultrasonic methods can also be applied to velocity measurements based on measurement of the Doppler shift in the frequency of an ultrasonic wave scattered from a moving particle. The angle between the velocity vector and the direction of ultrasound propagation must be known, which practically limits the appHcation of the technique to the measurement of unidirectional flows. However, this Hmitation may be overcome again by the use of an array of transducers [11]. 

Dunning, JW Angus, JC, Particle-Size Measurement by Doppler-Shifted Laser Light, a Test of the Stokes-Einstein Relation, Journal of Applied Physics 39, 2479, 1968. 

Appendix E An Introduction to Second-Order Doppler Shift. 547... 

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. 

Mass absorption is taken as independent of the velocity u, because the Doppler shift is only about 10 " times the y-energy, or less. 

Cahbration spectra must be measured at defined temperamres (ambient temperature for a-iron) because of the influence of second-order Doppler shift (see Sect. 4.2.1) for the standard absorber. After folding, the experimental spectrum should be simulated with Lorentzian lines to obtain the exact line positions in units of channel numbers which for calibration can be related to the hteramre values of the hyperfine splitting. As shown in Fig. 3.4, the velocity increment per channel, Ostep, is then obtained from the equation Ustep = D,(mm s )/D,(channel numbers). Different... 

The experimentally observed isomer shift, (5exp, includes a relativistic contribution, which is called second-order Doppler shift, sod> and which adds to the genuine isomer shift d. 

The temperature dependence of sod is related to that of the recoil-free fraction /(T) = Qxp[— x )Ey / Hc) ], where (x ) is the mean square displacement (2.14). Both quantities, (x ) and can be derived from the Debye model for the energy distribution of phonons in a solid (see Sect. 2.4). The second-order Doppler shift is thereby given as [20]... 

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...

In order to elucidate the physical origin of second-order Doppler shift, sod, we consider the Mossbauer nucleus Fe with mass M executing simple harmonic motion [1] (see Sect. 2.3). The equation of motion under isotropic and harmonic approximations can be written as... 

From a chemical point of view, the second-order Doppler shift is very interesting with respect to its simple relation connecting (5sod, the recoil-free fraction/, and the... 

The incident beam normal to the interface is quasi-elastically scattered by the capillary wave with a Doppler shift at an angle determined by the following equation (Fig. 1) ... 

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