Doppler motion

Mossbauer resonance of Zn to study the influence of the gravitational field on electromagnetic radiation. A Ga ZnO source (4.2 K) was used at a distance of 1 m from an enriched ZnO absorber (4.2 K). A red shift of the photons by about 5% of the width of the resonance line was observed. The corresponding shift with Fe as Mossbauer isotope would be only 0.01%. The result is in accordance with Einstein s equivalence principle. Further gravitational red shift experiments using the 93.3 keV Mossbauer resonance of Zn were performed later employing a superconducting quantum interference device-based displacement sensor to detect the tiny Doppler motion of the source [66, 67]. 

The normal experimental technique is to scan rapidly through the velocity range and repeat this scan many times imtil data of the required accuracy has been accumulated. The Doppler motion is provided by an electromechanical drive system controlled by a servo -amplifier. Usually, the source is attached to the drive shaft and driven either in a saw-tooth or a triangular constant acceleration wave form. The transducer is coupled to a multichannel analyser operating in the multiscaler mode, and the servo-amplifier is controlled by the channel advance frequency. The dwell time in each channel, corresponding to a specific velocity increment, is 100 ps, and while the channel gate is open it accepts pulses from the detector. 

A relativistic temperature-dependent contribution to the IS exists. Since the emitting (or absorbing) atom vibrates on its lattice site, the emitted photon is affected by this Doppler motion. The observed frequency, v, of the photon compared with its frequency, v, from a stationary source is given by... 

Since the Mossbauer effect is intimately related to any motion of the emitting or absorbing nucleus on either a microscopic or macroscopic scale, Mossbauer spectroscopy provides a potential means by which information on nuclear dynamics, and hence on the dynamics of a system in which the Mossbauer nucleus acts as a probe, can be obtained. Any motion of the Mossbauer nucleus can influence the Mossbauer spectrum in two ways. Firstly, because this motion may be related to the vibrational properties of the system it can influence the recoil-free fraction and hence the absorption intensity of the spectrum itself. Since the absolute absorption intensity is dependent on a large number of other factors, which may be diflicult to determine accurately, any change in recoil-free fraction is most usefully followed as a function of temperature in order to obtain information on the vibrational properties of the system. The second way in which the effects of any motion of the Mossbauer nucleus in the source or absorber are manifested is in the Mossbauer spectroscopic linewidths, as this motion can be thought of as an additional Doppler motion which may partially smear out the resonant absorption. Since the linewidths are also... 

Any motion of the Mossbauer nucleus can influence the spectrum in two ways, by affecting the absorption intensity of the spectrum itself, and also the linewidth, eventually the lineshape, as a result of a kind of additional Doppler motion. 

Nuclear y-ray resonance spectroscopy. This technique is based on the resonance absorption of y radiation and is more conventionally known as Mossbauer spectroscopy. The source of the radiation is a nuclide fixed in a solid crystal lattice held below the Debye temperature. In this condition, y radiation of energies less than 150 keV are emitted with no loss of energy. Such quantized y photons can undergo resonance absorption by the appropriate identical stable nuclide in a solid sample matrix. If the chemical environment of the absorbing nuclide is different from the emitter, energy must be added or subtracted from the radiation to establish resonance. This can be achieved by introducing net motion to the source or absorber to establish a Doppler motion energy term. 

Mossbauer measurements are relatively easy to perform for certain isotopes and give a surprising amount of information. The experiments involve determination of the counting rate of y rays emitted by a source and passed through an absorber. The counting rate is measured as a function of the Doppler motion of the source and absorber. Doppler velocities are low, generally less than 5 cm/sec. 

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... 

This expression shows diat if die detuning Acuj is negative (i.e. red detuned from resonance), dieii die cooling force will oppose die motion and be proportional to die atomic velocity. The one-diniensional motion of die atom, subject to an opposing force proportional to its velocity, is described by a damped haniionic oscillator. The Doppler damping or friction coefficient is die proportionality factor. 

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. 

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. 

Identification of a molecule known in the laboratory is usually unambiguous because of the uniqueness of the highly precise transition frequencies. However, before frequencies detected in the interstellar medium can be compared with laboratory frequencies they must be corrected for the Doppler effect (see Section 2.3.2) due to the motion of the clouds. In Sagittarius B2 the molecules are found to be travelling fairly uniformly with a velocity of... 

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-... 

In an actual Mdssbauer transmission experiment, the radioactive source is periodically moved with controlled velocities, +u toward and —d away from the absorber (cf. Fig. 2.6). The motion modulates the energy of the y-photons arriving at the absorber because of the Doppler effect Ey = Eq + d/c). Alternatively, the sample may be moved with the source remaining fixed. The transmitted y-rays are detected with a y-counter and recorded as a function of the Doppler velocity, which yields the Mdssbauer spectrum, r(u). The amount of resonant nuclear y-absorption is determined by the overlap of the shifted emission line and the absorption line, such that greater overlap yields less transmission maximum resonance occurs at complete overlap of emission and absorption lines. 

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... 

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