Relativistic Doppler effect

The second-order Doppler shift, (5sod> which is often called temperature shift, is a peak shift related to the relativistic Doppler effect originating from the thermal motion of the nuclei. If the Mossbauer atom has a speed u, and moves in a direction making angle a with the direction of the y ray it emits, then the v frequency of the emitted y ray will differ from the Vo frequency it had if the atom had been at rest. The v frequency is related to Vo in the following way ... 

The considerable Doppler shift in all collinear-beam experiments has opened up a few general applications beyond the spectroscopy of particular atomic or molecular systems. The scope of such applications ranges from simple beam velocity analyses to precision experiments related to metrology or problems of fundamental physics. These latter include the calibration of high voltages and measurements of the relativistic Doppler effect, for which the atomic transition frequency provides an intrinsic clock. 

The advantages of the collinear geometry and a purely relativistic Doppler effect can be combined in a resonant two-photon absorption experiment. The two photons are absorbed from the direct and the retroreflected laser beam of frequency pl, and a few atomic systems have intermediate states that can be tuned into resonance at a beam velocity selected by... 

The inherent resolution of collinear-beam spectroscopy is still limited by the residual Doppler broadening. In beams with a broad velocity distribution the labeling of one velocity class by optical pumping, probed in a second Doppler-tuning zone, was exploited already before narrow Doppler widths were achieved. The complete elimination of the first-order Doppler effect in resonant two-photon absorption on Ne I has been discussed in Section 3.3, in connection with a precision measurement of the relativistic Doppler effect. A similar experiment was performed on In I, where the 29p Rydberg state was excited from 5p Pi/2 via 6s Si/2 and detected by field ionization. The linewidth caused by the laser jitter can be reduced to the transit-time limit of a few hundred kilohertz. 

These three fluctuating effects, with their respective orders of magnitude, account for the observed standard deviation 6xi0-9 ( 2.5 kHz), which therefore represents the effective uncertainty on our measurement. Residual first order Doppler effect and relativistic corrections are negligible at this scale. 

Doppler-effect energy. Since F and v are both much smaller than the speed of light it is permissible to use non-relativistic mechanics. 

The relativistic equation [8] for the Doppler effect on an emitted photon gives the observed frequency v for a closing velocity v as... 

That is, in the non-relativistic afqrroximation. The Doppler effect, with the change of the electromagnetic wave frequency due to the motion (even uniform) of the emitting object, is seen in the experiment The effect is of the relativistic character i.e.. it vanishes if we assume the infinite velocity of light. 

The usual experimental set-up works in transmission geometry as shown in fig. 5 (top) The strength of resonance absorption is determined by the reduction of y-ray intensity reaching the detector. Not taking into account the hyperfine interactions, to be discussed later, and neglecting a small relativistic effect (the second-order Doppler shift) one has an exact energy match for the zero-phonon lines of N(E) and Resonance absorption is now strongest. 

The recoil effect, however, is not the only cause of a shift of the line center. Using the relativistic laws of conservation of energy and momentum yields the following exact formula for the Doppler shift ... 

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