Doppler relativistic

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. 

Now let us study Fig. 12 again and seek the direction (l) in which the traveler should experience zero Doppler shift. She should not look backward because in that direction there is a redshift. Nor should she look directly sideways because even then there is a redshift, the relativistic transverse redshift. As forward is the blueshift, she should look slightly forward. The way to find the zero Doppler shift for incoming light (a) is as follows ... 

Thus the Doppler shift is the difference between the Doppler-shifted wavelength (k) and the original wavelength (A0) divided by Aq- The numerator is the classical Doppler redshift from a moving light source, while the denominator represents the red-shift caused by the relativistic time dilation resulting from the total velocity, which is independent of the direction of motion. 

For laser light impinging onto an absorber moving at relativistic velocity, the resonance frequency is shifted relative to the transition frequency vq in the rest frame of the ions according to the relativistic Doppler formula... 

Abstract. Using Doppler-tuned fast-beam laser spectroscopy the ls2p 3Po - 3Pi fine structure interval in 24Mg10+ has been measured to be 833.133(15) cm-1. The calibration procedure used the intercombination ls2s 1So - ls2p 3Pi transition in 14N5+. The result tests quantum-electrodynamic and relativistic corrections to high precision calculations, which will be used to obtain a new value for the fine structure constant from the fine structure of helium. 

Using centroids obtained from the fits, together with eqn. 1 and the relativistic Doppler formula, our result for the 24Mg10+ 3Po - 3Pi fine structure interval is AEoi = 833.133(15) cm-1. The contributions to the final error are shown in table 1. The largest contribution is from the estimate of the difference of the actual, non-equilibrium, energy loss in the thin foil, and the standard, tabulated (thick foil) energy loss data [25],... 

The laser-induced X-ray count rate data, normalized to laser power and beam current, were fitted with a Lorentzian using a least-squares technique to obtain the resonance centroid in the laboratory frame. The average resonance width, corrected to the rest frame of the ions, was 8.5 0.4 cm-1, compared to the natural width of 8.0 cm-1. This is consistent with some saturation in the transition probability and also in the detection sensitivity of the proportional counter at increased count rate. The wavenumber of the resonance centroid, in the rest frame of the moving ion, is obtained using the relativistic Doppler formula,... 

Although various interchanges of laser wavelengths, power meters, etc. will be made to control systematics, the basic technique for the measurement is indicated in fig. 5. The lasers are set on laser lines approximately equidistant from, but on either side of the resonance centroid, and balanced in power. The lasers are chopped in anti-phase and the difference signal, S(u> 1) — S(u>2) is recorded. The beam velocity is varied till the zero-crossing (where the signals are equal) is found. The resonance centroid (in the ion s rest frame) is then obtained from the relativistic Doppler formula and the mean of the two laser frequencies. 

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. 

The fine structure interval AEqi is obtained from the laser wavenumber and the ion beam velocity using the relativistic Doppler formula. To caUbrate the 90° analysing magnet we tuned a beam from the tandem accelerator,... 

Using centroids obtained from the fits, together with eqn. 1 and the relativistic Doppler formula, our result for the Po - Pi fine structure interval... 

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

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