Linear Doppler shift

The first term represents the absorption frequency coq = Ek — Ei) of an atom at rest if the recoil of the absorbing atom is neglected. The second term describes the linear Doppler shift (first-order Doppler effect) caused by the motion of the atom at the time of absorption. The third term expresses the quadratic Doppler effect (second-order Doppler effect). Note that this term is independent of the direction of the velocity v. It is therefore not eliminated by the Doppler-free techniques described in Chaps. 2-5, which only overcome the linear Doppler effect. 

Example 9.1 A parallel beam of Ne ions accelerated by 10 keV moves with the velocity = 3 x 10 m/s. When the beam is crossed perpendicularly by a single-mode laser beam tuned to a transition with X = 500 nm, even ions with Vx =Vy=0 show a quadratic relativistic Doppler shift of Av/v = 5 X 10 , which yields an absolute shift of Av = 250 MHz. This should be compared with the linear Doppler shift of 600 GHz, which appears when the laser beam is parallel to the ion beam (Example 4.6). 

Note Equations (3.38) and (3.39) describe the linear Doppler shift. For higher accuracies, the quadratic Doppler effect must also be considered (Sect. 14.1). 

If the excited atom is moving and the projection U of its velocity onto the direction in which it emits a photon is such that Mu /2 3> R, the difference between the radiation frequency and the transition frequency is much greater. The shift of the frequency of the emitted photon with respect to the transition frequency is called the linear Doppler shift and is defined by the expression... 

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. 

The linear speed of the limb of Jupiter (from the text) is 43000 kmh-1 and so the Doppler shift is given by ... 

As shown in Fig. 12 fluid flow can be determined by measuring the doppler shift in laser radiation scattered from particles in the moving fluid stream. No sensor is required in the moving stream. The laser radiation focal point can be moved across the flow tube to measure velocity profiles. Fluid linear flows from 0.01 to 5000 inches (0.03 centimeter to 127 mctersi per second hate been measured. Contaminants, such as smoke, may have to be added to gases to provide scattering centers for the laser beam. 

The Doppler shift, even with a near co-linear geometry, is not a serious limitation to the precision, at least at the level of 0.002 cm-1 for the 2Si/2 2P3/2 interval. We are pursuing a set-up using a 5° intersection angle, with two 13C16C>2 lasers. The beam velocity calibration will make use of previously accurately measured transitions in heliumlike ions. 

PROBLEM 11.26.1 Compute the Doppler recoil energy ER for 26pe57 and a linear speed vr needed to counteract the Doppler shift. Calculate also the speed of a free recoiling nucleus vr, and comment on why this calculated speed is too big. 

Although IS is independent of T, variations with temperature are observed experimentally because ISqbs is in fact a linear combination of IS and a second shift which is sample-dependent, being called a second-order Doppler shift (SOD) ... 

Fig. 5.8.2. Spectra of light scattered from the protoplasm of Nitella. The horizontal axis is frequency in Hz and the vertical axis is relative intensity. Spectrum (a) was taken at a scattering angle of 19.5 deg. Spectra (b) and (c) were taken at a scattering angle of 36.1 deg. Spectrum (c) was taken from the same point on the cell as spectrum (b), immediately after addition of parachloromercuribenzoate, a streaming inhibitor. (Each of these spectra was collected in about 30 sec. The points are the output of the spectrum analyzer, and the dark lines have been drawn merely to make the data more perspicuous and to emphasize the reproducible features of the data.) Part (d) is a plot of the magnitude of the Doppler shift from a fixed point on a Nitella cell as a function of the sine of the scattering angle 9. The line is the best least-square fit to the points. The predicted linear dependence is verified, and the deviations from the line provide an estimate of the experimental precision. (From Mustacich and Ware, 1974.)...

The quadratic relationship of redshift to distance of the source is a complete departure from the conventionally assumed Doppler shift and Hubble s linear law. In order to test the quadratic model it is necessary (Segal, 1980) to eliminate the distance, which is not an observable quantity, using geometrical relations with parameters such as apparent luminosity or angular diameter. These relations were tested on data available for galaxies, quasars and radio sources. 

There is no more important concept in standard cosmology than Hubble s constant, which relates spectroscopically measured redshifts in galactic light to the estimated distance of the source and its inferred rate of recession. This definition specifies a proportionality constant only for Doppler shifts. It also occurs for redshifts with a linear distance dependence due to other causes, in which case it has no connotation to an expanding universe. It is undefined for redshifts, independent of distance. 

Example 4.3 In a supersonic beam with u = 10 m/s, e = 10 , the residual Doppler width for a visible transition with v = 6 x 10 is eAcoo 27t 20 MHz. For a crossing angle of 89° the Doppler shift between the two beams is 2Scod = 2jt -60 MHz. In this ease the Doppler shift 2Scod is larger than the residual Doppler width, and even in the linear speetrum with redueed Doppler width the lines would be doubled. No Lamb dips ean be observed with opposite laser beams. 

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