First-order Doppler shift

To eliminate the residual first order Doppler shift due to the failure of the direction of propagation of the rf field to be precisely perpendicular to the fast beam, measurements were taken with the rf drive on both the right and left sides of the beam. To eliminate the frequency shift due to phase errors in the rf drive system, measurements were made with the entire rf system, including the spectroscopy region, rotated 180° about an axis passing through the midpoint between the two... 

Once one has succeeded in trapping but a single ion, then the ion must be placed in the lower vibration levels (n = 1,2,3...) in the trap. First, micro-motion reduction is required. The amplitude of this micro-motion can be controlled thanks the so-called RF photon correlation . This procedure consists of modulating the output signal from the photomultiplier at the frequency of the RF drive potential. The amplitude of the micro-motion is then revealed by the amplitude of the fluorescence which depends on the first-order Doppler shift. It is, therefore, relatively easy to use precisely either laser detuning or to modify the potential voltages so as to reach the maximum reduction of the amplitude that corresponds to the lowest KE (Figure 11.10). 

In two-photon spectroscopy it is possible to record Doppler-free spectra without any need for velocity selection by excitation with two counterpropagating laser beams whose first order Doppler shifts cancel. 

The velocity of a fast accelerated atom is typically 1 mm/ns compared to an average thermal velocity of lO mm/s. Thus the kinematics becomes important the first-order Doppler shift can be as large as 100 A and the second-order shift several GHz. Thus resonant three-level spectroscopy, using only one laser field can be carried out by Doppler tuning the energy levels appropriate. A simplified three-level system is shown in Fig.2. The excited velocity classes determined by... 

Resonance gamma spectrometry or Mossbauer spectrometry can be used to study the hyperfine interactions between a nucleus and its chemical neighborhood [142], In order to examine these interactions with the help of a Mossbauer spectrometer, the first-order Doppler effect shift of the wave emitted by a moving source is applied. The arrangement used for a Mossbauer spectrometer consists of a radioactive source containing a Mossbauer isotope in an excited state (see Figure 4.54)... 

The first-order Doppler frequency shift, Av, of a wave emitted by a source moving at a velocity, v, is given by the following expression... 

First order Doppler broadening can be eliminated by using a standing wave geometry (i.e. oppositely running waves) to excite the two-photon transition. The fractional second order Doppler shift, v1 c2, is less than 2 x 10-16 at a temperature of 1 mK. 

The first quotient is a function of the velocity, v, of the atom vibrating on its lattice site in the direction of the y-ray and will average to zero over the lifetime of the excited state. The second term will not. It is referred to as a second-order Doppler shift given by ... 

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. 

As we have already mentioned, we should expeet the observed isomer shifts to be temperature-dependent, because the effects of vibrations will mean that the absorber nucleus is not rigidly fixed in its position. Accordingly, there are two contributions to the isomer shift. The first is the chemical isomer shift, 5c, which we have already discussed. This is temperature-independent The seeond is the second-order Doppler shift,... 

The first term wq = (Eg -Ej )/h represents the eigen frequency of the atom in rest if recoil is neglected. The second term is the linear (first-order) Doppler effect, describing the well-known Doppler shift Aw =J< in the absorption frequency of a moving atom. The third term represents the second-order Doppler effect. Note that this term is independent of the direction of V and cannot be eliminated by the methods, discussed in Chap.10, which only overcome the first-order Doppler effect. The last term in (13.14) describes the photon recoil effect, where has been approximated by wq. 

The linewidths observed in Fig. 14 are attributable to (i) a residual first order Doppler width due to the misalignment of the laser beam, (ii) the 800 MHz laser linewidth, (iii) the 200 MHz width due to the ionization rate, (iv) a v lOO MHz second order Doppler width due to the thermal energy of the Ps, (v) the nonuniform Stark shift due to inhomogeneous electric fields ( lOO MHz). The field-free natural linewidth is only the 1 MHz... 

In order to dissipate the recoil energy Mossbauer was the first to use atoms in solid crystal lattices as emitters and also to cool both emitter and absorber. In this way it could be shown that the 7-ray emission from radioactive cobalt metal was absorbed by metallic iron. However, it was also found that if the iron sample were in any other chemical state, the different chemical surroundings of the iron nucleus produce a sufficient effect on the nuclear energy levels for absorption no longer to occur. To enable a search for the precisely required absorption frequency, a scan based on the Doppler effect was developed. It was noted that a velocity of 102 ms-1 produced an enormous Doppler shift and using the same equation (7) it follows that a readily attainable displacement of the source at a velocity of 1 cms-1 produces a shift of 108 Hz. This shift corresponds to about 100 line-widths and provides a reasonable scan width. 

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