Doppler

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... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

The actual line shape in a spectrum is a convolution of the natural Lorentzian shape with the Doppler shape. It must be calculated for a given case as there is no simple fomuila for it. It is quite typical in electronic... 

Winnewisser G, Belov S P, Klaus T and Sohieder R 1997 Sub-Doppler measurements on the rotational transitions of oarbon monoxide J. Mol. Spectrosc. 184 468-72... 

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

He Y, Pochert J, Quack M, Ranz R and Seyfang G 1995 Dynamics of unimolecular reactions induced by monochromatic infrared radiation experiment and theory for C F XI—> C F X + I probed with hyperfine-, Doppler- and uncertainty limited time resolution of iodine atom infrared absorption J. Chem. Soc. Faraday Discuss. 102 275-300... 

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. 

However, die atom will not cool indefinitely. At some point die Doppler cooling rate will be balanced by die heating rate coming from die iiiomentum fluctuations of die atom absorbing and re-emitting photons. Setting diese... 

Equation (Cl.4.35) yields two remarkable predictions first, tliat tire sub-Doppler friction coefficient can be a big number compared to since at far detuning Aj /T is a big number and second, tliat a p is independent of tire applied field intensity. This last result contrasts sharjDly witli tire Doppler friction coefficient which is proportional to field intensity up to saturation (see equation (C1.4.24). However, even tliough a p looks impressive, tire range of atomic velocities over which is can operate are restricted by tire condition tliat T lcv. The ratio of tire capture velocities for Doppler versus sub-Doppler cooling is tlierefore only uipi/uj 2 Figure Cl. 4.6 illustrates... 

Figure C 1.4.6. Comparison of capture velocity for Doppler cooling and Tin-periD-lin sub-Doppler cooling. Notice tliat tire slope of tire curves, proportional to tire friction coefficient, is much steeper for tire sub-Doppler mechanism. (After [17].)...

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. 

Lett P D, Watts R N, Westbrook C I, Phillips W D, Gould P L and Metcalf H J 1988 Gbservation of atoms, laser-cooled belowthe Doppler limit Phys.Rev.Lett. 61 169-72... 

Dalibard J and Cohen-Tannoudji C 1989 Laser cooling belowthe Doppler limit by polarization gradients simple theoretical models J.Opt.Soc.Am. B 6 2023-45... 

Even more remarkable is tlie fact tliat tliese infrared diode lasers have sufficient resolution to measure tlie Doppler... 

Figure C3.3.3. A schematic drawing of tlie Doppler-lineshape profile for a typical infrared transition in a small...

Velocity recoils are measured at short times after tire initial ultraviolet excitation pulse by probing tire nascent Doppler profiles for tire different spectral lines probed in tliese last steps. 

Figure C3.3.6. Doppler-line profiles for molecules scattered into the CO COO O J= 72) state by collisions with hot methylpyrazine molecules as depicted by the equations above each half of the figure. The energy of methylpyrazine...

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