Doppler spectra

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

Radar Doppler spectra measured at co-polarisation (VV-pol.) and at cross-polarisation (HV-pol.) are shown in Figures 5 and 6, respectively. In each figure the solid curves denote Doppler spectra acquired at a rain rate of 160 mm/h, and the dashed curves correspond to Doppler spectra acquired without rain. During the measurements the water surface was covered with a monomolecular OLA slick. 

The solid curves in Figure 5 (160 mm h 1 rain rate) show that the raingenerated ring waves are the main scatterers at wind speeds up to 8 m s 1. It was already shown by Braun et al. (2002) that the occurrence of two peaks in the Doppler spectra (measured at co-polarisation) is caused by ring waves propagating towards and away from the radar antennae. These ring waves cause two separated peaks with an overall (mean) Doppler shift due to the wind-dependent surface drift. 

At 10 m s 1, the slicks are dispersed in both cases (wind only and wind plus rain). Thus, the Doppler spectra at co-polarisation measured with and without rain are similar and only a slight influence of the slick coverage is visible. 

The Doppler spectra measured at HV-polarisation, without rain (dashed curves in Figure 6), show that no radar backscattering from a slick-covered water surface was measured up to wind speed of about 4 ms"1. Moreover, at 6-8 m s 1 only a very weak backscattered signal was measured. At 10 m s 1, where the surface film has already started to disperse, a significant radar Doppler signal was measured. 

Fig. 5. Radar Doppler spectra measured at vertical polarizations (W) and different wind speeds (0, 2, 4,6, 8, 10 m s 1, from top to bottom, left to right). The water surface was covered by an OLA slick. Dashed line wind only, solid line rain and wind...

The Doppler spectra measured at HV-polarisation at a rain rate of 160 mm h 1 (solid curves in Figure 6) are very similar in the whole wind-speed range used in the present investigation they show a symmetric, broad peak with its maximum at about -40 dB. The location of this maximum, however, depends on wind speed because of the wind-induced surface drift. From this finding we conclude that the radar backscattering at cross-polarisation from a slick-covered water surface agitated by rain is... 

Figure 4. Some typical Doppler spectra for Tl+ ions in gramicidin channels at different applied potentials. Va is the applied constant potential, and Av is the average Doppler difference frequency.

The most recent example is the investigation of the ground state of Bal, the heaviest alkaline earth monohalide. For a long time the hfs in sub-Doppler spectra of the C n - system observed by Johnson et al. could not be Interpreted. A 5-GHz laser scan near the band origin of - x2z+ (0,0) is shown in Fig. 5. In this part of the spectrum... 

X. Xie and R.W. Field, The Ll2 aIEu" " b Hu Spin-Orbit Perturbations Sub-Doppler Spectra and Steady State Kinetic Lineshape Model, Chem. Phys. Submitted for publication. 

In this chapter the normal appearance of penile anatomical structures at ultrasound will be described, both while flaccid and during erection. Specific topics discussed will be ultrasound appearance of the corporal bodies and penile envelopes, visibility of normal penile vessels at color Doppler ultrasonography and normal changes of Doppler spectra during the onset of erection. 

After plaque assessment, Doppler interrogation of all visible vessels should be done, and the erectile response of the patient should be evaluated. Doppler spectra are recorded on both cavernosal arteries un-... 

From the variety of different techniques which recently have been developed to outwit the Doppler-width of spectral lines in gas phase spectroscopy only two examples are selected here. They shall illustrate the resolution achieved so far and the gain in information about molecular structures obtainable from resolved features in sub-Doppler spectra, which are completely masked in Doppler-limited spectroscopy. 

For tunable-diode-laser(TDL) studies where r(x) is much narrower than even a modestly pressure-broadened line, one might either attempt the former method characterized by Eq. (49) or perhaps simply ignore (cautiously) the impact of r(x). From the foregoing discussion, however, it should be obvious that the considerations and potential problems involved in going beyond removal of the effect of r(x) are in no way trivial. Nevertheless, we have successfully deconvolved some data beyond the limit of the removal of r(x). In many instances we have only taken 0.012-cm-1 data for a 0.005-cm 1 Doppler spectrum to. 0.004 cm -1 and have encountered no serious problems. (Quantities refer to FWHM of the peaks.) In other instances, we have deconvolved 0.002-cm-1 TDL spectra of C2H6 at 12 jim to 0.0009 cm-1, which is roughly one-half the Doppler limit. An example is shown in Chapter 7. 

We were able to show a significant relationship between increases in ICP and alteration of the Doppler spectrum and also a significant correlation between CPP and Doppler parameters in a patient who was continuously monitored over a period of 15 hours before transplantation and had severe ICP increase and CPP decrease during the last 6 hours before transplantation. In contrast, the TCD data were normal in 6 patients with acute liver failure and grades I-III HE, who did not present with increased intracranial pressnre (Schnittger et al., 1997). 

In addition to the local velocity information, the standard deviation of the Doppler spectrum gives the variance of local velocity and can be determined from the measured analytical fringe signal [8] ... 

Doppler Ultrasound. Doppler ultrasound has been widely used to provide quaUtative measurements of the average flow velocity in large to medium-size vessels if the vessel diameter is known. These include the extracranial circulation and peripheral limb vessels. It is also used in an assessment of mapped occlusive disease of the lower extremities. The frequency used for Doppler ultrasound is typically between 1 and 15 MHz. The basis of this method is the Doppler shift, which is the observed difference in ftequency between sound waves that are transmitted from simple piezoelectric transducers and those that are received back when both transmitter and receiver are in relative motion. The average frequency shift of the Doppler spectrum is proportional to the average particulate velocity over the cross-sectional area of the sample. When us to measure blood flow, the transducers are stationary and motion is imparted by the flowing blood cells. In this event, red cell velocity V is described by the relationship... 

Lin JT, Bradley WE (1985) Penile neuropathy in insulin-de-pendent diabetes mellitus. J Urol 133 213-215 Lue TP, Hricak H, Marich KW, Tanagho EA (1985) Vascu-logenic impotence evaluated by high-resolution ultrasonography and pulsed Doppler spectrum analysis. Radiology 155 777-781... 

The photons are detected by a photomultiplier and the signal is fed to the correlator. The resulting correlation function is analysed to determine the frequency (Doppler) spectrum and this is converted into the particle velocity V,... 

The Doppler spectrum of the normal hepatic artery shows low vascular resistance and continuous diastolic flow there is a rapid systolic upstroke with acceleration time inferior to 80 ms the resistive index [(peak systolic velocity - peak diastolic veloc-ity)/peak systolic velocity] should be between 0.5 and 0.7 (Crossin et al. 2003) (Fig. 4.2.17). Doppler criteria for diagnosing a significant hepatic artery complication are peak systolic velocities greater than 200cm/s, focal increase in velocity greater than threefold, resistive index less than 0.5, and acceleration time greater than 80 ms (tardus-parvus... 

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... 

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.

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

In an actual Mdssbauer transmission experiment, the radioactive source is periodically moved with controlled velocities, +u toward and —d away from the absorber (cf. Fig. 2.6). The motion modulates the energy of the y-photons arriving at the absorber because of the Doppler effect Ey = Eq + d/c). Alternatively, the sample may be moved with the source remaining fixed. The transmitted y-rays are detected with a y-counter and recorded as a function of the Doppler velocity, which yields the Mdssbauer spectrum, r(u). The amount of resonant nuclear y-absorption is determined by the overlap of the shifted emission line and the absorption line, such that greater overlap yields less transmission maximum resonance occurs at complete overlap of emission and absorption lines. 

Fig. 2.6 Schematic illustration of a Mossbauer transmission experiment in five steps. The Absorption bars indicate the strength of recoilless nuclear resonant absorption as determined by the overlap of emission and absorption lines when the emission line is shifted by Doppler modulation (velocities Uj,. .., 1)5). The transmission spectrum T v) is usually normalized to the transmission T oo) observed for v oo by dividing T(v)IT(oo). Experimental details are found in Chap. 3...

Cahbration spectra must be measured at defined temperamres (ambient temperature for a-iron) because of the influence of second-order Doppler shift (see Sect. 4.2.1) for the standard absorber. After folding, the experimental spectrum should be simulated with Lorentzian lines to obtain the exact line positions in units of channel numbers which for calibration can be related to the hteramre values of the hyperfine splitting. As shown in Fig. 3.4, the velocity increment per channel, Ostep, is then obtained from the equation Ustep = D,(mm s )/D,(channel numbers). Different... 

Fig. 3.19 Schematic illustration of the measurement geometry for Mossbauer spectrometers. In transmission geometry, the absorber (sample) is between the nuclear source of 14.4 keV y-rays (normally Co/Rh) and the detector. The peaks are negative features and the absorber should be thin with respect to absorption of the y-rays to minimize nonlinear effects. In emission (backscatter) Mossbauer spectroscopy, the radiation source and detector are on the same side of the sample. The peaks are positive features, corresponding to recoilless emission of 14.4 keV y-rays and conversion X-rays and electrons. For both measurement geometries Mossbauer spectra are counts per channel as a function of the Doppler velocity (normally in units of mm s relative to the mid-point of the spectrum of a-Fe in the case of Fe Mossbauer spectroscopy). MIMOS II operates in backscattering geometry circle), but the internal reference channel works in transmission mode...

The isomer shift of a resonance line (or the centroid of a line multiplet) in an experimental Mossbauer spectrum in terms of the Doppler velocity (mm s ) necessary to achieve resonance absorption is given by... 

To analyze the data, first perform the vx- and ty-corrections and the time-to-speed transformation to make the velocity volume element the same for all data points, and then normalize each Doppler-selected TOF spectrum according to the averaged ID Doppler profile from several independent scans, I vz) = )T)(, vyS(vy vx 0,vz)dvy. Due to the large exothermicity of this reaction, the problematic density-to-flux transformation is not negligible (despite the large probe laser size used to minimize its effects) and needs to be accounted for (the wy-correction , see Sec. 3.3). By combining all the resulting TOF spectra, the product 3D velocity flux contour... 

Fig. 20. A few examples of the Doppler-selected TOF data are exemplified. The TOF spectra have been converted into velocity space and weighted by a term. For each spectrum, the VUV laser frequency is selected to slice through the Newton sphere near the center-of-mass, i.e. wcm- The cap marked on the top corresponds to the (v, j ) state of the co-product F1F for Ec = 1.18kcal/mol. Note the slight tilt of the dashed lines which act as a visual guide for quantum state assignments.

Fig. 1. Model Spectra re-binned to CRIRES Resolution To demonstrate the potential for precise isotopic abundance determination two representative sample absorption spectra, normalized to unity, are shown. They result from a radiative transfer calculation using a hydrostatic MARCS model atmosphere for 3400 K. MARCS stands for Model Atmosphere in a Radiative Convective Scheme the methodology is described in detail e.g. in [1] and references therein. The models are calculated with a spectral bin size corresponding to a Doppler velocity of 1 They are re-binned to the nominal CRIRES resolution (3 p), which even for the slowest rotators is sufficient to resolve absorption lines. The spectral range covers ss of the CRIRES detector-array and has been centered at the band-head of a 29 Si16 O overtone transition at 4029 nm. In both spectra the band-head is clearly visible between the forest of well-separated low- and high-j transitions of the common isotope. The lower spectrum is based on the telluric ratio of the isotopes 28Si/29Si/30Si (92.23 4.67 3.10) whereas the upper spectrum, offset by 0.4 in y-direction, has been calculated for a ratio of 96.00 2.00 2.00.

Obvious species such as CO provide useful spectral standards and are plentifully abundant in space. The Doppler shift for CO can then be applied to other unidentified transitions to see if they are coincident with known transitions in the laboratory spectrum of a molecule. Different molecular environments may complicate matters, with some CO molecules along the line of site of the telescope having different Doppler shifts (Figure 3.12). The CO transition at 115 GHz may then appear to be split into several lines associated with a different Doppler shift in each cloud. The identification problem now also has to decide to which cloud the unknown transition belongs. 

The major requirement of the light source for atomic absorption is that it should emit the characteristic radiation (the spectrum) of the element to be determined at a half-width less than that of the absorption line. The natural absorption line width is about 10 4 (A), but due to broadening factors such as Doppler and collisional broadening, the real or total width for most elements at temperatures between 2000 ° and 3000 °K is typically 0.02 — 0.1 A. Hence, a high resolution monochromator is not required. 

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