Doppler spectrum, calculated

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... 

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.

Fig. 24 Tunable-diode-laser spectrum of RQ0 of v9 of ethane. Trace (a) is the average of 250,000 scans and exhibits linewidths of 0.0022 cm-1 (the Doppler width is 0.0018 cm-1). Trace (b) results from the deconvolution of the data in trace (a) using a gaussian with a FWHM of 0.0022 cm-1 as a response function. Trace (c) is the Q branch calculated using a model that includes torsional splitting effects Av = 1.95 mk. Trace (c) is calculated for Av = 0.00075 cm-1, which is less than one-half the 300 K Doppler width.

Fig. 28 Pure rotational spectrum of C>2. Trace (a) is the S3 transition recorded at a pressure of 1.0 atm. Trace (b) is the result of deconvolving the S3 profile with a Voigt profile to remove most of the pressure broadening, Doppler broadening, and instrument effects. Trace (c) was calculated using a 0.035-cm-1 Gaussian profile and calculated spin splittings. The traces are scaled to the same height.

The relatively weak dependence on the ratio Ktat/ i abs suggests that the modification to our calculated results will not be great except at very early times. The effective temperature calculated for Model 10H, for example, is, without modification, within 15% of the values inferred from the spectrum (Suntzeff, private communication) on days 1.14 (13,600 K), 1.51 (12,700 K), and 1.85 (11,690 K). Figure 5 illustrates the effect for K<0 0.3, and 0.1. The latter corresponds to a color temperature one third greater than the effective emission temperature. Karp et a1. (1977) have considered the effect of Doppler broadened lines on the bound-bound opacity. For typical photospheric densities (1012 g cm-3) and temperatures (5000 K to 50,000 K) the line opacity is approximately 20% to 200% that of electron scattering (see their Table 3). This should keep the color temperature within about 20% of the effective emission temperature. 

Having explicit formulas for a number of first moments we can approximately restore the envelope line of the radiation spectrum without its detailed calculations. If lines in the spectrum have one symmetric maximum, then its envelope line is approximated by a normal function whose reconstruction requires only the mean energy and variance of the spectrum. Such an approach is useful for the case of complex spectra consisting of many lines, which, due to low resolutions as well as Doppler and collisional broadening or large natural width, form continuous or quasi-continuous bands. Studies of variation of these statistical characteristics along isoelectronic sequences give a wealth of information on intra-atomic interactions. 

The data analysis chosen by these authors departs from that used by Mogensen and others [17, 18], who fit each ID angular correlation curve to a set of Gaussian functions. The minimum number of Gaussians is used to achieve a good fit, and the width of each is optimized. The momentum components of each 7-ray spectrum are then interpreted in terms of annihilation of core vs. valence electrons without appeal to a preconceived chemical model. The experiment-theory connection can be made if one has an adequate wave function in hand, for then the Doppler profiles or angular correlation curves can be calculated and compared to those measured. 

The application of laser Doppler velocimetry (LDV) to measure the electrophoretic mobility n of charged colloidal particles is known as laser Doppler electrophoresis (LDE). In a typical LDE experiment, an applied electric field drives the collective motion of charged colloidal particles. The particles pass through an interference pattern created by a dual-beam experimental setup (Section III.A.2). The collective electrophoretic velocity of the particles is then determined via intensity- or spectrum-based analysis of the scattered light, and the electrophoretic mobility n is calculated by dividing the velocity by the applied electric field strength. 

The nuclear design calculations for this 1000-MWe fast ceramic reactor used a conservative set of nuclear data. There is experimental evidence to suggest that calculations using these data predict (1) a neutron spectrum that is too hard (quantitative information is given in the paper by Greebler et al. (8) and (2) a positive Doppler contribution from Pu which is too large. 

The significance of these predictions is shown in Table XV. If the nuclear data are adjusted in line with this experimental information, the design calculations show that at least 50% of the BeO, which was included in the core to soften the neutron spectrum and to increase the Doppler coefficient, can be removed and still meet the Doppler and sodium loss criteria of the reference core. The fissile inventory required decreases by about 3%, and the breeding ratio increases from 1.18 to about 1.25. This results in a decrease in the fuel cycle cost of about 0.1 mill/kW-hr. If one assumes a favorable combination of nuclear data within the limits of uncertainties reported by Greebler (5) and, furthermore, if the safety criteria are relaxed to allow a calculated Doppler effect (T dkjdT) of — 0.004 (with sodium out) and a positive total sodium loss reactivity effect between 1 and 2, all of the BeO can be removed... 

Calculate the expected fwhm of the R(0) line in the HCl vibration-rotation spectrum of Fig. 3.3 if the linewidth is dominated by Dopper broadening. Assume that the gas temperature is 300 K. Is the observed broadening primarily Doppler broadening ... 

Problem 7.5. The flux of Na atoms desorbing from the surface (T = 400 K) obeys the Knudsen law. One observes the excitation spectrum of fluorescence by scanning the laser frequency across the 3P3/2 — 5Si/2 transition (A = 616 nm) with the laser beam (a) parallel to the surface (b) perpendicular to the surface, while fhe 3P3/2 state is populated by another laser. Calculate the frequency shift between the fluorescence line maxima in the two cases, provided that Doppler broadening dominates. 

Such power levels can be quite adequate for Doppler-free saturation spectroscopy, as demonstrated in a series of recent studies of ultraviolet transitions of neutral helium in our laboratory at Stanford. (35-37) Fig. 5 shows as an example a spectrum of the 2 S - 5 P transition of He near 294.5 nm, recorded by intermodulated fluorescence spectroscopy. The ultraviolet radiation was generated by a yellow cw ring cavity dye laser with cavity-enhanced external ADA (ammonium dihydrogen arsenate) frequency doubler. The absorbing metastable He atoms were produced by electron impact excitation of He gas at about 0.04 torr. The spectrum shows a cluster of resolved line components which could be assigned after the fine and hyperfine Hamiltonian had been diagonalized in an uncoupled representation. We were surprised to learn that the hyperfine structure of the 5 P state of this simple 3-body system had been neither measured nor calculated before. 

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