Resonance line center determination

The spectrum of the excitations is shown in Fig. 10.5 for 2 A = 80 meV. The dashed lines show the uncoupled molecular excitons and photons, and the solid lines show the coherent part of the spectrum with well-defined wavevector. The crosses show the end-points of the spectrum of excitations for which q is a good quantum number. The spectrum of incoherent (weakly coupled to light) states is shown by a broadened line centered at the energy Eq. It follows from the expression for the dielectric tensor that this spectrum is the same as the spectrum of out-of-cavity organics. The spectrum of absorption as well as the dielectric tensor depend on temperature. This means that in the calculation of the temperature dependence of the polariton spectrum we have to use the temperature dependence of the resonance frequency Eo as well as the temperature dependence of 7 determining the width of the absorption maximum. However, the spectrum of emission of local states which pump polariton states can be different from the spectrum of absorption. The Stokes shift in many cases... 

Electron Spin Resonance (ESR) spectroscopy was used to characterize sodium atoms in the highly non-stoichiometric Na Siigg clathrates [28, 88, 89]. In addition to an intense and broad line centered at g = 2.0021 due to the presence of Na clusters, four sharp lines of a hyperfine quadruplet with an isotropic hf splitting of 13.3 mT was observed, corresponding to isolated Na atoms (I = 3/2). From the observed hf splitting value, the spin density in the 3 s orbitals was estimated to be 45 % of one unit spin density [88]. With decreasing x values, the intensity of the cluster line decreases, whereas those of the hyperfine quadruplet lines increased. For the lowest x content, the contribution of the cluster line to the total intensity was very low and a quantitative determination of the residual x content was possible by comparison of the observed intensities with those of standards (diluted solutions of Cr " doped alum). The ultimate e sodium content in Na Siise was found to be close to 0.006, i.e. 35 ppm [89]. 

With techniques of sub-Doppler spectroscopy, even small collisional broadening effects can be investigated with high accuracy. One example is the measurement of pressure broadening and shifts of narrow Lamb dips (Sect. 7.2) of atomic and molecular transitions, which is possible with an accuracy of a few kilohertz if stable lasers are used. The most accurate measurements have been performed with stabilized HeNe lasers on the transitions at 633 nm [13.17] and 3.39 p.m [13.18]. When the laser frequency co is tuned across the absorption profiles of the absorbing sample inside the laser resonator, the output power of the laser Pl co) exhibits sharp Lamb peaks (inverse Lamb dip) at the line center of the absorbing transitions (Sect. 7.3). The line profiles of these peaks are determined by the pressure in the absorption cell, by saturation broadening, and by transit-time broad-... 

The fundamentals of SSS are based on the theory of impurity centers in a crystal. The optical spectrum of an organic molecule embedded in a matrix is defined by electron-vibrational interaction with intramolecular vibrations (vibronic coupling) and interaction with vibrations of the solvent (electron-phonon coupling). Each vibronic band consists of a narrow zero-phonon line (ZPL) and a relatively broad phonon wing (PW). ZPL corresponds to a molecular transition with no change in the number of phonons in the matrix (an optical analogy of the resonance -line in the Mossbauer effect). PW is determined by a transition which is accompanied by creation or annihilation of matrix phonons. The relative distribution of the integrated intensity of a band between ZPL and PW is characterized by the Debye-Waller factor ... 

Up to now the heterodyne technique is the most accurate method to determine such line splittings. Its accuracy is comparable with the optical-rf double-resonance method but its application range is more general. Two independent lasers are stabilized onto the line centers of two different molecular transitions (Fig.10.48). The output of the two lasers is superimposed on a nonlinear detector, such as a photomultiplier in the visible range or a semiconductor diode in the infrared. 

The fraction may be written as the function f(Ht — H, AH), where Hr is the resonance field, or center of the individual line. It should be pointed out that the resonance field is itself a function of orientation. Perhaps this concept can best be clarified by the illustration in Fig. 12. We are trying to determine the total energy absorption at the magnetic field H. One radical, oriented so that its absorption is centered at HIlt contributes to the absorption at H. It is clear that the extent of the contribution depends upon the value of Hr — H and upon the line width AH. Another orientation, corresponding to resonance at Hti, contributes less while a third orientation, with resonance at HT contributes a negligible amount at H. 

Here, H can be conveniently expressed as the deviation of the field from the center of the resonance in gauss units H=H —H0 yb,ym, and yn are the elementary spectra of the broad, the medium, and the narrow components, respectively. These are considered to be contributed from protons belonging to the crystalline region, and hindered-rotational and micro-Brownian mobile methylene groups in the amorphous region, respectively. pb,pm, and 0n determine the line-width and breadth of the respective elementary spectra wb, wm, and iv designate the respective mass fractions. Each elementary spectrum is normalized as... 

Fig. 6.8. A Principle of frequency-multiplexed CARS microspectroscopy A narrow-bandwidth pump pulse determines the inherent spectral resolution, while a broad-bandwidth Stokes pulse allows simultaneous detection over a wide range of Raman shifts. The multiplex CARS spectra shown originate from a 70 mM solution of cholesterol in CCI4 (solid line) and the nonresonant background of coverglass (dashed line) at a Raman shift centered at 2900 cm-1. B Energy level diagram for a multiplex CARS process. C Schematic of the multiplex CARS microscope (P polarizer HWP/QWP half/quarter-wave plate BC dichroic beam combiner Obj objective lens F filter A analyzer FM flip mirror L lens D detector S sample). D Measured normalized CARS spectrum of the cholesterol solution. E Maximum entropy method (MEM) phase spectrum (solid line) retrieved from (D) and the error background phase (dashed line) determined by a polynomial fit to those spectral regions without vibrational resonances. F Retrieved Raman response (solid line) calculated from the spectra shown in (E), directly reproducing the independently measured spontaneous Raman response (dashed line) of the same cholesterol sample...

Now we shall estimate the frequency xm, at which the absorption A(x) attains its maximum value. In accord with Eq. (53) at small (3, the absorption A(x) is mostly determined by a transverse component of the spectral function, to which the sum of terms with denominators (2/)2(ttw — X)2 — z1 in the integrand of Eq. (51) corresponds. These terms actually present the set of the resonance Lorentz lines, whose center frequencies are given by... 

In Fig. 34c (for H20) and Fig. 34d (for D20), solid lines show the absorption coefficients a calculated in the R-band the estimated contributions to this a(v) due to reorientations and vibrations are shown by dashed and dashed-and-dotted curves, respectively. The resonance peak at vR 200 cm-1 found for both water isotopes is actually determined by a vibrating nonrigid dipole. The distinction between the curves calculated for ordinary and heavy water is substantial. In the case of H20, Fig. 34c, the contributions of reorientations and vibrations to the resulting a(v) curve are commensurable near the center of the R-absorption peak, while in the case of D20 (Fig. 34d) the main contribution to ot(v) near the R-band peak comes from vibration of the H-bonded molecules. 

The EMR spectra of polymer films prepared without external field demonstrate quite broad lines (Figure 3). Center of these lines is strongly dependent on the sample orientation in MF of spectrometer. This results from the anisotropy of demagnetizing fields, which determine resonance conditions for the thin magnetic film ... 

Prom the electron paramagnetic resonance (EPR) spectmm of the nitroxide side chain, four primary parameters are obtained 1) solvent accessibility, 2) mobility of the R1 side chain, 3) a polarity index for its immediate environment, and 4) the distance between R1 and another paramagnetic center in the protein. Solvent accessibility of the side chain is determined from the collision frequency of the nitroxide with paramagnetic reagents in solution. The mobility, polarity, and distances are deduced from the EPR spectral line shape. For regular secondary stmc-tures, accessibility, mobility, and polarity are periodic functions of sequence position. The period and the phase of the function reveal the type of secondary stmcture and its orientation within the protein, respectively (71, 74). In the case of membrane proteins, the topography of the secondary stmcture with respect to the membrane surface can also be described (75, 76). 

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