Resonance spectra calculations

The ability to measure small index perturbations, (I/Ven. depends on the depth (i.e., the extinction ratio at resonance) and width of these resonances. The depth and width in turn depend on the relative values of the coupling coefficient t and the resonator loss a. Figure 9.16 shows typical ring resonator spectra calculated for two different loss values. The maximum extinction ratio is obtained at critical coupling when t = a, and the output intensity at resonance is exactly zero. The width of the resonances depends on the total round trip resonator loss, at, which is the product of waveguide losses within the ring (a) and coupling loss (t) at the coupler. 

Pd4oCu4oP2o, Pd5oCu3oP2o, and Pd6oCu2oP20 alloys were measured by resonant ultrasound spectroscopy (RUS). In this technique, the spectrum of mechanical resonances for a parallelepiped sample is measured and compared with a theoretical spectrum calculated for a given set of elastic constants. The true set of elastic constants is calculated by a recursive regression method that matches the two spectra [28,29]. 

Quantum Resonance Spectrum of the H3+ Molecular Ions for J=0. An Accurate Calculation Using Filter Diagonalization. 

Equations (126) and (127) can be used to calculate activity coefficients from evaporation data, for a, Zj, da fdt, and dz /dt are measurable quantities. The resonance spectrum of an evaporating droplet is highly sensitive to both size and refractive index, and the refractive index of a binary system is a unique... 

Next we deal with the nature of the correction Awc. The resonance signals in a spectrum may be composed of overlapping, closely spaced components. Usually this is caused by either weak spin-spin couplings (we consider here only those which are included explicitly in the assumed model of an exchanging spin system) or by almost degenerate transitions in the spin multiplets. (81) Such effects should be compensated for by the correction Awc which can be determined from measurement of an apparent line-width, wa, in a theoretical spectrum calculated for a reasonably assumed value of the natural line-width, wtheor The correction (wa — wtheor) is virtually independent of the value... 

W(C0 pyridine at 10 K. The solid line is the experimental spectrum. The dotted line is the spectrum calculated from the pre-resonance Raman intensities as discussed in the text. 

Figure 12-3. IR-UV double resonance spectrum of GC (structure C) in the mid-IR frequency range (recorded at the FELIX free electron laser facility), compared with three types of ab intio calculations. Harmonic frequencies were obtained at the RI-MP2/cc-pVDZ, RI-MP2/TZVPP, and semiempirical PM3 levels of electronic structure theory. Anharmonic frequencies were obtained by the CC-VSCF method with improved PM3 potential surfaces [30]...

Figure 4.3-25 Raman spectrum of natural CO2 in the Fermi resonance region at a pressure of 40 kPa. Slitwidth 0.8 cm laser power 9 W at 514.5 nm, multiple pass cell. Upper spectrum experimental, middle spectrum calculated, lower spectrum isotropic contribution to calculated spectrum (Finsterholzl, 1982),...

Many workers have in fact used density matrix methods for the calculation of line shapes and intensities in multiple resonance experiments, and two excellent reviews of the background theory are available. (49, 50) In addition there is also a simple guide (51) to the actual use of the method which is capable of predicting the results of quite elaborate experiments. Major applications have included the calculation of the complete double resonance spectrum from an AX spin system which gives 12 transitions in all (52) an extremely detailed study of the relaxation behaviour of the AX2 systems provided by 1,1,2-trichloroethane and 2,2-dichloroethanol (53) the effects of gating and of selective and non-selective pulses on AB and AX spin systems and the importance of the time evolution of the off-diagonal elements of the density matrix in repetitively pulsed FT NMR and spin-echo work (54) the use of double resonance to sort out relaxation mechanisms and transient responses (55) the calculation of general multiple resonance spectra (56) and triple resonance studies of relaxation in AB and AX spin systems. (57)... 

Another indirect technique, which enables one to calculate the resonance spectrum for many energies simultaneously, is the wave packet method [163-168], used, for example, in studies of non-rotating [47,169] and rotating [52] HCO, HO2 [170] and H2O [71]. One iteratively solves the time-dependent Schrodinger equation, Eq. (10),... 

Bowman and coworkers were the first to perform such calculations. They calculated a global three-dimensional PES [245] which subsequently was modified in order to better reproduce the available experimental data [246-248]. Much has been learned about the resonance spectrum of HCO from these studies. Nevertheless, with the new results of Tobiason et al. [16] for HCO and later of Stock et al. [14] for DCO it became apparent that a new PES is needed for explaining the data at high excitation energies. 

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