Vibrational excitation spectrum

In Euclidean cZ-dimensional spaces Flory exponent depends only on d. A good (although not exact) estimation was given by Flory formula, Eq. (9) [7, 8], It is well known [47] that the critical phenomena depend by the decisive mode on various ftactal characteristics of basic stmcture. It becomes obvious, that excepting the ftactal (Hausdorflf) dimension Dj. physical phenomena on ft actals depend on many other dimensions, including skeleton fractal dimension [48], dimension of minimum (or chemical) distance [29] and so on. It also becomes clear, that regular random walks on fractals have anomalous fractal dimension [49] and that the vibrational excitations spectrum is characterized by spectral (fiac-ton) dimension d=2D d [41, 50],... 

Figure B2.3.15. Laser fluorescence excitation spectrum of the A S -X ff (1,3) band for the OH product, in the V = 3 vibrational level, from tire H + NO2 reaction [44]- (By pemrission from AIP.)...

Nevertheless, 1,4-difluorobenzene has a rich two-photon fluorescence excitation spectrum, shown in Figure 9.29. The position of the forbidden Og (labelled 0-0) band is shown. All the vibronic transitions observed in the band system are induced by non-totally symmetric vibrations, rather like the one-photon case of benzene discussed in Section 7.3.4.2(b). The two-photon transition moment may become non-zero when certain vibrations are excited. 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

The V (OCO) ion has a structured electronic photodissociation spectrum, which allows us to measure its vibrational spectrum using vibrationally mediated photodissociation (VMP). This technique requires that the absorption spectrum (or, in our case, the photodissociation spectrum) of vibrationally excited molecules differ from that of vibrationally unexcited molecules. The photodissociation spectrum of V (OCO) has an extended progression in the V OCO stretch, indicating that the ground and excited electronic states have different equilibrium V "—OCO bond lengths. Thus, the OCO antisymmetric stretch frequency Vj should be different in the two states, and the... 

Raman scattering spectroscopy is used to probe the vibrational excitations of a sample, by measuring the wavelength change of a scattered monochromatic light beam. This is usually performed by impinging a monochromatic laser beam to the sample surface, and by recording the scattered beam spectrum. 

The time-of-flight spectrum of the H-atom product from the H20 photodissociation at 157 nm was measured using the HRTOF technique described above. The experimental TOF spectrum is then converted into the total product translational distribution of the photodissociation products. Figure 5 shows the total product translational energy spectrum of H20 photodissociation at 157.6 nm in the molecular beam condition (with rotational temperature 10 K or less). Five vibrational features have been observed in each of this spectrum, which can be easily assigned to the vibrationally excited OH (v = 0 to 4) products from the photodissociation of H20 at 157.6 nm. In the experiment under the molecular beam condition, rotational structures with larger N quantum numbers are partially resolved. By integrating the whole area of each vibrational manifold, the OH vibrational state distribution from the H2O sample at 10 K can be obtained. In... 

A small fraction of the molecules are in vibrationally excited states. Raman scattering from vibrationally excited molecules leaves the molecule in the ground state. The scattered photon appears at higher energy, as shown in Figure lb. This anti-Stokes-shifted Raman spectrum is always weaker than the Stokes-shifted spectrum, but at room temperature it is strong enough to be useful for vibrational frequencies less than about 1500 cm 1. The Stokes and anti-Stokes spectra contain the same frequency information. 

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