Inelastic spectral lines

Raman spectra are emission spectra excited by monochromatic radiation in the ultraviolet (UV, 0.2. .. 0.4 pm = 50000. .. 25(KK) cm ), visible (VIS, 0.4. .. 0.7 pm = 25000. .. 14300 cm" ), or near infrared (NIR, 0.7. .. 2.5 pm = 14300. .. 4000 cm ) region. They are due to modulation of incident light by molecular vibrations. This is an inelastic scattering process of low probability. Faint spectral lines are emitted - the Raman spectrum - whose energy difference relative to the energy of the exciting line is equal to the energy difference between the lower vibrational states. 

The two main sources of information about atomic and molecular structure and interatomic interactions are provided by spectroscopic measurements and by the investigation of elastic, inelastic, or reactive collision processes. For a long time these two branches of experimental research developed along separate lines without a strong mutual interaction. The main contributions of classical spectroscopy to the study of collision processes have been the investigations of collision-induced spectral line broadening and line shifts (Vol. 1, Sect. 3.3). 

In Vol. 1, Sect. 3.3. we discussed how elastic and inelastic collisions contribute to the broadening and shifts of spectral lines. In a semiclassical model of a collision between partners A and B, the particle B travels along a definite path r(t) in a coordinate system with its origin at the location of A. The path r t) is completely determined by the initial conditions r(0) and (dr/df)o and by the interaction potential V(r, Ex, E-b), which may depend on the internal energies Ex and b of the collision partners. In most models a spherically symmetric potential V r) is assumed, which may have a minimum at r = ro (Fig. 8.1). If the impact parameter b is large compared to tq the collision is classified as a soft collision, while for b hard collisions occur. 

In Sect. 3.3. we discussed how elastic and inelastic collisions contribute to the broadening and shifts of spectral lines. In a semiclassical model of a collision between partners A and B, the particle B travels along a definite path r t) in a coordinate system with its origin at the location of A. The path r t) is... 

Inelastic collisions of A with molecules B of the liquid host may cause radiationless transitions from the level Ei populated by optical pumping to lower levels En. These radiationless transitions shorten the lifetime of Ei and cause collisional line broadening. In liquids the mean time between successive inelastic collisions is of the order of 10 to 10 s. Therefore the spectral line Ei Ek is greatly broadened with a homogeneously broadened profile. When the line broadening becomes larger than the separation of the different spectral lines, a broad... 

The preceding discussion has shown that both elastic and inelastic collisions cause spectral line broadening. The elastic collisions may additionally pro-... 

The preceding discussion has shown that both elastic and inelastic collisions cause spectral line broadening. The elastic collisions may additionally cause a line shift which depends on the potential curves E. (R) and E (R). This can be quantitatively seen from a model introduced by LINDHOLM [3.6], which treats the excited atom A as a damped oscillator which suffers collisions with particles B (atoms or molecules). In this model inelastic collisions damp the amplitude of the oscillation. This is described by introducing a damping constant such that the sum of radiative and col-lisional damping is represented by y = y + y qi From the derivation in Sect.3.1 one obtains for the line broadened by inelastic collisions a Lorentzian profile with halfwidth (3.38)... 

In Sect.3.3, we saw that the spectral line profile is altered by two kinds of collisions. Inelastic collisions cause additional damping, resulting in pure broadening of the Lorentzian line profile. This broadening by inelastic collisions brings about a homogeneous Lorentzian line profile. 

In Section 3.3 we discussed how elastic and inelastic collisions contribute to the broadening of spectral lines. In a semi classical model, where the colliding particles travel along definite paths, an impact parameter b can be defined (see Fig.12.1) and the collisions may be classified as soft collisions (impact parameter b large compared to the minimum location r of the interaction potential) and hard collisions (bsoft collisions probe the... 

In either case, the information on the vibrational transition is contained in the energy difference between the excitation radiation and the inelastically scattered Raman photons. Consequently, the parameters of interest are the intensities of the lines and their position relative to the Rayleigh line, usually expressed in wavenumbers (cm 1). As the actually recorded emissions all are in the spectral range determined by the excitation radiation, Raman spectroscopy facilitates the acquisition of vibrational spectra through standard VIS and/or NIR spectroscopy. 

The resolution of overlapping spectral peaks depends on their separations, intensities, and widths. Whereas separation and intensity are predominantly functions of the sample, peak width is strongly influenced by the instrument s design. The observed line is a convolution of the natural line, a function characteristic of inelastically scattered electrons that produces a skewed base line, and the instrument function. The instrument function is, in turn, the convolution of the x-ray excitation line shape, the broadening inherent in the electron energy analyzer, and the effect of electrical filtering. This description is summarized in Table I. 

The inelastic scattering spectra between 100 and 4000 Raman shifted wavenumber (cm ) of self-supporting disks of silica A, P, and C were obtained with a spectrometer Coderg T800 and a spectral resolution of 7 cm . The 514.5 nm emission line of an Ar laser was used with a power of about 200 mW at the sample. The low frequency Raman between 2 and 30 cm are collected with a high resolution of 0.3 cm . ... 

Fig. 36. The spectral response y"(a)) for CeSn obtained on 1N4 with Ep = 50 meV (left) and 82 meV (right) at 7 = 5 and 95 K (100 K). The data have been corrected for intensity variation as a function of Q for fixed scattering angles with use of the Ce form factor dependence. The upper points give the measured spectra and the lower points the data after phonon subtraction. The solid curves represent the best fit to the data allowing for a quasi-elastic and an inelastic line of Lorentzian shape (Murani 1983a, b).

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