Lineshape homogeneous

The vibrational echo experiments yielded exponential decays at all temperatures. The Fourier-transfonn of the echo decay gives the homogeneous lineshape, in this case Lorentzian. The echo decay time constant is AT, where is... 

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

Low frequency spectra of liquids are notably deficient of any structure, and it has long been hoped that a technique would be discovered that provides the same type of line narrowing enjoyed in echo-based electronic and NMR spectroscopy. Tanimura and Mukamel observed that such a technique was possible, and proposed a two-time interval, fifth-order Raman pulse sequence capable of distinguishing, for example, inhomogeneous and homogeneous contributions to the lineshape.[4] The pulse sequence, shown in Fig. 1, is simply an extension of conventional time-domain third-order Raman-based methods. At the... 

One of the more interesting aspects of the collision process is the calculated dependence on the orientation of v relative to E. In particular, do the lineshapes for collisions with v E and v 1E differ as dramatically as shown in Fig. 14.6 To answer this question unambiguously required two improvements upon the initial measurements. First, the Na atoms must be in a well defined beam, otherwise v is not well defined. This requirement is easily met by enclosing the interaction region with a liquid N2 cooled box, which ensures that the only Na atoms in the interaction region are those in the beam. Second, the field homogeneity must be adequate, 1 part in 104, to resolve the intrinsic lineshape of the collisional resonances. A pair of Cu field plates 1.592(2) cm apart with 1 mm diameter holes in the top plate to allow the ions to be extracted is adequate to meet this requirement. 

It is quite important for the spectra measured to represent the pure absorption mode with neither saturation nor transient effects. They should be measured in a homogenous external magnetic field B0 in order to obtain purely Lorentzian lineshapes for individual spectral transitions. The signal-to-noise ratio should be as high as possible and experimental... 

The width (fwhm) of the electronic origin peak at 23,836 cm is 6.5 cm" at T = 1.2 K. Its lineshape can be well approximated by a Lorentzian Hneshape function, while a fit to a Gaussian lineshape is unsuccessful [74]. This indicates that the peak is homogeneously broadened [103,104]. Thus, the width of 6.5 cm" can be related to the lifetime of this Sj state to r(Si) = 8 x 10 s. (Compare Eq. (2).) Eurther, the high phosphorescence intensity that is observed from the Tj state when the Sj state is excited, indicates that the lifetime of this Sj state is largely determined by the intersystem crossing process from Sj to Tj. This would correspond to the rate of kjs = 1/r(Si) = 10 s. A value of the same order of magnitude has also been determined for Pd-phthalocyanine [144]. 

I.r. laser spectroscopy and quadrupole mass spectrometry were used by Fischer et al. to study vibrational predissociation of clusters of C2H4, and CsHg, but-l-ene, cis- and trans-but-2-ene, and isobutene. They obtained spectra in the range 2900—3200 cm and for C2H4 clusters predissociation was observed to result from excitation near the v-i, and vg fundamentals and the i 2 + V12 combination band. The vibrational bands were observed to have Lorentzian lineshapes with IWHM of ca. 5 cm. A homogeneous broadening mechanism was assumed and the widths were used to calculate excited-state lifetimes. Valentini and co-workers studied the predissociation of C2H4 clusters at 950 cm in a crossed laser/molecular beam apparatus. 

In order to resolve beyond mean-field processes in BEC, we must overcome inhomogeneous broadening, which masks homogeneous lineshapes we want to measure. One possibility is to resolve the radial modes (Sec. 1), or for appropriate parameters, the use of our echo spectroscopy scheme (Sec. 6). 

The Redfield equations that lead to Eqs (18.43) or (18.46) were obtained under the assumption that thennal environment is fast relative to the system and therefore correspond to this homogeneous limit. Consequently the absorption spectrum (18.49) obtained from these equations corresponds to a homogeneous lineshape. In contrast, the classical stochastic theory of lineshape, Section 7.5.4, can account for both limits and the transition between them. We will see in the next section that an equivalent theory can be also constructed as an extension of the Bloch equations (18.43). 

In general, the NMR spectrum of the object shows more than one resonance line, or in solids the lineshape is non-Lorentzian. Thus, the first exponential in Equation (5.6) needs to be replaced by the FID f t) in a homogeneous magnetic field. If the spectrum changes within the sample, the FID has to be placed inside the integral. 

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