Dephasing inhomogeneous

Although the band intensity in Eqn 24.1 is written with an infinitesimally narrow bandwidth (via the Dirac delta function), in practice the delta function is replaced by a more realistic band shape factor with a finite bandwidth. There are several contributions to the bandwidth including vibrational relaxation and dephasing, inhomogeneous broadening, and lifetime broadening. Since each of these separately is difficult to calculate exactly, the bandwidth is often represented by a phenomenological function based on an appropriate model. Bandwidth analyses are most... 

The echo amplitude decays with time. This decay is faster than transverse relaxation, since dephasing of nuclei is accelerated by varying local fields at different places in the sample due to inhomogeneity of B0, and since diffusion of nuclei within the sample from one homogeneity range to another may take place. The echo amplitude /l,echo therefore does not decay as a simple exponential. Rather, the decay follows eq. (2.28), the term f(t) accounting for inhomogeneity and diffusion. 

Magnetic field inhomogeneities and chemical shifts additionally dephase each doublet component in Fig. 2.38. These effects are also refocussed by a 180" pulse, provided it rotates the components about the x -axis, as is the case in experiments (a) and (c) of Fig. 2.38. 

To construct a model for the P band, the molecular parameters are adopted from Mathies results vibrational frequencies, the coupling constants, the inhomogeneous broadening, and electronic dephasing constant, etc. A microscopic model should contain these molecular parameters. Since... 

E>vib and Our also show up in the theory of spontaneous Raman spectroscopy describing fluctuations of the molecular system. The functions enter the CARS interaction involving vibrational excitation with subsequent dissipation as a consequence of the dissipation-fluctuation theorem and further approximations (21). Equations (2)-(5) refer to a simplified picture a collective, delocalized character of the vibrational mode is not included in the theoretical treatment. It is also assumed that vibrational and reori-entational relaxation are statistically independent. On the other hand, any specific assumption as to the time evolution of vib (or or), e.g., if exponential or nonexponential, is made unnecessary by the present approach. Homogeneous or inhomogeneous dephasing are included as special cases. It is the primary goal of time-domain CARS to determine the autocorrelation functions directly from experimental data. 

Isotropic scattering In addition to the dephasing time T2, the correlation time rc of the purely vibrational relaxation process can be measured, providing quantitative information on the question of homogeneous/inhomogeneous line broadening. 

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