Line shape function inhomogeneous

As expected, we find that the total response function Xa=i Ri = Xa=4 Ri = J2i=1 Ri = 0 (i.e., for each possible time ordering) vanishes exactly in the harmonic case, defined by A = 0 and /x2i 2 = 2 /r10 2. Furthermore, it can be easily seen that in the case of a strict separation of time scales of homogeneous and inhomogeneous broadening, the line shape function becomes g(t) = t/T2 + a212/2 and the total response function reduces exactly to the result obtained within a Bloch picture (see, for example Refs. 52 and 75), e.g.,... 

Inhomogeneous interaction (Gaussian line shape function)... 

The method to obtain relaxation times from CW microwave saturation measurements for an inhomogenously broadened line is based on assumptions given in the literature [77, 78], The ESR line shape is then expressed as a convolution of a Gauss and a Lorentz function [81] ... 

The line-shape given by (9.6) is a Voigt function that can be evaluated numerically by a standard procedure [81]. For a single inhomogenously broadened line, the transition probability is set to 1 as in a simple two-level system. The relaxation times are given by ... 

A sample should clearly dissolve completely, as solid particles will cause field inhomogeneity, which will distort the resonances. There is also the issue of viscosity because the rapid tumbling of the molecules, necessary to achieve the narrow line shapes, is hindered by low viscosity of the solvent (which could change as a function of temperature). The price of the solvent is also a factor. The cheapest deuterated solvent is D2O CDCI3 a little more expensive (about 2 per g in 2013), CeDg a factor of ten more, and dg-toluene, dg-THF and CD2CI2 another ten times more. Specialized NMR solvents can easily be more expensive than the chemicals needed to prepare a new compound. 

In eq. (10),y(co) is the shape function of a spin packet. When the line is purely inhomogeneous ... 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

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