Average characteristic linewidth

The characteristic spread in magnetic field is given by AB = kBT/jv For a temperature of 1 mK, AB = 1.6xlO 3T, and the spread in vz is Avz = 300 Hz. For a temperature of 30 pK the linewidth is 10 Hz. Thus, Zeeman-broadening in the trap is potentially significant However, as described below, it is reduced by motional averaging effects. 

Here, the first term empirically describes the motional averaging of the distribution of local conformations, where 5i is half the linewidth due to the distribution, a describes steepness of the transition, and To is a characteristic transition temperature. The second term describes the interference between motion and DD [58], where A is the reduction factor of the second moment M2, T is the correlation time of motion and cdi is the strength of DD. This shows that the interference is effective when the motional frequency comes close to the frequency of DD (tmi 1). The third term So is the intrinsic linewidth. 

A characteristic feature of many quadmpolar nuclei is the broad lines they produce, due to rapid quadmpolar relaxation (Section 2.5.5). The rapid recovery of the spins following excitation means they can often be acquired under conditions of very fast pulsing with full excitation by a 90° pulse, which is clearly beneficial for signal averaging purposes. However, the corresponding rapid decay of an FID can make the direct observation of nuclei with linewidths... 

Recently, an extensive effort has been made to improve the laser characteristics for the industrial application for laser lithography. Improvement in the high-repetition rate frequency, high average power, narrow linewidth, and operational long gas lifetime continues. 

Thus the chemical shift will have the same value for the field anywhere in the 2-3 plane but a different value when the field is perpendicular to the plane the chemical-shift tensor is axially symmetric. The chemical shift expected when the field is parallel to the unique axis is labeled a, whereas that expected for the field perpendicular to this axis is Figure 2B demonstrates this averaging and the resultant powder spectrum. Note the characteristic shape vwth the buildup of intensity at <7x- Both a, and individual components of the powder line shape (Seelig, 1978). 

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