Gaussian lineshape

A nuclear magnetic resonance line is usually found to have one of two ideal lineshapes - Gaussian, or more often, Lorentzian. A Gaussian line is found when there is a random distribution of static fields within the sample. A Lorentzian line by contrast arises because the spin lifetime follows a first-order decay law. Weighting functions can be applied to a free-induction decay to generate... 

Lineshape. The two most frequently encountered lineshapes are Lorentzian and Gaussian the latter generally arises from a large number of unresolved hyperfine splittings. In the absence of such complications, epr lines in solution almost always show a Lorentzian lineshape which is defined in the form ... 

Figure 16. Rosch and Ratner spectral density (direct damping) Rosch and Ratner lineshapes (lines) Lorentzian fit (circles) Gaussian fit (black dots).

Fig. 2. (a) Raw 300 MHz proton spectrum of a mixture of acetone and ethanol in deuteri-ochloroform (b) after reference deconvolution using the acetone signal as reference and an ideal lineshape of a 1 Hz wide Lorentzian and (c) after reference deconvolution with an ideal lineshape characterized by a negative Lorentzian width of 0.1 Hz and a Gaussian width of 0.4 Hz. The 0.1 Hz Lorentzian term represents the approximate difference in natural linewidth between the ethanol and acetone signals, and is responsible for the wings on... 

Figure 9.8 The formation of the BIT hole for unstructured continuum. Fq = 0.05 X 10 a.u., Fj = 0, and = 0. Shown is the lineshape (Eq. 9.45) at three different times, (X) - at the peak of the pulse i = 0, (I I) - as the pulse begins to wane, t = 0.75 X 10 a.u., and (full line) - at the tail of the pulse, t = 1.5x10 a.u.. A simple Gaussian pulse of the form EjCP = Ege was assumed. Reprinted figure by permission from Ref. [36]. Copyright 2007 by the American Physical Society.

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