Homogeneous versus inhomogeneous lines

Mathematically, this line shape is described by the Lorentz distribution 

We have seen in Chapter 2 that in EPR spectroscopy one usually varies the magnetic held instead of the frequency, because the use of a mechanically rigid micro-wave resonator dictates the frequency to be constant. For this reason, the Lorentzian distribution in Equation 4.5 is frequently rewritten as a distribution in resonance fields as 

Since in EPR we usually observe first-derivative spectra as a consequence of phase-sensitive detection (see 2.7) it is relevant to note that the first derivatives of the two distributions are features with a positive and a negative peak. The peak-to-peak separation App in field units for the two distributions is 

FIGURE 4.4 Line shapes. Lorentzian (broken lines) and Gaussian (solid lines) line shapes and their first derivatives are given. The outermost vertical lines delimit full width at half height (FWHH) of the absorption lines. 

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