Line shapes

The most common line shapes in EPR are Gaussian and Lorentzian. In addition, Dysonians and Voigtians are used.

The formula for a Gaussian absorption line shape normalized so that its integral is 1 is

where x₀ is the line centre and is the distance between the inflection points. It is related to the FWHM (full width at half height) via

At the center x₀ the value of the Gaussian is

The first derivative has a peak-to-peak distance of .

The formula for a Lorentzian absorption line shape normalized so that its integral is 1 is

where x₀ is the center and is the distance between the inflection points. It is related to the FWHM (full width at half height) via

At the center x₀ the value of the Lorentzian is

The first derivative has a peak-to-peak distance of .

The Voigt line shape is the convolution of Lorentzian and a Gaussian line shape. It cannot be expressed in closed analytical form. It can be approximated by a linear combination of a Lorentzian and a Gaussian, a so-called pseudo-Voigt function.