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Lorentzian

Description

A Lorentzian function is defined as:

\[\frac{A}{\pi} \left( \frac{\frac{\Gamma}{2}}{(x-x_0)^2 + (\frac{\Gamma}{2})^2}\right)\]

where:

  • A (Amplitude) - Intensity scaling

  • \(x_0\) (PeakCentre) - centre of peak

  • \(\Gamma/2\) (HWHM) - half-width at half-maximum

Note that the FWHM (Full Width Half Maximum) equals two times HWHM, and the integral over the Lorentzian equals the intensity scaling A.

The figure below illustrate this symmetric peakshape function fitted to a TOF peak:

LorentzianWithConstBackground.png

Properties (fitting parameters)

Name

Default

Description

Amplitude

1.0

Intensity scaling

PeakCentre

0.0

Centre of peak

FWHM

0.0

Full-width at half-maximum

Categories: FitFunctions | Peak | Muon\MuonModelling

Source

C++ header: Lorentzian.h

C++ source: Lorentzian.cpp