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ComptonPeakProfile¶

Description¶

The ComptonPeakProfile describes the Neutron Compton profile with either a Voigt or Gaussian approximation, depending on an energy cutoff value. It takes three input parameters:

Intensity: $I$
Position: $P$
SigmaGauss: $\sigma_G$

and three attributes,

WorkspaceIndex
Mass
VoigtEnergyCutOff

The VoigtEnergyCutOff is used to determine whether a Gaussian or Voigt function is used to fit the peak. If the final energy, as read from the input workspace, is greater than the VoigtEnergyCutOff a normalised Gaussian approximation is used,

$\frac{I}{2\pi \sigma_T^2}\exp \left( -0.5*\frac{(x-P)^2}{\sigma_T^2} \right)$

where $\sigma_T^2$ is the total variance, defined by

$\sigma_T^2 = \sigma_G^2 + \Gamma^2$

where $\Gamma$ is the half-width-half-maximum, estimated from the input data.

If instead, the energy is below the cutoff an approximation to a Voigt function is used with the following inputs:

$\text{LorentzAmp} = I$

$\text{LorentzPos} = P$

$\text{LorentzFWHM} = 2\Gamma$

$\text{GaussianFWHM}= 0.5 \sigma_G \sqrt{\ln(4)}$