peak_lorentz¶

A Lorentzian peak on a flat background

Parameter	Description	Units	Default value
scale	Scale factor or Volume fraction	None	1
background	Source background	cm^-1	0.001
peak_pos	Peak postion in q	Å^-1	0.05
peak_hwhm	HWHM of peak	Å^-1	0.005

The returned value is scaled to units of cm^-1 sr^-1, absolute scale.

This model describes a Lorentzian shaped peak on a flat background.

Definition

The scattering intensity \(I(q)\) is calculated as

\[I(q) = \frac{scale}{\bigl(1+\bigl(\frac{q-q_0}{B}\bigr)^2\bigr)} + background\]

with the peak having height of \(I_0\) centered at \(q_0\) and having a HWHM (half-width half-maximum) of B.

For 2D data the scattering intensity is calculated in the same way as 1D, where the \(q\) vector is defined as

\[q = \sqrt{q_x^2 + q_y^2}\]

Source

peak_lorentz.py

References

None.

Authorship and Verification