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## 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

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

Fig. 116 Figure 1: 1D plot corresponding to the default parameters of the model.

Source

`peak_lorentz.py`

References

None.

Authorship and Verification

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