.. _peak-lorentz:

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               |Ang^-1|          0.05
peak_hwhm  HWHM of peak                    |Ang^-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

.. math::

    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

.. math::

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



.. figure:: img/peak_lorentz_autogenfig.png

    1D plot corresponding to the default parameters of the model.


**Source**

:download:`peak_lorentz.py <src/peak_lorentz.py>`

**References**

None.

**Authorship and Verification**

* **Author:**
* **Last Modified by:**
* **Last Reviewed by:**