source: sasmodels/doc/ref/intro.rst @ 404ebbd

.. _models-intro:

************
Introduction
************

Many of our models use the form factor calculations implemented in a c-library provided by the NIST Center for Neutron
Research and thus some content and figures in this document are originated from or shared with the NIST SANS Igor-based
analysis package.

This software provides form factors for various particle shapes. After giving a mathematical definition of each model,
we show the list of parameters available to the user. Validation plots for each model are also presented.

Instructions on how to use SasView itself are available separately.

To easily compare to the scattering intensity measured in experiments, we normalize the form factors by the volume of
the particle

.. math::

    P(\vec q) = \frac{P_o(\vec q)}{V} = \frac{1}{V} F(\vec q) F^*(\vec q)

with

    F(\vec q) = \int\int\int dV\rho(\vec r) e^{-i\vec q \cdot \vec r}

where $P_0(\vec q)$ is the un-normalized form factor, $\rho(\vec r)$ is the scattering length density at a given
point in space and the integration is done over the volume $V$ of the scatterer.

For systems without inter-particle interference, the form factors we provide can be related to the scattering intensity
by the particle volume fraction

.. math::

    I(\vec q) = \Phi P(\vec q)

Our so-called 1D scattering intensity functions provide $P(Q)$ for the case where the scatterer is randomly oriented. In
that case, the scattering intensity only depends on the length of $Q$ . The intensity measured on the plane of the SAS
detector will have an azimuthal symmetry around $Q=0$.

Our so-called 2D scattering intensity functions provide $P(Q,\phi)$ for an oriented system as a function of a
$q$ vector in the plane of the detector. We define the angle $\phi$ as the angle between the $q$ vector and the horizontal
($x$) axis of the plane of the detector.

For information about polarised and magnetic scattering, see :ref:`magnetism`.