.. _core-multi-shell:

core_multi_shell
=======================================================

This model provides the scattering from a spherical core with 1 to 10  concentric shell structures. The SLDs of the core and each shell are  individually specified.

============ ==================================== ============ =============
Parameter    Description                          Units        Default value
============ ==================================== ============ =============
scale        Scale factor or Volume fraction      None                     1
background   Source background                    |cm^-1|              0.001
sld_core     Core scattering length density       |1e-6Ang^-2|             1
radius       Radius of the core                   |Ang|                  200
sld_solvent  Solvent scattering length density    |1e-6Ang^-2|           6.4
n            number of shells                     None                     1
sld[n]       scattering length density of shell k |1e-6Ang^-2|           1.7
thickness[n] Thickness of shell k                 |Ang|                   40
============ ==================================== ============ =============

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


**Definition**

This model is a trivial extension of the CoreShell function to a larger number
of shells. The scattering length density profile for the default sld values
(w/ 4 shells).

.. figure:: img/core_multi_shell_sld_default_profile.jpg

    SLD profile of the core_multi_shell object from the center of sphere out
    for the default SLDs.*

The 2D scattering intensity is the same as $P(q)$ above, regardless of the
orientation of the $\vec q$ vector which is defined as

.. math::

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

.. note:: **Be careful!** The SLDs and scale can be highly correlated. Hold as
         many of these parameters fixed as possible.

.. note:: The outer most radius (= *radius* + *thickness*) is used as the
          effective radius for $S(Q)$ when $P(Q)*S(Q)$ is applied.

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

Our model uses the form factor calculations implemented in a C-library provided
by the NIST Center for Neutron Research [#Kline2006]_.


.. figure:: img/core_multi_shell_autogenfig.png

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


**Source**

:download:`core_multi_shell.py <src/core_multi_shell.py>`
$\ \star\ $ :download:`core_multi_shell.c <src/core_multi_shell.c>`
$\ \star\ $ :download:`sas_3j1x_x.c <src/sas_3j1x_x.c>`

**References**

Also see the :ref:`core-shell-sphere` model documentation and [#Feigin1987]_

.. [#Kline2006] S R Kline, *J Appl. Cryst.*, 39 (2006) 895

.. [#Feigin1987] L A Feigin and D I Svergun, *Structure Analysis by
   Small-Angle X-Ray and Neutron Scattering*, Plenum Press, New York, 1987.

**Authorship and Verification**

* **Author:** NIST IGOR/DANSE **Date:** pre 2010
* **Last Modified by:** Paul Kienzle **Date:** September 12, 2016
* **Last Reviewed by:** Paul Kienzle **Date:** September 12, 2016