# sphere

Spheres with uniform scattering length density

Parameter | Description | Units | Default value |
---|---|---|---|

scale | Scale factor or Volume fraction | None | 1 |

background | Source background | cm^{-1} |
0.001 |

sld | Layer scattering length density | 10^{-6}Å^{-2} |
1 |

sld_solvent | Solvent scattering length density | 10^{-6}Å^{-2} |
6 |

radius | Sphere radius | Å | 50 |

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

For information about polarised and magnetic scattering, see the Polarisation/Magnetic Scattering documentation.

**Definition**

The 1D scattering intensity is calculated in the following way (Guinier, 1955)

where *scale* is a volume fraction, \(V\) is the volume of the scatterer,
\(r\) is the radius of the sphere and *background* is the background level.
*sld* and *sld_solvent* are the scattering length densities (SLDs) of the
scatterer and the solvent respectively, whose difference is \(\Delta\rho\).

Note that if your data is in absolute scale, the *scale* should represent
the volume fraction (which is unitless) if you have a good fit. If not,
it should represent the volume fraction times a factor (by which your data
might need to be rescaled).

The 2D scattering intensity is the same as above, regardless of the orientation of \(\vec q\).

**Validation**

Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006).

**Source**

`sphere.py`

\(\ \star\ \) `sphere.c`

\(\ \star\ \) `sas_3j1x_x.c`

**References**

- A Guinier and G. Fournet,
*Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955)

**Authorship and Verification**

**Author:****Last Modified by:****Last Reviewed by:**S King and P Parker**Date:**2013/09/09 and 2014/01/06