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

Definition

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

$$ I(q) = \frac{\text{scale}}{V} \cdot \left[ 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} \right]^2 + \text{background}

$$

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).

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

Created By |
sasview |

Uploaded |
Sept. 7, 2017, 3:56 p.m. |

Category |
Sphere |

Score |
0 |

Verified |
Verified by SasView Team on 07 Sep 2017 |

In Library |
This model is included in the SasView library by default |

Files |
sphere.py sphere.c |

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