.. _sphere: 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 |1e-6Ang^-2| 1 sld_solvent Solvent scattering length density |1e-6Ang^-2| 6 radius Sphere radius |Ang| 50 =========== ================================= ============ ============= The returned value is scaled to units of |cm^-1| |sr^-1|, absolute scale. For information about polarised and magnetic scattering, see the :ref:magnetism documentation. **Definition** The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: 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). .. figure:: img/sphere_autogenfig.png 1D plot corresponding to the default parameters of the model. **Source** :download:sphere.py  $\ \star\$ :download:sphere.c  $\ \star\$ :download: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