# core_shell_sphere

Form factor for a monodisperse spherical particle with particle with a core-shell structure.

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

scale | Source intensity | None | 1 |

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

radius | Sphere core radius | Å | 60 |

thickness | Sphere shell thickness | Å | 10 |

sld_core | core scattering length density | 10^{-6}Å^{-2} |
1 |

sld_shell | shell scattering length density | 10^{-6}Å^{-2} |
2 |

sld_solvent | Solvent scattering length density | 10^{-6}Å^{-2} |
3 |

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

This model provides the form factor, \(P(q)\), for a spherical particle with a core-shell structure. The form factor is normalized by the particle volume.

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

where \(V_s\) is the volume of the whole particle, \(V_c\) is the volume of the core, \(r_s\) = \(radius\) + \(thickness\) is the radius of the particle, \(r_c\) is the radius of the core, \(\rho_c\) is the scattering length density of the core, \(\rho_s\) is the scattering length density of the shell, \(\rho_\text{solv}\), is the scattering length density of the solvent.

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

NB: The outer most radius (ie, = radius + thickness) is used as the effective radius for \(S(Q)\) when \(P(Q) \cdot S(Q)\) is applied.

**References**

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

**Validation**

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