# hollow_cylinder

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

scale | Source intensity | None | 1 |

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

radius | Cylinder core radius | Å | 20 |

thickness | Cylinder wall thickness | Å | 10 |

length | Cylinder total length | Å | 400 |

sld | Cylinder sld | Å^{-2} |
6.3 |

sld_solvent | Solvent sld | Å^{-2} |
1 |

theta | Theta angle | degree | 90 |

phi | Phi angle | degree | 0 |

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

This model provides the form factor, \(P(q)\), for a monodisperse hollow right angle circular cylinder (rigid tube) where the form factor is normalized by the volume of the tube (i.e. not by the external volume).

where the averaging \(\left<\ldots\right>\) is applied only for the 1D calculation.

The inside and outside of the hollow cylinder are assumed have the same SLD.

**Definition**

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

where *scale* is a scale factor, \(H = L/2\) and \(J_1\) is the 1st order
Bessel function.

**NB**: The 2nd virial coefficient of the cylinder is calculated
based on the outer radius and full length, which give an the effective radius
for structure factor \(S(q)\) when \(P(q) \cdot S(q)\) is applied.

In the parameters,the *radius* is \(R_\text{core}\) while *thickness* is \(R_\text{outer} - R_\text{core}\).

To provide easy access to the orientation of the core-shell cylinder, we define the axis of the cylinder using two angles \(\theta\) and \(\phi\) (see cylinder model).

**References**

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:**Richard Heenan**Date:**October 06, 2016(reparametrised to use thickness, not outer radius)

**Last Reviewed by:**Richard Heenan**Date:**October 06, 2016