# pringle

The Pringle model provides the form factor, \(P(q)\), for a ‘pringle’ or ‘saddle-shaped’ disc that is bent in two directions.

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

scale | Source intensity | None | 1 |

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

radius | Pringle radius | Å | 60 |

thickness | Thickness of pringle | Å | 10 |

alpha | Curvature parameter alpha | None | 0.001 |

beta | Curvature paramter beta | None | 0.02 |

sld | Pringle sld | 10^{-6}Å^{-2} |
1 |

sld_solvent | Solvent sld | 10^{-6}Å^{-2} |
6.3 |

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

**Definition**

The form factor for this bent disc is essentially that of a hyperbolic paraboloid and calculated as

where

and \(\Delta \rho \text{ is } \rho_{pringle}-\rho_{solvent}\), \(V\) is the volume of
the disc, \(\psi\) is the angle between the normal to the disc and the q vector,
\(d\) and \(R\) are the “pringle” thickness and radius respectively, \(\alpha\) and
\(\beta\) are the two curvature parameters, and \(J_n\) is the n^{th} order
Bessel function of the first kind.

**Reference**

Karen Edler, Universtiy of Bath, Private Communication. 2012. Derivation by Stefan Alexandru Rautu.

**Author:** Andrew Jackson **on:** 2008

**Last Modified by:** Wojciech Wpotrzebowski **on:** March 20, 2016

**Last Reviewed by:** Andrew Jackson **on:** September 26, 2016