# two_lorentzian

This model calculates an empirical functional form for SAS data characterized by two Lorentzian-type functions.

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

scale | Source intensity | None | 1 |

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

lorentz_scale_1 | First power law scale factor | None | 10 |

lorentz_length_1 | First Lorentzian screening length | Å | 100 |

lorentz_exp_1 | First exponent of power law | None | 3 |

lorentz_scale_2 | Second scale factor for broad Lorentzian peak | None | 1 |

lorentz_length_2 | Second Lorentzian screening length | Å | 10 |

lorentz_exp_2 | Second exponent of power law | None | 2 |

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

**Definition**

The scattering intensity \(I(q)\) is calculated as

where \(A\) = Lorentzian scale factor #1, \(C\) = Lorentzian scale #2, \(\xi_1\) and \(\xi_2\) are the corresponding correlation lengths, and \(n\) and \(m\) are the respective power law exponents (set \(n = m = 2\) for Ornstein-Zernicke behaviour).

For 2D data the scattering intensity is calculated in the same way as 1D, where the \(q\) vector is defined as

**References**

None.

**Author:** NIST IGOR/DANSE **on:** pre 2010

**Last Modified by:** Piotr rozyczko **on:** January 29, 2016

**Last Reviewed by:** Paul Butler **on:** March 21, 2016