# two_lorentzian

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

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

scale |
Scale factor or Volume fraction |
None |
1 |

background |
Source background |
cm |
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

**Source**

**References**

None.

**Authorship and Verification**

**Author:**NIST IGOR/DANSE**Date:**pre 2010**Last Modified by:**Piotr rozyczko**Date:**January 29, 2016**Last Reviewed by:**Paul Butler**Date:**March 21, 2016