GauBroadGauKT

Description

Gaussian-Broadened Gaussian Kubo-Toyabe relaxation function given by:

A(t)=A_0\left(\frac{1}{3}+\frac{2}{3}\left(\frac{1+R^2}{1+R^2+R^2\Delta^2_\text{eff}t^2}\right)^{\frac{3}{2}}\left(1- \frac{\Delta^2_\text{eff}t^2}{1+R^2+R^2\Delta^2_\text{eff}t^2}\right)exp\left(\frac{-\Delta^2_\text{eff}t^2}{2(1+R^2+R^2\Delta^2_\text{eff}t^2)}\right)\right)

where R and \Delta^2_\text{eff} are defined by,

R = \frac{\omega}{\Delta_0},

\Delta^2_\text{eff} = \Delta^2_0 + \omega^2,

where,

A_0 is the amplitude,

R the Broadening ratio,

\Delta_0 is the central width,

\omega is the rms width,

and \Delta_{eff} is the effective width.

(Source code, png, hires.png, pdf)

../../_images/GauBroadGauKT-1.png

Properties (fitting parameters)

Name Default Description
A0 0.2  
R 0.1 Broadening ratio
Delta0 0.1 Central Field width

Source

Python: GauBroadGauKT.py (last modified: 2019-11-14)