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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)