.. index:: GauBroadGauKT
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.
.. plot::
from mantid.simpleapi import FunctionWrapper
import matplotlib.pyplot as plt
import numpy as np
x = np.arange(0.1,16,0.1)
y = FunctionWrapper("GauBroadGauKT")
fig, ax=plt.subplots()
ax.plot(x, y(x))
ax.set_xlabel('t($\mu$s)')
ax.set_ylabel('A(t)')
.. attributes::
.. properties::
[1] D.R. Noakes et al, PRB 56 2352 (1997).
[2] D.E. Maclaughlin et al, PRB 89 144419 (2014).
.. categories::
.. sourcelink::