.. index:: StaticLorentzianKT
Static Lorentzian Kubo-Toyabe function:
g_{z}^{L}(t,B_L) = A_0 \{1 - \frac{a}{\omega_{L}}j_1(\omega_{L}t)e^{-at}-\left(\frac{a}{\omega_L}\right)^2(j_o(\omega_{L}t)e^{-at}-1)-\left(1+\left(\frac{a}{\omega_L}\right)^2\right)a\int_{0}^{t}j_0(\omega_{L}\tau)e^{-a\tau}d\tau\}
where,
L refers to Lorentzian,
B_L refers to the longitudinal field applied to the z-axis,
j_{i} are the spheical Bessel functions of the First Kind,
\omega_L is is the precessing angular frequency and its relationship is given by B_L= \omega_{L} / \gamma_{\mu},
\gamma_{\mu} is the gyromagnetic ratio of muons,
and a (\mu s^{-1}) is the half-width at half maximum of the Lorentzian distribution.
.. 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("StaticLorentzianKT")
fig, ax=plt.subplots()
ax.plot(x, y(x))
ax.set_xlabel('t($\mu$s)')
ax.set_ylabel('A(t)')
.. attributes::
.. properties::
[1] Y. Uemura et al., Phys. Rev. B 31 546 (1985).
.. categories::
.. sourcelink::