.. index:: Meier
Time dependence of the polarization function for a static muon interacting with nuclear spin [1].
A(t)=\frac13(2P_x+P_z)
,where
P_z(t) = \frac{1}{2J+1}\left\{1+\sum^J_{m=-J+1}[\cos^2(2\alpha_m)+\sin^2(2\alpha_m)\cos(\lambda^+_m-\lambda^-_m)t]\right\},
P_x(t) = \frac{1}{2J+1}\sum^J_{m=-J} \{ \cos^2\alpha_{m+1}\sin^2\alpha_m\cos(\lambda_{m+1}^+-\lambda_m^+)t +\cos^2\alpha_{m+1}\cos^2\alpha_m\cos(\lambda_{m+1}^+-\lambda_m^-)t +\sin^2\alpha_{m+1}\sin^2\alpha_m\cos(\lambda_{m+1}^--\lambda_m^+)t +\sin^2\alpha_{m+1}\cos^2\alpha_m\cos(\lambda_{m+1}^--\lambda_m^-)t\},
\lambda_m^\pm = \frac{1}{2}[\omega_Q(2m^2-2m+1)+\omega_D\pm W_m],
W_m = \{(\omega_D+\omega_Q)^2(2m-1)^2+\omega_D^2[J(J+1)-m(m-1)]\}^\frac{1}{2},
\tan(2\alpha_m)=\frac{\omega_D[J(J+1)-m(m-1)]^\frac{1}{2}}{(1-2m)(\omega_D+\omega_Q)},
\omega_D is the angular frequency due to dipolar coupling,
\omega_Q is the angular frequency due to quadrupole interaction of the nuclear spin J due to a field gradient exerted by the presence of the muon,
J is the total angular momentum quantum number,
and m is the z-component of the total orbital quantum number.
.. 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("Meier")
fig, ax=plt.subplots()
ax.plot(x, y(x))
ax.set_xlabel('t($\mu$s)')
ax.set_ylabel('A(t)')
.. attributes::
[1] P.H. Meier, HFI 17-19 427-434 (1984).
.. properties::
.. categories::
.. sourcelink::