.. index:: TFMuonium
General case TF muonium rotation
A(t)=\frac{A_0}{4}\{(1+\delta)a_{12}\cos(\omega_{12}+\phi)+ (1-\delta)a_{14}\cos(\omega_{14}+\phi)+(1+\delta)a_{34}\cos(\omega_{34}+\phi)+(1-\delta)a_{23}\cos(\omega_{23}+\phi)\}
and,
\delta= \frac{\chi}{\sqrt{1+\chi^2}},
\chi = (g_\mu+g_e)\frac{B}{A},
d = \frac{(g_e-g_\mu)}{g_e+g_\mu},
E_1=\frac{A}{4}(1+2d\chi) \qquad E_2=\frac{A}{4}(-1+2\sqrt{1+\chi^2})
E_3=\frac{A}{4}(1-2d\chi) \qquad E_4=\frac{A}{4}(-1-2\sqrt{1+\chi^2}),
\omega_{ij}= 2 \pi (E_i - E_j),
a_{ij}=\frac{1}{(1+(\omega_{ij}/(2\pi f_\text{cut}))^2)},
where,
A_0 is the amplitude,
A (MHz) is the isotropic hyperfine coupling constant,
\phi (rad) is the phase at time t=0,
g_\mu = 0.01355342 , the gyromagnetic ratio of muon,
g_e = 2.8024 , the gyromagnetic ratio of electron,
and f_\text{cut} = 10^{32}.
.. 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("TFMuonium")
fig, ax=plt.subplots()
ax.plot(x, y(x))
ax.set_xlabel('t($\mu$s)')
ax.set_ylabel('A(t)')
.. attributes::
.. properties::
[1] P. Percival, TRIUMF Summer Institute 2011.
.. categories::
.. sourcelink::