ZFMuonium.rst

ZFMuonium

.. index:: ZFMuonium

Description

ZF rotation for axial muonium

A(t)=\frac{A_0}{6}\{A_1\cos(\omega_{1}+\phi)+A_2\cos(\omega_{2}+\phi)+A_{3}\cos(\omega_{3}+\phi)\}

and,

\delta= \frac{\chi}{\sqrt{1+\chi^2}},

\omega_{1}= 2\pi(\text{FreqA} - \text{FreqD}),

\omega_{2}= 2\pi\left(\text{FreqA} + \frac{\text{FreqD}}{2}\right),

\omega_{3}= 3\pi \text{FreqD},

A_{i}=\frac{1}{(1+(\omega_{i}/(2\pi F_\text{cut}))^2)}, 0<i<4

where,

A_0 is the amplitude,

FreqA (MHz) is the isotropic hyperfine coupling constant,

FreqD (MHz) is the anisotropic hyperfine coupling constant,

F_\text{cut} is the frequency cut,

and \phi (rad) is the phase at time t=0 .

.. 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("ZFMuonium")
   fig, ax=plt.subplots()
   ax.plot(x, y(x))
   ax.set_xlabel('t($\mu$s)')
   ax.set_ylabel('A(t)')

.. attributes::

.. properties::

References

[1] P. Percival, TRIUMF Summer Institute 2011.

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