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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 \(t=0\) .

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Properties (fitting parameters)

Name

Default

Description

A0

0.2

FreqA

0.3

Isotropic hyperfine coupling constant (MHz)

FreqD

0.2

Anisotropic hyperfine coupling constant (MHz)

FCut

1.0

Frequency cut (MHz)

Phi

0.0

Phase

References

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

Categories: FitFunctions | Muon\MuonSpecific

Source

Python: ZFMuonium.py