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 \(t=0\) .
(Source code, png, hires.png, pdf)
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