\(\renewcommand\AA{\unicode{x212B}}\)
TFMuonium¶
Description¶
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 \(f_\text{cut} = 10^{32}\).
Properties (fitting parameters)¶
Name |
Default |
Description |
---|---|---|
A0 |
0.5 |
Amplitude |
Field |
5.0 |
B-field (G) |
A |
600.0 |
Isotropic hyperfine coupling constant (MHz) |
Phi |
0.0 |
Phase |
References¶
[1] P. Percival, TRIUMF Summer Institute 2011.
Categories: FitFunctions | Muon\MuonSpecific
Source¶
Python: TFMuonium.py