\(\renewcommand\AA{\unicode{x212B}}\)

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 \(f_\text{cut} = 10^{32}\).

Enable :plots: using DOCS_PLOTDIRECTIVE in CMake

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