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}.

(Source code, png, hires.png, pdf)

../../_images/TFMuonium-1.png

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

Source

Python: TFMuonium.py (last modified: 2019-11-14)