LowTFMuonium

Description

A relaxation function for a pair of transver field triplet muonium frequencies.

A(t)=\frac{A_0}{4}\{(1+\delta)a_{12}\cos(\omega_{12}+\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),

E_2=\frac{A}{4}(-1+2\sqrt{1+\chi^2}),

E_3=\frac{A}{4}(1-2d\chi),

\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} (MHz).

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

../../_images/LowTFMuonium-1.png

Properties (fitting parameters)

Name Default Description
A0 0.2 Amplitude
Field 0.1 Magnetic Field (G)
A 0.2 Isotropic hyperfine coupling constant (MHz)
Phi 0.0 Phase (rad)

Source

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