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).

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)

Categories: FitFunctions | MuonSpecific

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