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FmuF

Description

A fitting function for muon-fluorine bonds in ionic crystals.

\[A(t)=A_0e^{-\frac{(\sigma t)^2}{2}}e^{-\lambda t}G(t)\]

where,

\(\lambda\) is the exponential decay rate,

\(\sigma\) is the Gaussian decay rate,

\(\omega_D\) (rad/s) is the dipolar interaction angular frequency,

and the expression for \(G(t)\) and \(\omega_D\) are given by

\[G(t)=\frac{1}{6}\left[3+\cos(\sqrt{3} \omega_\text{D} t)+\left(1-\frac{1}{\sqrt{3}}\right)\cos(\frac{3-\sqrt{3}}{2}\omega_\text{D} t)+\left(1+\frac{1}{\sqrt{3}}\right)\cos(\frac{3+\sqrt{3}}{2}\omega_\text{D} t)\right]\]

and

\[\omega_D = 2\pi\nu\]

where \(\nu\) (MHz) is the dipolar interaction frequency.

Properties (fitting parameters)

Name	Default	Description
A0	0.5	Amplitude
FreqD	0.2	Dipolar interaction frequency (MHz)
Lambda	0.1	Exponential decay rate
Sigma	0.2	Gaussian decay rate

References

[1] J.H.Brewer et al., PRB 33 11 (1986).

Categories: FitFunctions | Muon\MuonSpecific

Source

Python: FmuF.py