6.4

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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.

../../_images/FmuF.png

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

Source

Python: FmuF.py