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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 (last modified: 2020-03-20)