6.4

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MuH

Description

Fitting function for use by Muon scientists defined by:

\[A(t)=\frac{A_0(t)}{6}e^{-\lambda t}e^{-\frac{(\sigma t)^2}{2}}\left(1+\cos(\omega_{D}t + \phi)+2\cos\left(\frac{\omega_D}{2}t+\phi\right)+2\cos\left(\frac{3\omega_D}{2}t+\phi\right)\right)\]

\(A_0\) is the amplitude,

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

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

\(\omega_D = 2 \pi \nu_D\) where \(\nu_D\) (MHz) is the oscillating frequency,

and \(\phi\) (rad) is the phase at time \(t=0\).

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

../../_images/MuH-1.png

Properties (fitting parameters)

Name Default Description
A0 0.5 Amplitude
NuD 0.5 Oscillating Frequency (MHz)
Lambda 0.3 Exponential decay rate
Sigma 0.05 Gaussian decay rate
Phi 0.0 Phase (rad)

Source

Python: MuH.py