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StaticLorentzianKT¶
Description¶
Static Lorentzian Kubo-Toyabe function:
\[g_{z}^{L}(t,B_L) = A_0 \{1 - \frac{a}{\omega_{L}}j_1(\omega_{L}t)e^{-at}-\left(\frac{a}{\omega_L}\right)^2(j_o(\omega_{L}t)e^{-at}-1)-\left(1+\left(\frac{a}{\omega_L}\right)^2\right)a\int_{0}^{t}j_0(\omega_{L}\tau)e^{-a\tau}d\tau\}\]
where,
\(L\) refers to Lorentzian,
\(B_L\) refers to the longitudinal field applied to the z-axis,
\(j_{i}\) are the spheical Bessel functions of the First Kind,
\(\omega_L\) is is the precessing angular frequency and its relationship is given by \(B_L= \omega_{L} / \gamma_{\mu}\),
\(\gamma_{\mu}\) is the gyromagnetic ratio of muons,
and \(a (\mu s^{-1})\) is the half-width at half maximum of the Lorentzian distribution.
Properties (fitting parameters)¶
Name |
Default |
Description |
---|---|---|
A0 |
0.2 |
|
A |
0.1 |
Half-width of half maximum of Lorentzian distribution (microsecs) |
Field |
0.1 |
Longitudinal B-field (G) |
References¶
[1] Y. Uemura et al., Phys. Rev. B 31 546 (1985).
Categories: FitFunctions | Muon\MuonGeneric
Source¶
Python: StaticLorentzianKT.py