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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¶

Categories: FitFunctions | Muon\MuonGeneric

## Source¶

Python: StaticLorentzianKT.py