$$

StaticLorentzianKT

Description

Static Lorentzian Kubo-Toyabe function:

$$g_z^L(t,B_L)=A_0\{1-\frac{a}{{\omega }_L}{j}_1({\omega }_{L}t)e^{-at}-{\left(\frac{a}{{\omega }_L}\right)}^2(j_o({\omega }_{L}t)e^{-at}-1)-(1+{\left(\frac{a}{{\omega }_L}\right)}^2)a{\int }_0^t{j}_0({\omega }_L\tau )e^{-a\tau }d\tau \}$$

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.

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

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