SpinDiffusion

Description

The Spin diffusion fitting function, models the diffusion of isotropic muonium as a function of applied field for 1D, 2D and 3D behaviour [1]. The data fitted using this fit function is assumed to be in units of Gauss.

λ(B)=A24J(ω)J(ω)=20+S(t)cos(ωt)S(t)=i=13exp(2Dit)I0(2Dit)ω=2πf=γμB

where:

  • I0(x) is the zeroth order modified Bessel function.

  • ω is the angular momentum (MHz).

  • γμ is the Muon gyromagnetic ratio (2π×0.001356MHz/G).

  • S(t) is the autocorrelation function, represented by an anisotropic random walk.

  • J(ω) is the spectral density (MHz1). It is the Fourier Transform of S(t).

  • A is a parameter to be fitted.

  • Di are the fast and slow rate dipolar terms. These are also fitting parameters.

Systems of different dimensionality d can simply be represented in terms of fast and slow rates D and D:

D1=D,D2,D3=D(d=1)D1,D2=D,D3=D(d=2)D1,D2,D3=D(d=3)

For the d=3 case, the D parameter has no significance. It may be a good idea to fix this parameter to prevent the minimizer from performing unnecessary optimization steps in this case.

Attributes (non-fitting parameters)

Name

Type

Default

Description

NDimensions

Properties (fitting parameters)

Name

Default

Description

A

1.0

Amplitude, or Scaling factor

DParallel

1000.0

Dipolar parallel, the fast rate dipolar term (MHz)

DPerpendicular

0.01

Dipolar perpendicular, the slow rate dipolar term (MHz)

References

Categories: FitFunctions | Muon\MuonSpecific

Source

Python: SpinDiffusion.py