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This fitting function models the diffusion of a particle confined in a cylinder of radius \(R\) and length \(L\) [1].
\(A_0(Q_z)\) implements diffusion along the cylinder axis. \(B_0^0(Q_{\perp})\) implements diffusion perpendicular to the cylinder axis. Both diffusions are assumed to be decoupled. Finally, the integration in \(\theta\) implements a powder average (spherical Bessel functions).
\(R\) and \(L\) units are inverse of \(Q\) units.
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Example - fit of Q-dependence:
from __future__ import print_function
q = [0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9]
# A=1.0, R=3.5, L=1.7
eisf = [0.8327688, 0.60447105, 0.36837178, 0.18538092, 0.07615478,
0.02660468, 0.00973061, 0.00461192, 0.00222067]
w = CreateWorkspace(q, eisf, NSpec=1)
results = Fit('name=EISFDiffCylinder,A=1,R=2.0,L=1,constraints=(0.01<R,0.01<L),ties=(A=1)', w, WorkspaceIndex=0)
print(results.Function)
Output:
name=EISFDiffCylinder,A=1,R=3.5,L=1.7,constraints=(0.01<R,0.01<L),ties=(A=1)
Name | Default | Description |
---|---|---|
A | 1.0 | Amplitude, or Scaling factor |
R | 1.0 | Cylinder radius, inverse units of Q. |
L | 2.0 | Cylinder length, inverse units of Q. |
Categories: FitFunctions | QuasiElastic
Python: EISFDiffCylinder.py (last modified: 2020-03-27)