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EISFDiffSphere¶
Description¶
This fitting function models the elastic incoherent intensity of a particle undergoing continuous diffusion but confined to a spherical volume [1], EISFDiffSphere.
\[EISF(Q) = (3 \frac{j_1(QR)}{QR})^2(Q\cdot R)\]
\(R\) units are inverse of \(Q\) units. Because of the spherical symmetry of the problem, the structure factor is expressed in terms of the \(j_l(z)\) spherical Bessel functions.
Related functions: - ElasticDiffSphere - InelasticDiffSphere - DiffSphere
References¶
Usage¶
Example - fit of Q-dependence:
q = [0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7, 1.9]
# A=2.0 and R=0.5
eisf = [1.9910173378712506, 1.9751335160492454,
1.9515113999365767, 1.9203919612905054,
1.8820909475511156, 1.8369942556092735,
1.7855523076069868, 1.7282735296640419,
1.6657170499144847]
w = CreateWorkspace(q, eisf, NSpec=1)
results = Fit('name=EISFDiffSphere', w, WorkspaceIndex=0)
print(results.Function)
Output:
name=EISFDiffSphere,A=2,R=0.5
Properties (fitting parameters)¶
Name |
Default |
Description |
---|---|---|
A |
1.0 |
Amplitude |
R |
1.0 |
Sphere radius, inverse units of Q. |
Categories: FitFunctions | QuasiElastic
Source¶
Python: EISFDiffSphere.py