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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

[1]

6. Volino and A. J. Dianoux, Molecular Physics 41(2):271-279.

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