.. index:: EISFDiffSphereAlkyl
This fitting function models the elastic incoherent intensity of a linear polycarbon chain (alkyl) where the local diffusion of each unit in the chain is modeled as undergoing continuous diffusion but confined to a spherical volume whose radius varies from a minimal value r to a maximum value R [1].
R_i = (R -r) * (i/M) + r
EISF(Q) = \frac{1}{M} \sum_{i=1}^{M} (3 \frac{j_1(QR_i)}{QR_i})^2(Q\cdot R_i)
r and 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: - :ref:`EISFDiffSphere <func-EISFDiffSphere>` - :ref:`ElasticDiffSphere <func-ElasticDiffSphere>` - :ref:`InelasticDiffSphere <func-InelasticDiffSphere>` - :ref:`DiffSphere <func-DiffSphere>`
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Example - fit of Q-dependence:
.. testcode:: QdependenceFit
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=2.0, r=0.12, R=1.6, M=9
eisf = [1.96561499215648, 1.90667574712235, 1.82327109734092,
1.72075639596568, 1.60529662348532, 1.48322421137169,
1.36043655237770, 1.24191091785048, 1.13138963884055]
w = CreateWorkspace(q, eisf, NSpec=1)
results = Fit('name=EISFDiffSphereAlkyl, M=9', w, WorkspaceIndex=0)
print(results.Function)
Output:
.. testoutput:: QdependenceFit
name=EISFDiffSphereAlkyl,M=9,A=2,Rmin=0.12,Rmax=1.6
.. properties::
.. categories::
.. sourcelink::