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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

## 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