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InelasticDiffSphere¶

Description¶

This fitting function models the inelastic part of the dynamics structure factor of a particle undergoing continuous diffusion but confined to a spherical volume, DiffSphere.

\[S(Q,E\equiv \hbar \omega) = \frac{1}{\pi} \sum_{l=1}^{N-1} (2l+1) A_{n,l} (Q\cdot R) \frac{x_{n,l}^2 D/R^2}{[x_{n,l}^2 D/R^2]^21+\omega^2}\]

\[A_{n,l} = \frac{6x_{n,l}^2}{x_{n,l}^2-l(l+1)} [\frac{QRj_{l+1}(QR) - lj_l(QR)}{(QR)^2 - x_{n,l}^2}]^2\]

Because of the spherical symmetry of the problem, the structure factor is expressed in terms of the \(j_l(z)\) spherical Bessel functions.

The value of the momentum transfer can be obtained either through attribute \(Q\), or can be calculated from the input workspace using attribute \(WorkspaceIndex\). The value calculated using the workspace is used whenever attribute \(Q\) is set empty.

Attributes (non-fitting parameters)¶

Name	Type	Default	Description
Q
WorkspaceIndex

\(Q\) (double, default=1.0) Momentum transfer - \(WorkspaceIndex\) (integer, default=0)

Properties (fitting parameters)¶

Name	Default	Description
Intensity	1.0	scaling factor
Radius	2.0	Sphere radius, in Angstroms
Diffusion	0.05	Diffusion coefficient, in units of A^2THz, if energy in meV, or A^2PHz if energy in ueV
Shift	0.0	Shift in domain

Categories: FitFunctions | QuasiElastic

Source¶

C++ header: InelasticDiffSphere.h (last modified: 2021-03-31)

C++ source: InelasticDiffSphere.cpp (last modified: 2021-03-31)