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 attibute $Q$ 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++ source: InelasticDiffSphere.cpp

C++ header: InelasticDiffSphere.h