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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

2.0

Diffusion

0.05

Diffusion coefficient, in units of A^2*THz, if energy in meV, or A^2*PHz if energy in ueV

Shift

0.0

Shift in domain

Categories: FitFunctions | QuasiElastic