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# ChudleyElliotSQE¶

## Description¶

This fitting function models the dynamic structure factor for a particle undergoing jump diffusion using the Chudley-Elliot Jump diffusion model [1].

\begin{align}\begin{aligned}S(Q,E) = Height \cdot \frac{1}{\pi} \frac{\Gamma}{\Gamma^2+(E-Centre)^2}\\\Gamma = \frac{\hbar}{\tau} \cdot \left(1 - \frac{sin(Ql)}{Ql}\right)\end{aligned}\end{align}

where:

• $$Height$$ - Intensity scaling, a fit parameter

• $$Centre$$ - Centre of peak, a fit parameter

• $$Tau$$ - Residence time, a fit parameter

• $$l$$ - Jump lengths, a fit parameter

• $$Q$$ - Momentum transfer, an attribute (non-fitting)

Units of $$l$$ are inverse units of $$Q$$.

Units of $$HWHM$$ are $$meV$$ if units of $$\tau$$ are ps. Alternatively, units of $$HWHM$$ are $$\mu eV$$ if units of $$\tau$$ are ns.

Name

Type

Default

Description

Q

WorkspaceIndex

## Properties (fitting parameters)¶

Name

Default

Description

Height

1.0

scaling factor

Centre

0.0

Shift along the X-axis

Tau

1.25

Residence time

L

1.25

Jump length

## References¶

Categories: FitFunctions | QuasiElastic