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HallRossSQE

Description

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

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

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.

Attributes (non-fitting parameters)

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

[1]

16. 12. Hall and D. K. Ross, Mol. Phys. 42, 673 (1981) <http://dx.doi.org/10.1080/00268978100100521>

Categories: FitFunctions | QuasiElastic

Source

C++ header: HallRossSQE.h

C++ source: HallRossSQE.cpp