6.3

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InelasticDiffRotDiscreteCircle

Description

Summary

This fitting function models the inelastic part of the dynamics structure factor of a particle undergoing discrete jumps on N-sites evenly distributed in a circle. The particle can only jump to neighboring sites. This is the most common type of discrete rotational diffusion in a circle.

\[S(Q,E) \equiv = \int e^{-iEt/\hbar} I(Q,t) dt = \frac{1}{\pi} \sum_{l=1}^{N-1} A_l (Q,r) \frac{\hbar \tau_l^{-1}}{(\hbar \tau_l^{-1})^2+E^2}\]
\[A_l(Q,r) = \frac{1}{N} \sum_{k=1}^{N} j_0( 2 Q r \sin(\frac{\pi k}{N}) ) \cos(\frac{2\pi lk}{N})\]
\[\tau_l^{-1} = 4 \tau^{-1} \sin^2(\frac{\pi l}{N})\]

with h = 4.135665616 meV ps.

This function makes up the inelastic part of DiffRotDiscreteCircle.

Attributes (non-fitting parameters)

Name Type Default Description
N      
Q      
WorkspaceIndex      

\(N\) (integer, default=3) number of sites - \(Q\) (double, default=0.5) Momentum transfer - \(WorkspaceIndex\) (integer, default=0)

Properties (fitting parameters)

Name Default Description
Intensity 1.0 scaling factor [no units]
Radius 1.0 Circle radius [Angstroms]
Decay 1.0 Inverse of transition rate, in nanoseconds if energy in micro-ev, or picoseconds if energy in mili-eV
Shift 0.0 Shift in the centre of the peak

Categories: FitFunctions | QuasiElastic