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TeixeiraWaterIqt

Description

It models the intermediate scattering function for the inelastic spectra of water molecules, based on Teixeira’s model [1].

\[\begin{split}F_s(Q,t) &= A R(Q,t) T(Q,t) \\ T(Q,t) &= e^{- \Gamma t} \\ R(Q,t) &= j_{0}^{2}(Qa)+3j_{1}^{2}(Qa) e^{-t/{3\tau_1}}+5j_{2}^{2}(Qa) e^{-t/\tau_1}\end{split}\]

where:

• \(j_{n}(x)\) are the spherical bessel functions of order n.

• \(A\) is the amplitude.

• \(\Gamma\) is the spectrum linewidth.

• \(\tau_{1}\) is the relaxation time associated with rotation diffusion.

• \(Q\) is the elastic momentum transfer, \(0.4\AA^{-1}\) by default, but should be set to a correct value prior to fitting.

• \(a\) is the molecular radius of rotation, set by default to \(0.98\AA\).

Units of \(a\) are inverse units of \(Q\).

Units of \(\Gamma\) inverse units of \(t\). After fitting, if scaled by correct \(\hbar\), units are \(meV\) if units of \(\tau_1\) are ps. Alternatively, units of \(\Gamma\) are \(\mu eV\) if units of \(\tau_{1}\) are ns.

Attributes (non-fitting parameters)

Name	Type	Default	Description
Q
a

Properties (fitting parameters)

Name	Default	Description
Amp	1.0	Amplitude
Tau1	0.05	Relaxation time
Gamma	1.2	Line Width

References

[1]

10. Teixeira, M.-C. Bellissent-Funel, S. H. Chen, and A. J. Dianoux. Phys. Rev. A, 31:1913–1917

Categories: FitFunctions | QuasiElastic

Source

Python: TeixeiraWaterIqt.py