.. _func-TeixeiraWaterIqt: ================ TeixeiraWaterIqt ================ .. index:: TeixeiraWaterIqt Description ----------- It models the intermediate scattering function for the inelastic spectra of water molecules, based on Teixeira's model [1]_. .. math:: 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} where: - :math:`j_{n}(x)` are the spherical bessel functions of order *n*. - :math:`A` is the amplitude. - :math:`\Gamma` is the spectrum linewidth. - :math:`\tau_{1}` is the relaxation time associated with rotation diffusion. - :math:`Q` is the elastic momentum transfer, :math:`0.4\AA^{-1}` by default, but should be set to a correct value prior to fitting. - :math:`a` is the molecular radius of rotation, set by default to :math:`0.98\AA`. Units of :math:`a` are inverse units of :math:`Q`. Units of :math:`\Gamma` inverse units of :math:`t`. After fitting, if scaled by correct :math:`\hbar`, units are :math:`meV` if units of :math:`\tau_1` are *ps*. Alternatively, units of :math:`\Gamma` are :math:`\mu eV` if units of :math:`\tau_{1}` are *ns*. .. attributes:: .. properties:: References ---------- .. [1] J. Teixeira, M.-C. Bellissent-Funel, S. H. Chen, and A. J. Dianoux. `Phys. Rev. A, 31:1913–1917 `__ .. categories:: .. sourcelink::