.. _func-DiffSphere: ========== DiffSphere ========== .. index:: DiffSphere Description ----------- This fitting function models the dynamics structure factor of a particle undergoing continuous diffusion but confined to a spherical volume. According to Volino and Dianoux `1 `__, .. math:: S(Q,E\equiv \hbar \omega) = A_{0,0}(Q\cdot R) \delta (\omega) + \frac{1}{\pi} \sum_{l=1}^{N-1} (2l+1) A_{n,l} (Q\cdot R) \frac{x_{n,l}^2 D/R^2}{[x_{n,l}^2 D/R^2]^21+\omega^2} .. math:: A_{n,l} = \frac{6x_{n,l}^2}{x_{n,l}^2-l(l+1)} [\frac{QRj_{l+1}(QR) - lj_l(QR)}{(QR)^2 - x_{n,l}^2}]^2 Because of the spherical symmetry of the problem, the structure factor is expressed in terms of the :math:`j_l(z)` `spherical Bessel functions `__. Furthermore, the requirement that no particle flux can escape the sphere leads to the following boundary condition\ `2 `__: .. math:: \frac{d}{dr}j_l(rx_{n,l}/R)|_{r=R}=0 \,\,\,\, \forall l The roots of this set of equations are the numerical coefficients :math:`x_{n,l}`. The fit function DiffSphere has an elastic part modeled by fitting function :ref:`ElasticDiffSphere `, and an inelastic part modeled by :ref:`InelasticDiffSphere `. .. attributes:: :math:`NumDeriv` (boolean, default=true) carry out numerical derivative - :math:`Q` (double, default=1.0) Momentum transfer .. properties:: .. categories:: .. sourcelink::