.. index:: DiffSphere
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,
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}
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 j_l(z) spherical Bessel functions. Furthermore, the requirement that no particle flux can escape the sphere leads to the following boundary condition2:
\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 x_{n,l}.
The fit function DiffSphere has an elastic part modeled by fitting function :ref:`ElasticDiffSphere <func-ElasticDiffSphere>`, and an inelastic part modeled by :ref:`InelasticDiffSphere <func-InelasticDiffSphere>`.
.. attributes::
NumDeriv (boolean, default=true) carry out numerical derivative - Q (double, default=1.0) Momentum transfer
.. properties::
.. categories::
.. sourcelink::