diff --git a/Doc/UserManual/Scattering.tex b/Doc/UserManual/Scattering.tex index 2a8e4ae37fe47aa1f692c03aaf5985e2d6191622..22126f805d63444616b196cb68e3974a8342627b 100644 --- a/Doc/UserManual/Scattering.tex +++ b/Doc/UserManual/Scattering.tex @@ -583,7 +583,7 @@ Vineyard \cite{Vin82} discussed X-ray scattering, but failed to account for the distortion of the scattered wave; Mazur and Mills \cite{MaMi82} derived the inelastic neutron scattering cross section of ferromagnetic surface spin waves from scratch. -A correct and readable derivation of the DWBA cross section +A concise derivation of the DWBA cross section was provided by Dietrich and Wagner (1984/85) for X-rays \cite{DiWa84} and neutrons \cite{DiWa85}.} this requirement is dropped. @@ -742,8 +742,14 @@ Since magnetic refraction or scattering is beyong the scope of BornAgain, the relative magnetic permeability tensor is always $\v{\mu}(\r)=1$. \index{Permeability}% \index{Magnetic permeability}% -As customary in GISAXS, we assume with Laue \cite{Lau31} -that the dielectric properties of the material are those of a polarizable electron cloud. +As customary in SAXS and GISAXS, +\index{Grazing-incidence small-angle scattering!dielectric model}% +\index{Small-angle scattering!dielectric model}% +we assume +that the dielectric properties of the material are those of a polarizable electron cloud.\footnote +{This is occasionally called the \E{Laue model} +\index{Laue model}% + \cite{Lau31}.} Thereby the relative dielectric permittivity tensor~$\v{\eps}$ \index{Dielectric permittivity}% \index{Permittivity}% @@ -786,13 +792,13 @@ into a slowly varying component and one that fluctuates on atomic scales, 1ε030 2r040]{$\delta\eps(\r)$}{Fast varying part of the permittivity~$\eps(\r)$}% With the additional notation \begin{equation} - k(\r)^2 \coloneqq K^2 \overline{\eps}(\r) + k(\r)^2 \coloneqq K^2 \overline{\eps}(\r), \end{equation} -and +compatible with~\cref{Ekkn}, and \begin{equation} 4\pi\delta v(\r) \coloneqq - K^2\delta\eps, \end{equation} -the wave equation~\cref{EwaveE2} takes the form +the wave equation~\cref{ENabNabE} takes the form \begin{equation}\label{EwaveE3} \left\{-\Nabla\times\Nabla\times\v{1} + k(\r)^2\right\}\v{E}(\r) = 4\pi\delta v(\r)\v{E}(\r). @@ -802,7 +808,7 @@ the wave equation~\cref{EwaveE2} takes the form This is very similar to the perturbed Schrödinger equation~\cref{ESchrodiK}. There are only two differences: the more complicated differential operator, -and the fact that $\v{E}$ is vector valued, +and the fact that $\v{E}(\r)$ is vector valued, whereas unpolarized neutrons are described by a scalar wave function~$\psi(\r)$. %===============================================================================