Aluminium static Rayleigh weight
================================

The gallery example :doc:`/gen_examples/plot_al_rayleigh_weight` computes a
static elastic-scattering weight for aluminium at ``Te=Ti=10 eV`` and
``rho = 2.7, 8.1, 15 g/cc``. It uses the public Otter workflow directly and
writes ``PNG`` and vector ``PDF`` copies of the figure.

For each density, the script exports the screening-cloud transform ``q(k)``
and ionic form factor ``f(k)`` from :func:`otter.io.state.build_state_arrays`,
uses the one-component ``Sii(k)`` from QOZ/HNC, and evaluates

.. math::

   W(k)=|q(k)+f(k)|^2 S_{ii}(k).

The default mode reads a checksummed archive generated by this exact script,
which keeps documentation builds fast. To regenerate all three states, run

.. code-block:: console

   OTTER_RECOMPUTE_AL_RAYLEIGH=1 python docs/examples/plot_al_rayleigh_weight.py

The calculation path is entirely in the downloaded example source; no external
benchmark runner is imported. ``q`` is the charge-closed pseudoatom screening
cloud used by QOZ, while ``f`` is the bound-electron transform. The
ion-structure convention follows Starrett and Saumon (2014),
:cite:t:`StarrettSaumon2014`.