  We show how the entanglement contained in states of spins arranged on a
lattice may be quantified with observables arising in scattering experiments.
We focus on the partial differential cross-section obtained in neutron
scattering from magnetic materials but our results are sufficiently general
such that they may also be applied to, e.g., optical Bragg scattering from
ultracold atoms in optical lattices or from ion chains. We discuss resonating
valence bond states and ground and thermal states of experimentally relevant
models--such as Heisenberg, Majumdar-Ghosh, and XY model--in different
geometries and with different spin numbers. As a by-product, we find that for
the one-dimensional XY model in a transverse field such measurements reveal
factorization and the quantum phase transition at zero temperature.
