  We compute continuum and infinite volume limit extrapolations of the
structure factors of neutron matter at finite temperature and density. Using a
lattice formulation of leading-order pionless effective field theory, we
compute the momentum dependence of the structure factors at finite temperature
and at densities beyond the reach of the virial expansion. The Tan contact
parameter is computed and the result agrees with the high momentum tail of the
vector structure factor. All errors, statistical and systematic, are controlled
for. This calculation is a first step towards a model-independent understanding
of the linear response of neutron matter at finite temperature, a realm until
now little explored.
