  Liquid hydrogen is a dense Bose fluid whose equilibrium properties are both
calculable from first principles using various theoretical approaches and of
interest for the understanding of a wide range of questions in many body
physics. Unfortunately, the pair correlation function $g(r)$ inferred from
neutron scattering measurements of the differential cross section $d\sigma
\over d\Omega$ from different measurements reported in the literature are
inconsistent. We have measured the energy dependence of the total cross section
and the scattering cross section for slow neutrons with energies between
0.43~meV and 16.1~meV on liquid hydrogen at 15.6~K (which is dominated by the
parahydrogen component) using neutron transmission measurements on the hydrogen
target of the NPDGamma collaboration at the Spallation Neutron Source at Oak
Ridge National Laboratory. The relationship between the neutron transmission
measurement we perform and the total cross section is unambiguous, and the
energy range accesses length scales where the pair correlation function is
rapidly varying. At 1~meV our measurement is a factor of 3 below the data from
previous work. We present evidence that these previous measurements of the
hydrogen cross section, which assumed that the equilibrium value for the ratio
of orthohydrogen and parahydrogen has been reached in the target liquid, were
in fact contaminated with an extra non-equilibrium component of orthohydrogen.
Liquid parahydrogen is also a widely-used neutron moderator medium, and an
accurate knowledge of its slow neutron cross section is essential for the
design and optimization of intense slow neutron sources. We describe our
measurements and compare them with previous work.
