  In a recent numerical optimization study we have found that liquid
para-hydrogen coupled cold neutron moderators deliver 3 - 5 times higher cold
neutron brightness at a spallation neutron source if they take the form of a
flat, quasi 2-dimensional disc, in contrast to the conventional more voluminous
shapes used by now. In the present paper we describe a simple theoretical
explanation of this unexpected behavior, which is based on the large difference
in para-hydrogen between the values of the scattering mean free path for
thermal neutrons (in the range of 1 cm) and its much larger equivalent for cold
neutrons. This model leads to the conclusions that the optimal shape for high
brightness para-hydrogen neutron moderators is the quasi 1-dimensional tube and
these low dimensional moderators can also deliver much enhanced cold neutron
brightness in fission reactor neutron sources, compared to much more voluminous
liquid D2 or H2 moderators currently used. Neutronic simulation calculations
confirm both of these theoretical conclusions.
