A Simple Relation for Effective Neutron Temperature in Cold Moderators with Lattice Vibrational Modes

Abstract

The effective neutron temperature in cold hydrogenous solid moderators is analyzed in phonon approximation with use made of two simple models representing the frequency distribution of lattice vibrations, and simple relations are derived between the variation of the effective neutron temperature and the moderator temperature, as also, an equation expressing the limiting neutron temperature in a moderator at absolute zero temperature. Good agreement is obtained between the calculated and experimental results in cold light water ice. It is indicated that unbounded cooling of the moderator is not necessarily effective in improving the moderating efficacy, in the case of slowing-down by lattice vibrations; it generally suffices to cool the moderator down to the limiting neutron temperature. It is revealed that approach of the neutron temperature to the limiting value is largely determined by the shape of the frequency distribution of the lattices, while the limiting value itself is influenced by such paramete...