  Ultra-cold neutrons (UCN) are neutrons with energies so low they can be
stored in material bottles and magnetic traps. They have been used to provide
the currently most accurate experiments on the neutron life time and electric
dipole moment. UCN can be produced in superfluid Helium at significantly higher
densities than by other methods. The predominant production process is usually
by one phonon emission which can only occur at a single incident neutron energy
because of momentum and energy conservation. However UCN can also be produced
by multiphonon processes. It is the purpose of this work to examine this
multiphonon production of UCN. We look at several different incident neutron
spectra, including cases where the multiphonon production is significant, and
see how the relative importance of multiphonon production is influenced by the
incident spectrum.
