Ultra cold neutron production by multiphonon processes in superfluid helium under pressure

Cold neutrons are converted to ultra cold neutrons (UCN) by the excitation of a single phonon or multiphonons in superfluid helium. The dynamic scattering function S ( q , ℏ ω ) of the superfluid helium strongly depends on pressure, leading to a pressure-dependent differential UCN production rate. A phenomenological expression for the multiphonon part of the scattering function s ( λ ) describing UCN production has been derived from inelastic neutron scattering data. When combined with the production rate from single phonon processes this allows us to calculate the UCN production for any incident neutron flux. For calculations of the UCN production from single phonon processes we propose to use the values S * = 0.118 ( 8 ) at saturated vapour pressure and S * = 0.066 ( 6 ) at 20 bar. As an example we will calculate the expected UCN production rate at the cold neutron beam for fundamental physics PF1b at the Institut Laue Langevin. We conclude that UCN production in superfluid helium under pressure is not attractive.