  We have investigated experimentally the pressure dependence of the production
of ultracold neutrons (UCN) in superfluid helium in the range from saturated
vapor pressure to 20bar. A neutron velocity selector allowed the separation of
underlying single-phonon and multiphonon pro- cesses by varying the incident
cold neutron (CN) wavelength in the range from 3.5 to 10{\AA}. The predicted
pressure dependence of UCN production derived from inelastic neutron scattering
data was confirmed for the single-phonon excitation. For multiphonon based UCN
production we found no significant dependence on pressure whereas calculations
from inelastic neutron scattering data predict an increase of 43(6)% at 20bar
relative to saturated vapor pressure. From our data we conclude that applying
pressure to superfluid helium does not increase the overall UCN production rate
at a typical CN guide.
