Surface density profiles and the rate of loss of stored ultracold neutrons

Abstract The reflection losses for stored ultracold neutrons have been calculated for various profiles of molecular number density at the wall surface. The results show relatively low sensitivity to realistic departures from a simple step function. For a surface density rising as a linear ramp extending over a depth of 100 A, in the case where the mean Fermi potentials is 100 neV, the losses are only about 4% higher than those for the abrupt step case. The same degree of insensitivity has been found for other shapes of profile. The effect on the losses of a reduced Debye temperature in the first few atomic layers of the surface is also considered.