  We review the diffuse scattering and the loss coefficient in ultracold
neutron reflection from slightly rough surfaces, report a surprising reduction
in loss coefficient due to roughness, and discuss the possibility of transition
from quantum treatment to ray optics. The results are used in a computer
simulation of neutron storage in a recent neutron lifetime experiment that
re-ported a large discrepancy of neutron lifetime with the current particle
data value. Our partial re-analysis suggests the possibility of systematic
effects that were not included in this publication.
