We describe a method and present the results of the measurements of
spectral change of stored ultra-cold neutrons and the sub-barrier neutron
up-scattering from solid surfaces to the energy range higher than the
boundary energy of the sample.
The method consists in measuring the neutron absorption curves
as a function of UCN storage time and the thickness of the absorbers.
The quasi-elastic and inelastic UCN up-scattering probability is determined
at room temperature.
The neutron spectra are inferred in monochromatic and more detailed
approximations.