Interference in the ultracold neutron transmission through thin layers

At the time-of-flight spectrometer for ultracold neutrons (UCN) with energies below 10^?4 eV at the FRM, Munich, the perpendicular neutron transmission through carbon and gold films of thickness 450 to 800 Å was measured as a function of neutron velocity in the range 11≧v _z≧3.7 m/s. The transmission curves obtained show the expected interference patterns due to interference between the partial waves transmitted and reflected at the two surfaces. From these curves absolute values for the thickness and density could be obtained. From the UCN transmission through a 4.71 μm thick copper foil a value a_coh=7.5±0.15 F was derived for the nuclear scattering length of Cu.