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Scattering of ultracold neutrons from rough surfaces of metal foils

The transparency of metal foils for ultracold neutrons (UCNs) plays an important role in the design of future high-density UCN sources, which will feed a number of fundamental physics experiments. In this work, we describe and discuss the measured transmission of a collimated beam of very slow neutrons (UCNs and very cold neutrons) through foils of Al, Cu, and Zr of various thicknesses at room temperature. Our goal was to separate scattering and absorption in the sample bulk from surface scattering, and to quantify the contribution of the surface. We were able to demonstrate that the surface roughness of these foils caused a significant fraction of UCN scattering. The surface roughness parameter $b$ extracted from UCN measurements was shown to be of the same order of magnitude as the surface parameter determined by atomic-force microscopy. They lie in the order of several hundreds of angstroms. Using the formalism developed here, transmission data from previous neutron-optical experiments were re-analyzed and their surface roughness parameter $b$ was extracted.