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.

Figure 1

Measured transmissivity of Cu foils for UCNs plotted over UCN velocity. The in-medium velocity of 4.1 m/s (equivalent to 7 m/s out of medium) is marked with a vertical red line. The vertical blue line marks 8.2 m/s (equivalent to 10 m/s out of medium). For data treatment, a sliding average of 16 time bins was used. The error bars account for this. To improve legibility, only every fourth error bar is shown.

Figure 2

The measured transmissivity of Cu foils of three different thicknesses is plotted for UCNs of an in-medium velocity of 4.1 m/s (equivalent to 7 m/s out of medium). The red line represents a fit to the data using the transmission equation including a surface scattering term, see Eq. (2). The dashed green line represents the transmissivity as expected if the sample caused no surface scattering. For both curves, ${\sigma }_{\text{tot}}=2072$ b (at 4.1 m/s in medium) was used as UCN loss cross section of the sample bulk.