The whispering gallery effect in neutron scattering

We present the first experimental evidence for neutron localization (whispering gallery wave) in the quasistationary quantum states near a cylindrical mirror surface. The boundary effective well is formed by the centrifugal effective potential and the mirror neutron-matter optical potential. We present a formalism that describes quantitatively the neutron scattering at a cylindrical mirror surface and compare the experimental results to this model. We discuss further prospects based on this study.