Scattering of slow neutrons on layered media

The theory of the coherent scattering of slow neutrons on media with one-dimensional periodicity of parameters is developed. A system of two linear first-order equations is obtained for the amplitude of the incident and reflected waves. A solution to this system of equations for a semi-infinite medium with a periodic three-dimensional scattering amplitude determines the reflection and absorption factors, This makes it possible to find the parameters of a layered medium that correspond to a neutron-reflection factor close to the maximum one. The results presented here can be used in calculating the focusing of beams in experiments employing slow neutrons having a Maxwell spectrum.