We report an experiment demonstrating diffraction of cold neutrons by surface acoustic waves. We show that, in contrast to analogous experiments with light, the motion of the surface-acoustic-wave deformation of the surface requires significant modification of the diffraction equation applicable to stationary gratings. Diffracted beam intensities are in reasonable agreement with a simple theoretical treatment.PACS numbers: 61.12.Ex, 43.20.+g, The diffraction of light by the moving "grating" formed by a surface acoustic wave (SAW) is a wellknown phenomenon,^ which has been routinely used to investigate SAW propagation and attenuation characteristics.^ We report here an experiment which demonstrates the neutron-optical analogy of this effect.There are two main differences between the scattering of neutrons and the scattering of light by surface acoustic waves. Firstly, the refractive index ^ of matter for neutrons is very close to unity, i.e., for neutrons 1-//~10~^, whereas for light ^ -1 -1. This fact necessitates the use of grazing incidence for neutron investigations of surface phenomena. Secondly, for light, the SAW may be treated as a stationary grating to a very good approximation, while for neutrons this is not the case since the neutron speeds are an order of magnitude smaller than the SAW speed. We deal with this problem by transforming from the frame in which the SAW is stationary. An important consequence of this rapid motion of the grating is that the diffraction angles are much larger than those for neutrons diffracted by a stationary grating of the same spatial periodicity as the surface acoustic wavelength."*"^ Kinematics. -Consider a SAW propagating along the X axis on the surface of the material which occupies the space j; < 0. In the primed frame in which the SAW is stationary the diffraction-grating equation for reflected neutrons incident in the A'-K plane may be writtenwhere k' is the neutron wave number, 0' the glancing angle of incidence, and 9'n the angle of the nth diffracted beam (n =0, ± 1, ± 2, . . . ). ^ is the SAW wave number, and the integer ^ is ± 1 depending on whether the propagation of the SAW and the incident neutrons have the same or opposite senses. A Galilean transformation from the stationary to the (unprimed) laboratory frame yields the resultwhere K = mu/h, m is the neutron mass, and u is the SAW speed. The second of these equations corresponds to a neutron energy change due to the absorption of n phonons, and the diffracted-beam neutron wave number is consequently subscripted. For our experiment K<^{k,K) and (0,^")<^1, which yields the approximation el-0^^2n{K/k)[K/k-s].(3)The factor K/k-s is the ratio of the SAW velocity in the neutron rest frame to the neutron velocity in the laboratory. For cold neutrons this factor is an order of magnitude greater than unity, its value for a stationary grating of the same spatial frequency, and results in a significant enhancement of the diffraction angles.Dynamics. -In the stationary SAW frame, the relevant Schrodinger equation is dx...
