Generalized distorted-wave Born approximation for neutron reflection
- Atomic Energy of Canada Limited Research, Chalk River, Ontario, K0J 1J0 (Canada)
A theory is developed for the specular reflection of thermal neutrons from an arbitrary smooth surface or interface using a Green-function technique and leads to a family of Born approximations that includes both the familiar plane-wave Born approximation (PWBA) and a generalized distorted-wave Born approximation (DWBA). The DWBA reduces to the PWBA if the wave-vector transfer, [ital q][sub [ital z]], is much larger than the critical wave vector for total reflection, [ital q][sub [ital c]], and to Fresnel's formula for reflection from a sharp surface if [ital q][sub [ital z]] is much less than the inverse surface thickness. Detailed numerical calculations of the reflectivity for a number of symmetric model surfaces show that it is only when [ital q][sub [ital z]][much gt][ital q][sub [ital c]] that the reflectivity [ital R] is sensitive to the detailed shape and thickness of the surface potential. In particular, one requires experiments with [ital q][sub [ital z]]/[ital q][sub [ital c]] ranging from about 3 to 30, where [ital R] decreases from about 10[sup [minus]3] to 10[sup [minus]7], to obtain useful information on the shape and thickness of symmetric surfaces. From a comparison with the exact reflectivity for one particular surface, we find that the DWBA is typically three orders of magnitude more accurate than both the PWBA and an [ital ad] [ital hoc] model commonly used by experimenters for all values of [ital q][sub [ital z]], and that the relative error in the DWBA is almost everywhere less than 0.01% which is, therefore, of the same order of magnitude as the intrinsic error in the Fermi pseudopotential itself. The high accuracy that we have found when the DWBA is applied to symmetric surfaces is in contrast to the relatively low accuracy that others have found when they applied this kind of approximation to thin films on substrates of low intrinsic reflectivity. The reason for this is discussed.
- OSTI ID:
- 5539562
- Journal Information:
- Physical Review, B: Condensed Matter; (United States), Vol. 48:23; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SURFACES
REFLECTIVITY
THERMAL NEUTRONS
ELASTIC SCATTERING
BORN APPROXIMATION
DISTORTED WAVE THEORY
GREEN FUNCTION
NUMERICAL SOLUTION
BARYONS
ELEMENTARY PARTICLES
FERMIONS
FUNCTIONS
HADRONS
NEUTRONS
NUCLEONS
OPTICAL PROPERTIES
PHYSICAL PROPERTIES
SCATTERING
SURFACE PROPERTIES
663610* - Neutron Physics- (1992-)