Volume: Page/Article: ------------------------------------------------------------------------ Article Collection: View Collection Help (Click on the Check Box to add an article.) ------------------------------------------------------------------------ Phys. Rev. B 48, 17477?17485 (1993) [Issue 23 ? 15 December 1993 ] [ Previous article | Next article | Issue 23 contents ] Add to article collection View Page Images or PDF (1126 kB) ------------------------------------------------------------------------ Generalized distorted-wave Born approximation for neutron reflection V. F. Sears Atomic Energy of Canada Limited Research, Chalk River, Ontario, Canada K0J 1J0 Received 13 August 1993 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, qz, is much larger than the critical wave vector for total reflection, qc, and to Fresnel's formula for reflection from a sharp surface if qz 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 qz >> qc that the reflectivity R is sensitive to the detailed shape and thickness of the surface potential. In particular, one requires experiments with qz/qc ranging from about 3 to 30, where R decreases from about 10-3 to 10-7, 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 ad hoc model commonly used by experimenters for all values of qz, 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. ©1993 The American Physical Society URL: http://link.aps.org/abstract/PRB/v48/p17477 DOI: 10.1103/PhysRevB.48.17477 PACS: 61.12.Bt, 68.90.+g ------------------------------------------------------------------------ Add to article collection View Page Images or PDF (1126 kB) [ Previous article | Next article | Issue 23 contents ] ------------------------------------------------------------------------ References (Reference links marked with dot may require a separate subscription.) 1. G. P. Felcher, SPIE Conf. Proc. 983, 2 (1988). 2. J. Penfold and R. K. Thomas, J. Phys. Condens. Matter 2, 1369 (1990) [dot INSPEC ]. 3. T. P. Russell, Mater. Sci. Rep. 5, 171 (1990) [dot INSPEC ]. 4. M. M a hat_aza, C. Sella, and M. K a hat_abouchi, Appl. Surf. Sci. 60/61, 573 (1992). 5. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975). 6. L. Névot and P. Croce, Rev. Phys. Appl. 15, 761 (1980) [dot INSPEC ]. 7. A. Steyerl, Z. 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