84 ISSN 1063-7745, Crystallography Reports, 2016, Vol. 61, No. 1, pp. 84–88. © Pleiades Publishing, Inc., 2016. Original Russian Text © V.A. Artem’ev, A.Yu. Nezvanov, V.V. Nesvizhevsky, 2016, published in Kristallografiya, 2016, Vol. 61, No. 1, pp. 93–97. Precise Calculations in Simulations of the Interaction of Low Energy Neutrons with Nano-Dispersed Media 1 V. A. Artem’ev a, b , A. Yu. Nezvanov b , and V. V. Nesvizhevsky c a Research Institute of Materials Technology, Moscow, Russia b Moscow State Industrial University, Russia c Institut Max von Laue—Paul Langevin, Grenoble, France e-mail: niitm@inbox.ru Received March 6, 2014 Abstract—We discuss properties of the interaction of slow neutrons with nano-dispersed media and their application for neutron reflectors. In order to increase the accuracy of model simulation of the interaction of neutrons with nanopowders, we perform precise quantum mechanical calculation of potential scattering of neutrons on single nanoparticles using the method of phase functions. We compare results of precise calcu- lations with those performed within first Born approximation for nanodiamonds with the radius of 2–5 nm and for neutron energies 3 × 10 −7 –10 −3 eV. Born approximation overestimates the probability of scattering to large angles, while the accuracy of evaluation of integral characteristics (cross sections, albedo) is acceptable. Using Monte-Carlo method, we calculate albedo of neutrons from different layers of piled up diamond nano- powder. DOI: 10.1134/S1063774516010028 Investigation of propagation of radiation (photons, neutrons) through nano-dispersed media revealed energy ranges associated with significant deviations from the interaction with corresponding solid materi- als. For propagation of radiation with the wavelength λ ∼ a, where a is the characteristic size of dispersed nanoparticles, coherent effects in its interaction with matter are essential—the diffraction of radiation on structural and density inhomogeneities. Coherent interaction of radiation with matter inhomogeneities appears as additional (compared to solid material) intense scattering of radiation. We will consider pecu- liar properties of the interaction of low energy neu- trons with nano-dispersed media. For neutrons with wavelengths λ > λ d , where λ d ∼ (an) 1/4 , n is the atomic (nuclear) density of matter of dispersed nanoparticles, the diffraction on matter density inhomogeneities is the principal mechanism, which defines neutron propagation. Due to the multi- ple scattering, the propagation of neutrons could be considered as their diffusion in the medium. Addi- tional coherent scattering on dispersed nanoparticles increases the effective path of neutrons in matter and thus it increases the probability of radiation absorp- tion. This process is described via the decrease of the neutron diffusion length L c = (3Σ tr Σ c ) −1/2 , where Σ tr and Σ c are the macroscopic transport cross section and the cross section of neutron absorption in matter respectively. The probability of neutron absorption is w a ∝ 1L c . For neutrons with wavelength λ > λ d we get w a ∝ a −1/2 λ 5/2 . Increase in the intensity of scattering by dispersed nanoparticles increases the number of neutrons escap- ing from a matter sample that appears as increase in the number of neutrons diffusively reflected from the sample. Increase in the scattering intensity is described via decrease of the neutron diffusion coeffi- cient D = (3Σ tr ) −1 . The probability of neutron scatter- ing to large angles is w s ∝ Σ tr . For λ > λ d we get w s ∝ λ 4 a. The ratio of probabilities is w s w a ∝ λ 3/2 a −1/2 . Thus for small neutron energies and small characteris- tic sizes of dispersed nanoparticles, the probability of diffusive neutron reflection from nano-dispersed material increases sharper than the probability of neu- tron absorption in this material. The neutron wave- lengths ∼λ d corresponds to energies of cold and very cold neutrons (CN and VCN respectively). The phe- nomenon of intense coherent elastic scattering of slow neutrons on dispersed nanoparticles allows applica- tion of materials containing nanoparticles for con- structing novel efficient reflectors of VCNs and CNs. Most efficient currently VCN reflectors are based on diamond nanopowders [1–4]. Neutron reflectors based on nano-structured materials are promising tools for performing physics experiments, for improving parameters of CN, VCN 1 The article was translated by the authors. DIFFRACTION AND SCATTERING OF NEUTRONS