Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.3, pp. 68-69

Section Refractive index for neutrons

C. J. Howarda* and E. H. Kisia

aSchool of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia
Correspondence e-mail: Refractive index for neutrons

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The coherent scattering lengths of the nuclei determine the refractive index for neutrons through the relationship (Squires, 1978[link])[n=1-{{1}\over{2\pi }}{\lambda }^{2}N{b}_{\rm coh}, \eqno(2.3.4)]where N is the number of nuclei per unit volume. For elements with positive values of the coherent scattering length the refractive index is slightly less than one, and that leads to the possibility of total external reflection of the neutrons by the element in question. In fact, when the coherent scattering length is positive, neutrons will undergo total external reflection for glancing angles less than a critical angle γc given by[\cos{\gamma }_{c}= n=1-{{1}\over{2\pi }}{\lambda }^{2}N{b}_{\rm coh}, \eqno(2.3.5)]which, since γc is small, reduces to[{\gamma }_{c}=\lambda \left({{{N{b}_{\rm coh}}\over{\pi }}}\right)^{1/2}.\eqno(2.3.6)]

It can be seen that the pertinent material quantity is Nbcoh, the `coherent scattering length density'; for materials comprising more than one element this is the quantity that would be computed. Since the critical angle for total external reflection is proportional to the neutron wavelength, it is convenient to express this as degrees per ångstrom of neutron wavelength. These are important considerations in the design and development of neutron guides (Section[link]).


Squires, G. L. (1978). Introduction to the Theory of Thermal Neutron Scattering. Cambridge University Press.Google Scholar

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