Page 132 - Neutrons for Sciences and Society

Neutrons for Science
than the critical angle γ83 defined by the relation cos(γ) = n. This index is linked to the coherent scattering length a of the medium and the wavelength λ
n = 1 - (N.a.λ2)/2π
where N is the number of nuclei with scattering length a per unit volume.
The material most often used at that time was a glass plate (which could be made industrially with a perfectly flat surface) covered with a layer of nickel to increase the scattering length, and hence the critical angle. The total internal reflection allowed the beam of neutrons to be led away over several tens of metres into zones where the background was much smaller than adjacent to the reactor. The guides could also be gently curved which stopped fast neutrons reaching the sample, and allowed more space and a greater number of instruments. The guides, of course, had to be within an evacuated tube to minimise neutron loss. This method of eliminating the fast neutrons obviated use of neutron filters which had been necessary up to then. The filters were made of a material which did not absorb neutrons, and had a very small incoherent cross-section. Only neutrons with a wavelength longer than the inter-planar distances were transmitted; shorter wavelengths were diffracted out of the beam. Beryllium was a preferred substance. The British project of 1962 foresaw placing these filters in the beam tubes inside the reactor. In the ILL beam tubes there is no solid material (which would lead to a reduction in flux) along the flight path from the interior of the reactor.
83 The γ used here is the complement of the angle of incidence used in conventional optics text books relative to the normal to the surface plane; here this is a small angle otherwise all angles would be close to 90 degrees. This changes the equation from sine to cosine.
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