PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

Neutron optics has since made great strides in diverse directions. Many of the fundamental
relations of neutron optics concerning magnetic effects in neutron scattering, theory of coherent
and incoherent scattering, magnetic crystal diffraction, and refraction were developed in a series of
papers by Halpern and co-workers [29-31] and Hamermesh [32]. Refraction, in analogy with
visible photon optics, is described by introducing a refractive index n defined as the ratio of the
neutron wave vector inside a material medium to that in vacuum. For most materials, n [see
Chapter 2] differs from unity by about 10 -6 -10 -5 . The neutron refraction effects have been studied
[33-38] extensively and applied to build lenses and prisms to respectively focus and deflect neutron
beams. Refraction for thermal neutrons, though miniscule, has been effectively used to observe a
focusing effect using symmetric concave lenses made of amorphous MgF 2 [39], stacked layers of
small amorphous prisms and stacked Fresnel-shape discs [40-42]. Spin dependent refraction using
a quadrupole magnet was observed by Oku et al., [43].
Materials with n less than unity effect total external reflection of neutrons incident at grazing
angles less than the critical angle θ c given by
cosθ c =n. (2)
Neutron transportation through a neutron guide tube, the inner wall of which is made of a material
with n
400 Å and E < 500 neV, get totally reflected and bounce elastically from the material walls at all
angles of incidence including normal incidence as neutrons with such energies (~100 neV) can’t
overcome the optical potential barriers of most materials [36,45]. Some extremely important
questions pertaining to fundamental physics [44-47], have been addressed using UCN. The effect
of the magnetic interaction on n is merely to add a term of opposite signs for the two spin states
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