PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

total reflectivity domain. These arise since unreflected neutrons propagate into the crystal at an
angle Δ to the incidence surface due to dynamical diffraction and emerge from the side face, if the
apex angle A between the front and side faces lies between θ B +θ S and π−θ B +θ S (cf. Fig.12, Chapter
3). The prism diffracted beam, albeit weaker than the Bragg reflection, can be made much
narrower. Its intensity can furthermore be made to drop to zero within a fraction of an arcsec on
either side of the peak centre by judiciously positioning the incident beam and tailoring the exit
face orientation at large depths. We have named this super collimator-monochromator device a
‘Bragg prism collimator’ (Fig.26).
4.1 Bragg prism diffraction
We revisit neutron beam incidence on a single crystal prism (Fig.12) just outside the total
reflectivity domain such that the incident vacuum wave vector is RO in reciprocal space
corresponding to the angle of incidence, B +LR/k O (Fig.27). Continuity of the tangential
components of the wave vectors at the incidence interface and physical constraint on the energy
flow direction into the thick single crystal allow the excitation of only a single tie point T on the
dispersion surface (Chapter 3). At the exit surface, which subtends an angle A with the front face,
following the same boundary condition, a line is drawn from T along the exit surface normal n e to
intersect vacuum spheres of incidence and diffraction at point S and E respectively. The emergent
wave vectors are therefore SO and EH in forward diffracted and Bragg diffracted directions,
respectively.
The Bragg diffracted intensity fraction I H of the Bragg prism as a function of the incidence angle
can be written as
I ( ) C( )
H
2
H
. (58)
O
60