PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

2
(1)
-(δk i .Δ i ) /2
Γ (Δ) = e , (73)
i=x,y,z
is obtained. In this case, the wave vector distribution and coherence length i are related by
Heisenberg uncertainty relation [95],
δk Δ = 1/ 2 . (74)
i
i
Diffraction from a macroscopic grating
Diffraction of neutrons of wavelength for near normal incidence at a grating of period d>>
gives rise to a pattern with an angular separation ~ /d between successive intensity maxima. With
a grating period of even a few microns, scattering angles become as small as a few arcsec for
thermal and cold neutrons. A collimation of the incident neutron beam to within ~ arcsec is
therefore necessary to record a well resolved diffraction pattern. Our super collimated beam
facilitated measurement of the diffraction pattern from a large-period grating and determination
therefrom of the transverse coherence length of the beam.
A grating of ~ 200 μm period, made by winding a steel wire of 100 μm diameter tightly on a 50x50
mm 2 aluminium frame (inset of Fig.44), was mounted between the monochromator and analyser
for near normal neutron incidence. SUSANS (Super Ultra-Small Angle Neutron Scattering) spectra
recorded with and without the grating in the mount are depicted in Fig.47. The two peaks in the
grating pattern are considerably broadened due to multiple scattering and refraction in the
cylindrical wires, and modulated by clearly resolved diffraction oscillations corresponding to the
grating period [154]. The average peak broadening on transmission through the steel wires in the
grating was least-square fitted to a Gaussian angular profile of standard deviation equal to about
0.41 arcsec, by deconvoluting each peak from that in the no-grating SUSANS pattern. At a
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