PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

III. High precision determination of neutron coherent scattering
In Chapter 5, a proposal for high-precision determination of the neutron coherent scattering length
is described. With this proposal, the neutron coherent scattering length and refractive index for Si
become determinable to within a few parts per million and a few parts per trillion respectively, for
slow neutrons. When such ultra high precision is achieved, the refraction correction at the ambientsample
interface becomes mandatory. We have derived the correct formula for the phase and b c . In
a proof-of-principle measurement, we used a dual non-dispersive sample to measure the largest
non-dispersive phase (911 interference orders) to date, to within 1 ppm and the Si b c value of
4.1479 0.0023 fm was arrived at after adding a correction of 0.009137 fm for ambient air. The
major part of the b c error arose from the 10 μm error in the 18 mm sample thickness. The
correction of –1.01x10 -5 fm to b c due to refraction at air-sample interfaces was too small in
comparison.
A repeat experiment with a better polished sample, to within 1 μm, yielded a Si b c value of
4.15195 0.00011 fm after correcting for all possible sources of errors. Thus, Si b c could be
determined to within 27 parts per million.
By further reducing mechanical vibrations and thermal variations of the IFM set-up and using a
sample polished to better flatness, the proposed ppm precision in bc
determination is achievable.
Rauch et al.’s [126] nondispersive sample configuration afforded precise interferometric
determination of neutron coherent scattering lengths and Ioffe et al. [127] improved the precision
further by an order of magnitude by alternating the sample between the two paths of the
interferometer. We have presented here a dual nondispersive sample which is more nondispersive
than the single “nondispersive” sample by several orders of magnitude. This advantage will be
especially interesting for cold neutron interferometry. The dual sample generates double the phase
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