PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

since |n 2 –1|< 10 –5 . Eq.(82) is the approximate formula hitherto used by earlier researchers. Here, b c
signifies the coherent scattering length of sample, N a and b a stand for atomic number density and
coherent scattering length respectively, of air and denotes the neutron wavelength. Precision of
b c determination can be improved by increasing Ф I . However, in a symmetric LLL IFM, neutrons
of wavelengths and + propagate at corresponding Bragg angles θ B and θ B +θ B to the IFM
Bragg planes and hence are incident at angles θ and θ+θ B on the sample (Fig.51). The phase Ф I ,
acquired by neutrons with wavelength + can be written as
2 2
D
sin B 4d NbC NbC sin
B
I ,
2
d sin B B sin
B
B
(83)
using Eq.(81). Here d denotes Bragg planar spacing of the IFM single crystal. The phase Ф I at
+ differs from Ф I at . The -dependence of Ф I (Fig.52), thus smears out interferograms,
reducing the interference contrast and hence b c precision since
i I ( )
i IO
I
O
( )e d / I
O( )d fe
with f