PHYS01200804001 Sohrab Abbas - Homi Bhabha National Institute

Here the term C() accounts for the phase space volume conservation of the neutron beam, and is
calculated in the same manner as in Eq.(51) i.e., by computing the H-beam cross section,
C( )
sin sin(A )
sin( )sin(A )
B S
B
S
. (59)
Employing Eq.(48), Bragg diffraction fraction can be written as
2
sin( )
H
B S
O
sin( B
S
)
. (60)
Thus, Eq.(58) becomes,
I
H
sin sin(A )sin( )
sin( )sin(A )sin( )
. (61)
B S B S
B S B S
Bragg diffracted H-beam cross section C(), vanishes at A=θ B +θ S (cf. Eq.(61)) making forward
diffracted beam I O () stronger at the expense of H-beam. To obtain strong I H () beam from side
face, the apex angle A must lie close to π−θ B +θ S .
The exit angle B –LE/k O , of the Bragg Diffracted neutron beam I H () from side face is derived to
be
H
B S
H
( )
sin(A
B S) b B B S
up to an additive constant.
We rewrite Eq. (62) as
2
y sin(A )
sinA 1 1 y
, (62)
sin(2 ) 2sin( )
2
2 n 1 y F sin(A )
sinA 1 1 y
. (63)
F sin(2 ) 2sin( )
H
B S
H
( )
sin(A
B S) b O
B B S
As can be seen from Eq.(63), θ H depends on the Bragg reflection through F H , S and the apex angle
A. So a judicious choice of these parameters can make the derivative θ H /θ approach 0. The single
62