Neutron Scattering

S(Q)
rnn
=21r/r nn
Figure 5 .1 :
Schematic representation of interaction potential V (r), pair correlation function
g(r), and scattering function S(Q) .
= Ibl2 (N
+ f v d3rl IV d 3r2n(r l , r2) exp ( 1Q' (ri - r2)
= Ibl (N+P02Vfvd3r12g(rl2)eXP(iQ .r12)/
= IbI2N (1 + Po IV d 3 r12g(L12) exP (iQ . r12)/
(5 .9)
This equation states that the scattering cross section can be represented as the Fourier
transform of the pair correlation function . Assuming isotropy (as is found in the homogeneous
liquid discussed here) one can replace g(r 12 ) by the radial correlation function
y (r) :
(dS2)
coh
= I bI 2N Cl + 47rpo
f
r2d3rg(r) Sin
(5 .10)
Equation (5 .l0) follows from (5 .9) by radial averaging of exp (iQ - r 12) (i .e . an average
over all possible orientations of r12) .
5-3