Neutron Scattering

Q = Q = k2 + k2 - 2kk' cos2B
(3 .3)
During a scattering experiment, the intensity distribution is being determined as a function of
the scattering vector :
I M (Q-)
(3 .4)
The proportionality factors arise from thé detailed geometiy ofthé experiment . Our task is to
détermine thé arrangement of thé atoms in thé sample from thé knowledge of thé scattering
cross section da/dÇ2(Q) . The relationship between scattered intensity and thé structure of thé
sample is especially simple in thé approximation ofthé so-called kinematic scattering. In this
case, multiple scattering events and thé extinction ofthé primary beam due to scattering in thé
sample are being neglected . Following figure 3 .2, thé phase différence between a wave
scattered at thé origin ofthé co-ordinate system and at thé position r is given by :
k .r-k '.r=Q .r
(3 .5)
Fit. 3 .2 : A sketch illustrating thé phase différence between a beam being scattered at thé
origin ofthé co-ordinate system and a beam scattered at thé position r.
The scattered amplitude at thé position r is proportional to thé scatteringpower density ps (r) .
The meaning of p, in thé case of neutron scattering will bc given later . The total scattered
amplitude is given by a coherent superposition of thé scattering from all positions r within thé
sample, i . e . by thé integral :
3-3