ABSTRACT
Atoms are not distributed arbitrarily in condensed matter. In liquids and amorphous glasses a local order on an atomic scale is present. In perfect single crystals the order extends to macroscopic scales. Therefore, also the electrons are not arbitrarily positioned in space but exhibit order. The scattering amplitude of a single electron has been derived in the earlier sections. As has been shown in Born approximation, the scattering amplitude of a multi electron system can be calculated by simply summing up the single scattering amplitudes of each electron in the far-field regime. By using Eq. (1.2), the scattered amplitude A(q) of a many electron system with N electrons is A A i ij f i j
( ) ( ) exp[ ( ) ] exp( )q q k k r q rµ µ - ◊ = ◊  =1 . (1.5) Such as for a single electron, this equation can be slightly
rewritten by artificially introducing the d function d(r – ri) at the position of the charges by exp( ) ( )exp( )( ) exp(
i i d rj j
q r r r q r
r r
◊ = - ◊
= - Ê
Ë ÁÁ
ˆ
¯ ˜˜
d
d
3 i d rq r◊ ) 3 .
