Coherent and Incoherent Nuclear Scattering

The incident and diffracted neutron wave-vectors are denoted by k and k, respectively ( =23t/A) and the scattering vector x = k — k. The neutron state I A ) can be represented by a plane wave exp(ife -r). 

The total cross section, ai is the sum of the absorption (ua) and scattering cross sections (ffg). oa is small for most elements in the case of low-energy thermal 

For nuclear scattering, which is short range and isotropic and may be formalized within the Born approximation, the cross section of a single nucleus is related to the scattering length h (which may be positive or negative) 

The scattering from a sample is not generally isotropic, however, and it is convenient to define a differential cross section 

The master formula for the scattering of neutrons of initial and final states I A) and I A ) by a sample of initial and final states A) and A is (7) 

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