Neutron scattering length table by NIST [1] When we do calculations relevant to neutron scattering, it is unavoidable that we will come across either coherent, incoherent or total scattering length of elements, which describes the strength of scattering neutrons by different elements, either coherently, incoherently or both. In this article, I will try to uncover the three different types of neutron scattering length, by going through the derivation in details. First, the differential cross section for neutron scattering by a certain structure is given as below -- here we do the derivation for a single-species system so we can derive the relevant scattering length conveniently. \[\frac{d\sigma}{d\Omega} = \sum_{i,j}b_ib_je^{-i\vec{Q}\cdot (\vec{R}_i - \vec{R}_j)}\] where \(i\), \(j\) refers to atoms located at different locations in the structure under beam. In practice, every single \(b_i\), \(b_j\) depends on the corresponding nuclear isotope, spin orientation relative to neutron, nu

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