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Rutherford crosssection gives convenient formulas to calculate the elastic scattering angle and total elastic cross section so that it is often used to describe the elastic scattering of electron. However, its accuracy becomes worse in lowenergy region or in high atomicnumber materials. The Rutherford scattering cross section, or electronnucleus scattering is given by,
 [4425a]
where,
θ  The scattering angle.
The Rutherford theory predicted the cross section of elastic scattering σ(Z) ∼ Z^{2}. However, it neglected the electronic structure of the scattering atom. Therefore, the Z^{2} law is only a first approximation. Therefore, we also can have,
 [4425b] where,
T  The kinetic energy of incident electrons.
Furthermore, based on the Rutherford theory above, the total probability of scattering an electron can be estimated (see page2673). The physical mechanism for the Zdependent behavior of HAADFSTEM contrast is that highangle scattering is mostly from the electrons scattered by the inner cores of atoms. The partial screening of the atomic nucleus by the inner shell electronic charges is responsible for the value of n to be less than 2 for a pure Rutherford scattering.
