In the literature, various relatively simple models of elastic scattering such as a free-atom Thomas–Fermi
model with partial wave expansion 
and Mott cross-sections for a screened Coulomb potential
 had been proposed. On the other hand, Lenz model is a very simple atomic model. In this model, the single elastic scattering distribution is
given by [1, 3],
here, θ0 -- the characteristic screening angle of elastic
scattering. For the
binary materials, θ0 is taken as the mean characteristic
angle of each element weighted by the atomic fraction.
R -- is the screening radius of
atomic electrons ( ).
Z -- the atomic number for a single element, or the effective atomic number for a component.
λ -- the electron wavelength,
a0 -- the Bohr radius.
Noted that θ0 ≈ 100θE. Here, θE stands for the characteristic angular range of inelastically scattered electrons as given by θE = E/γm0v2 with the usual relativistic factor γ.
The elastic differential cross-section in the Lenz model can be given by,
e -- the elementary
E0 -- the energy of the incident electrons.
In combination of Equations 964a and 964b, one is able to obtain,
The Lenz model can also give the elastic-scattering intensity dIe
within an angular range dθ by, 
C - a constant.
The simple Lenz atomic model of scattering suggested that the cross section (per atom) for inelastic scattering can be given by a power-law dependence,
However, more sophisticated calculations suggested: 
The exponent x actually depends on collection semi-angle.
atomic model shows that:
i) the Lenz
values are mostly higher than the experimental ones at low angles,
but lower at high angles (no objective aperture). 
ii) the consideration of multiple scattering and aperture effects (represented by θ) is important to the correct interpretation of an energy-loss
atomic model predicted that:
i) the total cross section per atom σt increases with increasing atomic number. 
The elastic Lenz model had been used to:
i) correct the effects of elastic scattering in amorphous materials.  However, since the Lenz model is atomic in nature and thus it does not
account for solid-state effects such as Bragg scattering and channelling.
ii) calculate the effective contrast thickness in transmission electron microscopy. 
iii) discuss the effects of elastic
scattering on the core-loss and low-loss electrons. 
Table 964. Single and multiple electron scattering.
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 Huai-Ruo Zhang, Ray F. Egerton, Marek Malac, Local thickness measurement through scattering contrast and electron energy-loss spectroscopy, Micron 43 (2012) 8-15.
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