Single-atom scattering

Applications that would benefit from the described achievements are commonly bottlenecked by a lack of general procedures to interpret intensity data. Recently, it was suggested to interpret STEM data by extraction of single atom scattering cross sections For HRTEM, Figure 8 highlights a suitable method for intensity quantification from reconstructed electron exit waves. 

While neat-resonant light exerts both scattering forces and dipole forces on single atoms, similar forces ate also exerted on larger dielectric objects. 

Here is the position operator of atom j, or, if the correlation function is calculated classically as in an MD simulation, is a position vector N is the number of scatterers (i.e., H atoms) and the angular brackets denote an ensemble average. Note that in Eq. (3) we left out a factor equal to the square of the scattering length. This is convenient in the case of a single dominant scatterer because it gives 7(Q, 0) = 1 and 6 u,c(Q, CO) normalized to unity. 

Earlier studies of ion scattering were directed primarily at gas-ion interactions. As studies of ion—solid surfaces became common the energy of the scattered ions was eventually related mathematically to a simple binary elastic event involving a single atom on a surface element and a single probe ion. 

Let us first examine the scattering of a neutron plane wave by a single atom, which is supposed fixed. The behaviour of this system is represented by the wave equation... 

The atomic form factor accounts for the internal structure of the different atoms or molecules. It will also be different for X-rays and neutrons, since the former probe the electron distribution of the target, while the latter interact with the nuclei of the atoms. Therefore, the analysis of the positions of the reflexes indicates mainly the lattice constants and angles. The intensity of the reflexes contains mainly information about the atomic configuration within an unit cell (structure factor) and the scattering behavior of the single atoms (form factor). 

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