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Influence of crystal structure on the differential cross section for elastic scattering and influence exchange effect on the stopping power


V.A. Smolar – Dr. Sc. (Phys.-Math.), Professor, Department «Physics», Volgograd State Technical University. E-mail:
A.V. Eremin – Ph. D. (Phys.-Math.), Associate Professor, Department «Physics», Volgograd State Technical University. E-mail:
V.V. Eremin – Ph. D. (Phys.-Math.), Associate Professor, Department «Physics», Volgograd State Technical University. E-mail:
A.S. Burakov – Post-graduate Student, Department «Physics», Volgograd State Technical University. E-mail:

Atom differential elastic scattering cross section for electrons in condensed matter was calculated on the basis of modified Muffin-tin model. Applied model takes into account not only the neighboring atoms, but also the structure of a crystal in difference from usually used the Muffin-tin model. This is achieved by finding a superposition of potentials from individual atoms that are placed in knots of crystal lattice. Potentials of the individual atoms were calculated as a superposition of Yukawa potentials for representing the potential of free atom by Dirac-Hartree-Fock-Slater potential. Note that we remain within that Muffin-tin model averaging on corners the found potential of crystal lattice atom. According to the results of present work was found that if the crystal lattice in the approximation of the spherical symmetrical potential is taken into account in the field of low-energy, it leads to a significant change in the differential cross sections for elastic scattering in comparison with similar cross sections for electron scattering by individual atoms. The changes of elastic scattering cross section can reach order of magnitude for energies below 30 eV for substances with low atomic number. Effect of the crystal lattice remains significant at higher energies about 1000 eV, but only at small angles. The higher the energy, the smaller angular region has significant influence. In calculations of a stopping power was applied the dielectric approach. In this algorithm was added an additional restriction on the maximum transmission energy as taking into account the principle of indistinguishability of particles in collisions of primary electron with electrons of the atom. The main advantage of dielectric approach is the possibility to move lower bound electron energy down to several eV for calculating stopping power and many other characteristics. Thus, we significantly improve this algorithm and the shape of the stopping power at low energies, adding the principle of indistinguishability of particles because the greatest influence of this phenomenon is apparent at low energies.

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