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This study provides accurate results for the electronic stopping cross sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross section, and induced-density approach. Recent experimental findings [Ntemou et al., Phys. Rev. B 107, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and the observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the deeper silicon bands for ion velocities approaching zero (v â 0). This indicates that mechanisms such as "elevator" and "promotion," which can dynamically excite deeper-band electrons, are active, enabling a localized free-electron gas to emulate ion energy loss, as pointed out by Lim et al. [Phys. Rev. Lett. 116, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross sections at very low velocities are considered to be a signature of the contributions of deeper-band electrons.
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We present a study of the stopping power of plasmas using two main approaches: the collisional (scattering theory) and the dielectric formalisms. In the former case, we use a semiclassical method based on quantum scattering theory. In the latter case, we use the full description given by the extension of the Lindhard dielectric function for plasmas of all degeneracies. We compare these two theories and show that the dielectric formalism has limitations when it is used for slow heavy ions or atoms in dense plasmas. We present a study of these limitations and show the regimes where the dielectric formalism can be used, with appropriate corrections to include the usual quantum and classical limits. On the other hand, the semiclassical method shows the correct behavior for all plasma conditions and projectile velocity and charge. We consider different models for the ion charge distributions, including bare and dressed ions as well as neutral atoms.
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We apply a semiclassical partial-wave-scattering method based on the Wentzel-Kramers-Brillouin approximation to study the transport cross section and the energy loss of neutral or ionized atomic beams in plasmas. This approach reproduces the exact quantum result in a satisfactory manner, even in several extreme conditions of plasma densities and temperatures, and agrees with the results of linear or perturbative calculations for bare ions in the appropriate limits. We pay special attention to low projectile speeds where strong oscillations in the transport cross section and energy loss-as a function of projectile's atomic number-are observed. We study these oscillatory phenomena varying the projectile speed and its ionization degree and the plasma temperature and density. We analyze in physical terms these effects and present a diagram of plasma conditions showing the regions where these oscillations may occur for both neutral and ionized beams.
RESUMO
We present a theoretical approach to study the screening charge density n(s)(r) and the respective stopping coefficient Q for hydrogen and helium at the low velocity limit. An electron gas, with electronic density n(e), is used to represent the conduction or valence electrons of the target material. Solving numerically the Schrödinger radial equation, for a given potential V (r), the phase shifts δ(l) and the corresponding stopping coefficient Q are calculated as a function of n(e). The cusp condition and the Friedel sum rule are imposed on the charge density n(r) = n(s)(r)+n(e) at the origin and to the phase shifts, respectively. The results are compared with density functional calculations and with available experimental results.