Dynamic Screening of Ions in Condensed Matter

Echenique, Pedro M.; Flóres, F.; Ritchie, R.H.

doi:10.1016/s0081-1947(08)60325-2

Cited by 242 publications

(84 citation statements)

References 157 publications

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“…Such behaviour has been observed experimentally in many sp-bonded metals [11,12], and the jellium model has allowed deep understanding of the dynamic screening of the projectile and its relation to stopping [13]. Even the jellium prediction of an oscillation of the proportionality coefficient with the projectile's atomic number Z has been verified [6] and reproduced by ab initio atomistic simulations [14]. However, phenomena that cannot be accounted for within the jellium paradigm have been described only qualitatively so far [15][16][17][18].…”

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confidence: 99%

Electronic Stopping Power in Gold: The Role ofdElectrons and theH/HeAnomaly

et al. 2012

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The electronic stopping power of H and He moving through gold is obtained to high accuracy using time-evolving density-functional theory, thereby bringing usual first-principles accuracies into this kind of strongly coupled, continuum non-adiabatic processes in condensed matter. The two key unexplained features of what observed experimentally have been reproduced and understood: (i) The non-linear behaviour of stopping power versus velocity is a gradual crossover as excitations tail into the d-electron spectrum; and (ii) the low-velocity H/He anomaly (the relative stopping powers are contrary to established theory) is explained by the substantial involvement of the d electrons in the screening of the projectile even at the lowest velocities where the energy loss is generated by s-like electron-hole pair formation only.Non-adiabatic processes are at the heart of aspects of science and technology as important as radiation damage of materials in the nuclear and space industries, and radiotherapy in medicine. Yet, in spite of a long history, the quantitative understanding of non-adiabatic processes in condensed matter and our ability to perform predictive theoretical simulations of processes coupling many adiabatic energy surfaces is very much behind what accomplished for adiabatic situations, for which first-principles calculations provide predictions of varied properties within a few percent accuracy. Substantial progress has been made for weakly non-adiabatic problems such as the chemistry of vibrationally excited molecules landing on metal surfaces [1], but not in the stronger coupling regime of radiation damage. Recently, the electronic stopping power for swift ions in gold has been carefully characterized by experiments [2-4], showing flagrant discrepancies with the established paradigm for such problems [5,6], and only qualitative agreement with time-dependent tight-binding studies [7], and with detailed studies for protons based on first principles [8], leaving very fundamental questions unanswered in spite of the apparent simplicity of the system. Most notably the H/He anomaly: the present understanding predicts a stopping power for H higher than for He at low velocities [6], which strongly contradicts the recent experiments [4].A particle moving through a solid material interacts with it and loses its kinetic energy to both the nuclei and the electrons inside it. At projectile velocities between 0.1 and 1 atomic units (a.u. henceforth) both the nuclear and the electronic contributions to the stopping power (energy lost by the projectile per unit length) are sizeable [7]. Based on the jellium model (homogeneous electron gas) the electronic stopping power, S e , is predicted to be S e ∝ v for a slow projectile traversing a metallic medium [9,10]. Such behaviour has been observed experimentally in many sp-bonded metals [11,12], and the jellium model has allowed deep understanding of the dynamic screening of the projectile and its relation to stopping [13]. Even the jellium prediction of an oscillation of the ...

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Electronic Stopping Power in Gold: The Role ofdElectrons and theH/HeAnomaly

et al. 2012

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“…1 While at relativistic velocities radiative losses may become important, for moving charged particles in the non-relativistic regime the energy loss is primarily due to electron-electron (e-e) interactions giving rise to the generation of electron-hole pairs, collective excitations such as plasmons, and innershell excitations and ionizations. Energy losses due to nuclear recoil are negligible, unless the projectile velocity is very small compared to the mean speed of electrons in the solid.…”

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Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation

Río‐Gaztelurrutia¹,

Pitarke

2000

Phys. Rev. B

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A nonlinear description of the interaction of charged particles penetrating a solid has become of basic importance in the interpretation of a variety of physical phenomena. Here we develop a manybody theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in an interacting free electron gas. Explicit expressions for these quantities are obtained either within the random-phase approximation (RPA) or with full inclusion of short-range exchange and correlation effects. The Z 3 1 correction to the energy loss of ions is evaluated beyond RPA, in the limit of low velocities.When charged particles pass through a solid, energy can be lost to the medium through various types of elastic and inelastic collision processes. 1 While at relativistic velocities radiative losses may become important, for moving charged particles in the non-relativistic regime the energy loss is primarily due to electron-electron (e-e) interactions giving rise to the generation of electron-hole pairs, collective excitations such as plasmons, and innershell excitations and ionizations. Energy losses due to nuclear recoil are negligible, unless the projectile velocity is very small compared to the mean speed of electrons in the solid. 2 The inelastic decay rate of charged particles in a degenerate interacting free electron gas (FEG) has been calculated for many years in the first-Born approximation or, equivalently, within linear-response theory. This is a good approximation when the velocity of the projectile is much greater than the average velocity of target electrons. However, in the case of projectiles moving with smaller velocities, nonlinearities have been shown to play a key role in the interpretation of a variety of experiments. Energy-loss measurements have revealed differences, not present within linear-response theory, between the energy loss of protons and antiprotons. 3,4 Moreover, experimentally observed coherent double-plasmon excitations 5,6 cannot be described within linear-response theory, and nonlinearities may also play an important role in the electronic wake generated by moving ions in a FEG. 7 Pioneering nonlinear calculations of the electronic energy loss of low-energy ions in an electron gas were performed by Echenique et al . 8 These authors computed the scattering cross section for a statically screened potential, which was determined self-consistently using densityfunctional theory (DFT). 9 These static-screening calculations have recently been extended to velocities approaching the Fermi velocity. 10 Second-order perturbative calculations, which do not have the limitation of being restricted to low projectile velocities, have been reported by different authors with use of the random-phase approximation (RPA) and by treating the moving charged particle as a prescribed source of energy and momentum. [11][12][13][14][15] In this paper, we report a many-body theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in ...

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“…While dealing with localized potentials in a Fermi gas, we shall also treat in section 3 the excess electrical resistivity caused by a central potential V (r). This, as will be emphasized, involves only the imaginary part of the Green function (and now at the Fermi level) displayed already in equation (1.1), and we stress is also intimately related to stopping power (see the review by Echenique et al [5]). …”

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confidence: 70%

Nonlinear theory of scattering by localized potentials in metals

Howard

March

Echenique

2003

J. Phys. A: Math. Gen.

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In early work, March and Murray gave a perturbation theory of the Dirac density matrix γ (r, r ) generated by a localized potential V (r) embedded in an initially uniform Fermi gas to all orders in V (r). For potentials sufficiently slowly varying in space, they summed the resulting series for r = r to regain the Thomas-Fermi density ρ(r) ∝ [µ − V (r)] 3/2 , with µ the chemical potential of the Fermi gas. For an admittedly simplistic repulsive central potential V (r) = |A| exp(−cr), it is first shown here that what amounts to the sum of the March-Murray series for the s-wave (only) contribution to the density, namely ρ s (r, µ), can be obtained in closed form. Furthermore, for specific numerical values of A and c in this exponential potential, the long-range behaviour of ρ s (r, µ) is related to the zero-potential form of March and Murray, which merely suffers a µ-dependent phase shift. This result is interpreted in relation to the recent high density screening theorem of Zaremba, Nagy and Echenique. A brief discussion of excess electrical resistivity caused by nonlinear scattering in a Fermi gas is added; this now involves an off-diagonal local density of states. Finally, for periodic lattices, contact is made with the quantum-mechanical defect centre models of Koster and Slater (1954 Phys. Rev. 96 1208) and of Beeby (1967, and also with the semiclassical approximation of Friedel (1954 Adv. Phys. 3 446). In appendices, solvable low-dimensional models are briefly summarized.PACS number: 31.15.Bs Background and outlineIn early work, March and Murray [1, 2] gave a perturbation theory of the Dirac density matrix γ (r, r ) to all orders in the localized scattering potential V (r) introduced into an originally

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Dynamic Screening of Ions in Condensed Matter

Cited by 242 publications

References 157 publications

Electronic Stopping Power in Gold: The Role ofdElectrons and theH/HeAnomaly

Electronic Stopping Power in Gold: The Role ofdElectrons and theH/HeAnomaly

Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation

Nonlinear theory of scattering by localized potentials in metals

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