Cross sections for electron interactions in condensed matter

Fernández-Varea, José M.; Llovet, Xavier; Salvat, F.

doi:10.1002/sia.2101

Cited by 25 publications

(14 citation statements)

References 50 publications

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“…It can be shown that Eqs. (25) and (26) provide an ''exact'' expression for the screened interaction between a test-charge and an electron; equivalent to the so-called ''GWC'' approximation of many-body perturbation theory for the electron selfenergy (87). In the case now where both test-charges are substituted by electrons, no exact expression exists but an approximate expression is provided by the KukkonenOverhauser (KO) theory (88).…”

Section: Vertex Correctionmentioning

confidence: 98%

“…(24,25) and references therein]. The idea behind such models is that the dielectric function at the optical limit (i.e., at zero-momentum transfer) can be determined from experimental data, while extrapolation to non-zero momentum transfer, where experimental data are limited (or nonexisting), may be provided by theoretically motivated so-called extension algorithms (26).…”

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confidence: 99%

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Inelastic Cross Sections for Low-Energy Electrons in Liquid Water: Exchange and Correlation Effects

et al. 2013

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Low-energy electrons play a prominent role in radiation therapy and biology as they are the largest contributor to the absorbed dose. However, no tractable theory exists to describe the interaction of low-energy electrons with condensed media. This article presents a new approach to include exchange and correlation (XC) effects in inelastic electron scattering at low energies (below ∼10 keV) in the context of the dielectric theory. Specifically, an optical-data model of the dielectric response function of liquid water is developed that goes beyond the random phase approximation (RPA) by accounting for XC effects using the concept of the many-body local-field correction (LFC). It is shown that the experimental energy-loss-function of liquid water can be reproduced by including into the RPA dispersion relations XC effects (up to second order) calculated in the time-dependent local-density approximation with the addition of phonon-induced broadening in N. D. Mermin's relaxation-time approximation. Additional XC effects related to the incident and/or struck electrons are included by means of the vertex correction calculated by a modified Hubbard formula for the exchange-only LFC. Within the first Born approximation, the present XC corrections cause a significantly larger reduction (∼10-50%) to the inelastic cross section compared to the commonly used Mott and Ochkur approximations, while also yielding much better agreement with the recent experimental data for amorphous ice. The current work offers a manageable, yet rigorous, approach for including non-Born effects in the calculation of inelastic cross sections for low-energy electrons in liquid water, which due to its generality, can be easily extended to other condensed media.

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Section: Vertex Correctionmentioning

confidence: 98%

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confidence: 99%

Inelastic Cross Sections for Low-Energy Electrons in Liquid Water: Exchange and Correlation Effects

et al. 2013

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“…The calculation of electron IMFP using any of the standard models discussed earlier is carried out using the non‐relativistic expression of the Born approximation

Σ_{model} = \frac{2}{π υ^{2}} true \int d ω true \int \frac{d k}{k} normalI normalm {[\frac{- sans-serif1}{ε ((),, ω, k)}]}_{model}

where υ is the velocity of the incident electron,

normalI normalm {[+1 \frac{- 1}{ε (ω, k)}]}_{model}

is the ELF determined by the RH, or Penn (FPM or SPM) or MELF model and

Σ_{model}^{prefix- 1}

equals the corresponding IMFP. It is important to recognize that, as long as

normalI normalm {[\frac{- 1}{ε (ω, k)}]}_{model}

is only an approximation to the ‘true’ ELF of the material, Eqn will yield an approximation to the IMFP of the Born approximation.…”

Section: The ‘Standard’ Modelsmentioning

confidence: 99%

“…[27] Because of the aforementioned properties, the use of the MELF model is expanding. [28][29][30][31] The calculation of electron IMFP using any of the standard models discussed earlier is carried out using the non-relativistic expression of the Born approximation [32] Σ model ¼ 2…”

Section: Melf Modelmentioning

confidence: 99%

Inelastic mean free path of low‐energy electrons in condensed media: beyond the standard models

Emfietzoglou

Kyriakou

García-Molina

et al. 2015

Surface & Interface Analysis

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The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low‐energy electrons (~10 eV to ~10 keV) is based on optical‐data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low‐energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random‐phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical‐data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so‐called many‐body local‐field correction (LFC). XC effects among the screening electrons are included using a time‐dependent local‐density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened‐Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Over the past decades several TS codes have been developed in the context of microdosimetry and radiobiological modeling of cellular effects, e.g., NOREC [6], PARTRAC [7], KURBUC [8], RETRACKS (RITRACKS) [9], Geant4-DNA [10], among others [11]. The main problem with TS models is that they contain a high-degree of detail and, therefore, they are difficult to develop [12]. As a result, TS models are commonly tailored to a single medium (e.g., water) which prohibits their use in general-purpose codes [13].…”

Section: Introductionmentioning

confidence: 99%

Influence of track structure and condensed history physics models of Geant4 to nanoscale electron transport in liquid water

et al. 2019

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The Geant4 toolkit offers a range of electromagnetic (EM) models for simulating the transport of charged particles down to sub-keV energies. They can be divided to condensed-history (CH) models (like the Livermore and Penelope models) and the track-structure (TS) models included in the Geant4-DNA low-energy extension of Geant4. Although TS models are considered the state-of-the-art for nanoscale electron transport, they are difficult to develop, computationally intensive, and commonly tailored to a single medium (e.g., water) which prohibits their use in a wide range of applications. Thus, the use of CH models down to sub-keV energies is particularly intriguing in the context of general-purpose Monte Carlo codes. The aim of the present work is to compare the performance of the CH models of Geant4 against the recently implemented TS models of Geant4-DNA for nanoscale electron transport. Calculations are presented for two fundamental quantities, the dose-pointkernel and the microdosimetric lineal energy. The influence of user-defined simulation parameters (tracking and production cuts, and maximum step size) on the above calculations is also examined. It is shown that Livermore offers the best performance among the CH models of Geant4 for nanoscale electron transport. However, even under optimally-chosen simulation parameters, the differences between the CH and TS models examined may be sizeable for low energy electrons (< 1 keV) and/or nanometer size targets (< 100 nm).

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Cross sections for electron interactions in condensed matter

Cited by 25 publications

References 50 publications

Inelastic Cross Sections for Low-Energy Electrons in Liquid Water: Exchange and Correlation Effects

Inelastic Cross Sections for Low-Energy Electrons in Liquid Water: Exchange and Correlation Effects

Inelastic mean free path of low‐energy electrons in condensed media: beyond the standard models

Influence of track structure and condensed history physics models of Geant4 to nanoscale electron transport in liquid water

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