Calculation of electron interaction models in N2 and O2.

Cosmic rays have the potential to significantly affect the atmospheric composition by increasing the rate and changing the types of chemical reactions through ion production. The amount and states of ionization, and the spatial distribution of ions produced are still open questions for atmospheric models. To precisely estimate these quantities, it is necessary to simulate particle-molecule interactions, down to very low energies. Models enabling such simulations require interaction probabilities over a broad energy range and for all energetically allowed scattering processes. In this paper, we focus on electron interaction with the two most abundant molecules in the atmosphere, i.e., N2 and O2, as an initial step. A set of elastic and inelastic cross section models for electron transportation in oxygen and nitrogen molecules valid in the energy range 10 eV - 1 MeV, is presented. Comparison is made with available theoretical and experimental data and a reasonable good agreement is observed. Stopping power is calculated and compared with published data to assess the general consistency and reliability of our results. Good overall agreement is observed, with relative differences lower than 6% with the ESTAR database.

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

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-point-kernel 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).

Radiation track, DNA damage and response-a review.

The purpose of this paper has been to review the current status and progress of the field of radiation biophysics, and draw attention to the fact that physics, in general, and radiation physics in particular, with the aid of mathematical modeling, can help elucidate biological mechanisms and cancer therapies. We hypothesize that concepts of condensed-matter physics along with the new genomic knowledge and technologies and mechanistic mathematical modeling in conjunction with advances in experimental DNA (Deoxyrinonucleic acid molecule) repair and cell signaling have now provided us with unprecedented opportunities in radiation biophysics to address problems in targeted cancer therapy, and genetic risk estimation in humans. Obviously, one is not dealing with 'low-hanging fruit', but it will be a major scientific achievement if it becomes possible to state, in another decade or so, that we can link mechanistically the stages between the initial radiation-induced DNA damage; in particular, at doses of radiation less than 2 Gy and with structural changes in genomic DNA as a precursor to cell inactivation and/or mutations leading to genetic diseases. The paper presents recent development in the physics of radiation track structure contained in the computer code system KURBUC, in particular for low-energy electrons in the condensed phase of water for which we provide a comprehensive discussion of the dielectric response function approach. The state-of-the-art in the simulation of proton and carbon ion tracks in the Bragg peak region is also presented. The paper presents a critical discussion of the models used for elastic scattering, and the validity of the trajectory approach in low-electron transport. Brief discussions of mechanistic and quantitative aspects of microdosimetry, DNA damage and DNA repair are also included as developed by the authors' work.

Alpha particle and proton relative thermoluminescence efficiencies in LiF:Mg,Cu,P:is track structure theory up to the task?

Low-energy alpha particle and proton heavy charged particle (HCP) relative thermoluminescence (TL) efficiencies are calculated for the major dosimetric glow peak in LiF:Mg,Cu,P (MCP-N) in the framework of track structure theory (TST). The calculations employ previously published TRIPOS-E Monte Carlo track segment values of the radial dose in condensed phase LiF calculated at the Instituto National de Investigaciones Nucleares (Mexico) and experimentally measured normalised (60)Co gamma-induced TL dose-response functions, f(D), carried out at the Institute of Nuclear Physics (Poland). The motivation for the calculations is to test the validity of TST in a TL system in which f(D) is not supralinear (f(D) >1) and is not significantly dependent on photon energy contrary to the behaviour of the dose-response of composite peak 5 in the glow curve of LiF:Mg,Ti (TLD-100). The calculated HCP relative efficiencies in LiF:MCP-N are 23-87% lower than the experimentally measured values, indicating a weakness in the major premise of TST which exclusively relates HCP effects to the radiation action of the secondary electrons liberated by the HCP slowing down. However, an analysis of the uncertainties involved in the TST calculations and experiments (i.e. experimental measurement of f(D) at high levels of dose, sample light self-absorption and accuracy in the estimation of D(r), especially towards the end of the HCP track) indicate that these may be too large to enable a definite conclusion. More accurate estimation of sample light self-absorption, improved measurements of f(D) and full-track Monte Carlo calculations of D(r) incorporating improvements of the low-energy electron transport are indicated in order to reduce uncertainties and enable a final conclusion.

Inelastic scattering of low-energy electrons in liquid water computed from optical-data models of the Bethe surface.

PURPOSE: We provide a short overview of optical-data models for the description of inelastic scattering of low-energy electrons (10-10,000 eV) in liquid water. The effect on the inelastic scattering cross section due to different optical data and extension algorithms is examined with emphasis on some recent developments. MATERIALS AND METHODS: The optical-data method whereby experimental optical data and theoretical extension algorithms are used to describe the dependence of the dielectric response function on energy- and momentum-transfer and obtain the Bethe surface of the material, currently represents the most used method for computing the inelastic scattering of low-energy electrons in condensed media. Two sets of experimental optical data for liquid water obtained from reflectance and inelastic X-ray scattering spectroscopy, respectively, and the extension algorithms of Ritchie, Penn, and Ashley are examined. Recent developments are discussed along with the role of corrections to the random phase approximation (RPA) of electron gas theory. RESULTS: The inelastic scattering cross section in the energy range 200-10,000 eV was found to be rather insensitive (to within 10%) to the choice of optical data or the extension algorithm. In contrast, differences between model calculations increase rapidly below 200 eV with the influence of the extension algorithm being dominant. CONCLUSION: The choice of the extension algorithm used to extrapolate optical data to finite momentum transfer and obtain the Bethe surface is crucial in modelling the inelastic scattering of electrons with energies below 200 eV. A new set of measurements on the dielectric response function of liquid water beyond the optical limit and the development of extension algorithms that will go beyond RPA by considering the effect of (short-range) electron exchange and correlation should be of some priority.

A database of frequency distributions of energy depositions in small-size targets by electrons and ions.

Linear energy transfer (LET) is an average quantity, which cannot display the stochastics of the interactions of radiation tracks in the target volume. For this reason, microdosimetry distributions have been defined to overcome the LET shortcomings. In this paper, model calculations of frequency distributions for energy depositions in nanometre size targets, diameters 1-100 nm, and for a 1 µm diameter wall-less TEPC, for electrons, protons, alpha particles and carbon ions are reported. Frequency distributions for energy depositions in small-size targets with dimensions similar to those of biological molecules are useful for modelling and calculations of DNA damage. Monte Carlo track structure codes KURBUC and PITS99 were used to generate tracks of primary electrons 10 eV to 1 MeV, and ions 1 keV µm(-1) to 300 MeV µm(-1) energies. Distribution of absolute frequencies of energy depositions in volumes with diameters of 1-100 nm randomly positioned in unit density water irradiated with 1 Gy of the given radiation was obtained. Data are presented for frequency of energy depositions and microdosimetry quantities including mean lineal energy, dose mean lineal energy, frequency mean specific energy and dose mean specific energy. The modelling and calculations presented in this work are useful for characterisation of the quality of radiation beam in biophysical studies and in radiation therapy.

Monte Carlo single-cell dosimetry of Auger-electron emitting radionuclides.

A hybrid Monte Carlo transport scheme combining event-by-event and condensed-history simulation with a full account of energy-loss straggling was used to study the dosimetric characteristics of the Auger-emitting radionuclides 67Ga, 99mTc, 111In, 123I, 125I and 201Tl at the single-cell level. The influence of the intracellular localization of the Auger radionuclide upon cellular S-values, radial dose rate profiles and dose-volume-histograms (DVHs) was investigated. For the case where the radiopharmaceutical was either internalized into the cytoplasm or remained bound onto the cell surface (non-internalized), the dose to the cell nucleus was found to differ significantly from the MIRD values and other published data. In this case, the assumption of a homogeneous distribution throughout the cell is shown to significantly overestimate the nuclear dose. A dosimetric case study relevant to the radioimmunotherapy of single lymphoma B-cells with 125I and 123I is presented.

A Monte Carlo study of cellular S-factors for 1 keV to 1 MeV electrons.

A systematic study of cellular S-factors and absorbed fractions for monoenergetic electrons of initial energy from 1 keV to 1 MeV is presented. The calculations are based on our in-house Monte Carlo codes which have been developed to simulate electron transport up to a few MeV using both event-by-event and condensed-history techniques. An extensive comparison with the MIRD tabulations is presented for spherical volumes of 1-10 microm radius and various source-to-target combinations relevant to the intracellular localization of the emitted electrons. When the primary electron range is comparable to the sphere radius, we find significantly higher values from the MIRD, while with increasing electron energy the escape of delta-rays leads gradually to the opposite effect. The largest differences with the MIRD are found for geometries where the target region is at some distance from the source region (e.g. surface-to-nucleus or cytoplasm-to-nucleus). The sensitivity of the results to different transport approximations is examined. The grouping of inelastic collisions is found adequate as long as delta-rays are explicitly simulated, while the inclusion of straggling for soft collisions has a negligible effect.

A dielectric response study of the electronic stopping power of liquid water for energetic protons and a new I-value for water.

The electronic stopping power of liquid water for protons over the 50 keV to 10 MeV energy range is studied using an improved dielectric response model which is in good agreement with the best available experimental data. The mean excitation energy (I) of stopping power theory is calculated to be 77.8 eV. Shell corrections are accounted for in a self-consistent manner through analytic dispersion relations for the momentum dependence of the dielectric function. It is shown that widely used dispersion schemes based on the random-phase approximation (RPA) can result in sizeable errors due to the neglect of damping and local field effects that lead to a momentum broadening and shifting of the energy-loss function. Low-energy Born corrections for the Barkas, Bloch and charge-state effects practically cancel out down to 100 keV proton energies. Differences with ICRU Report 49 stopping power values and earlier calculations are found to be at the approximately 20% level in the region of the stopping maximum. The present work overcomes the limitations of the Bethe formula below 1 MeV and improves the accuracy of previous calculations through a more consistent account of the dielectric response properties of liquid water.

The Auger effect in physical and biological research.

PURPOSE: The paper reports on progress in physics of radiationless transitions and new Auger spectra of (125)I and (124)I. We report progress in Monte Carlo track structure simulation of low energy electrons comprising majority electrons released in decay most Auger emitters. MATERIALS AND METHODS: The input data for electron capture (EC) and internal conversion(IC) were obtained from various physics data libraries. Monte Carlo technique was used for the simulation of Auger electron spectra. Similarly, electron tracks were generated using Monte Carlo track structure methods. RESULTS: Data are presented for the EC, IC and binding energy (BE) of radionuclides (124)I and (125)I. For each of the radionuclides (125)I and (124)I some examples of electron spectra of individual decays are given. Because most Auger electrons are low energy and short range, data and a short discussion are presented on recent Monte Carlo track structure development in condensed media and their accuracy. CONCLUSIONS: Accuracy of electron spectra calculated in the decay of electron shower by Auger emitting radionuclides depends on availability of accurate physics data. There are many gaps in these libraries and there is a need for detailed comparison between analytical method and Monte Carlo calculations to refine the method of calculations. On simulation of electron tracks, although improved models for sub-keV electron interaction cross sections for liquid water are now available, more experimental data are needed for benchmarking. In addition, it is desirable to make data and programs for calculations of Auger spectra available online for use by students and researchers.

Subcellular S-factors for low-energy electrons: a comparison of Monte Carlo simulations and continuous-slowing-down calculations.

PURPOSE: To study the energy deposition by low-energy electrons in submicron tissue-equivalent targets by comparing two widely used methodologies, namely, the continuous-slowing-down-approximation (CSDA) convolution integral and the Monte Carlo (MC) simulation. METHODS: An MC track-structure code that simulates collision-by-collision the complete slowing down process is used to calculate the energy deposition in spherical volumes of unit density water medium. Comparisons are made with calculations based on the CSDA convolution integral using both empirical and MC-based range-energy analytic formulae. RESULTS: We present self-irradiation absorbed fractions and S-factors for monoenergetic electrons of initial energies from 0.1-10 keV distributed uniformly in spheres of 5, 10, 50, 100, 500, and 1000 nm radius. The MC and CSDA results were found, in some cases, to differ by a factor of 2 or more; differences generally increase with decreasing sphere size. Contrary to high energies, the uncertainties associated with the straight-ahead approximation implicit in the CSDA calculations are of the same order as those related to straggling and delta-ray effects. CONCLUSION: The use of the CSDA methodology may be unsuitable for the sub-micron scale where a more realistic description of electron transport becomes important.

A Monte Carlo study of absorbed dose distributions in both the vapor and liquid phases of water by intermediate energy electrons based on different condensed-history transport schemes.

Monte Carlo transport calculations of dose point kernels (DPKs) and depth dose profiles (DDPs) in both the vapor and liquid phases of water are presented for electrons with initial energy between 10 keV and 1 MeV. The results are obtained by the MC4 code using three different implementations of the condensed-history technique for inelastic collisions, namely the continuous slowing down approximation, the mixed-simulation with delta-ray transport and the addition of straggling distributions for soft collisions derived from accurate relativistic Born cross sections. In all schemes, elastic collisions are simulated individually based on single-scattering cross sections. Electron transport below 10 keV is performed in an event-by-event mode. Differences on inelastic interactions between the vapor and liquid phase are treated explicitly using our recently developed dielectric response function which is supplemented by relativistic corrections and the transverse contribution. On the whole, the interaction coefficients used agree to better than approximately 5% with NIST/ICRU values. It is shown that condensed phase effects in both DPKs and DDPs practically vanish above 100 keV. The effect of delta-rays, although decreases with energy, is sizeable leading to more diffused distributions, especially for DPKs. The addition of straggling for soft collisions is practically inconsequential above a few hundred keV. An extensive benchmarking with other condensed-history codes is provided.

Electronic stopping power of liquid water for protons down to the Bragg peak.

An improved dielectric response model that accurately represents the recent experimental data for liquid water over the whole Bethe surface is used to calculate the electronic stopping power of protons (of fixed-charge) in liquid water from several MeV down to the Bragg peak region. The results are by approximately 20% lower than the ICRU values and earlier studies. A shell-correction term with a contribution of 15-20% to Bethe's high-energy stopping number is obtained. The present work offers a first-principle approach for stopping power calculations that overcomes the well-known limitations of Bethe's stopping theory, namely, the need for separate determination of the mean excitation energy (the I-value) and the shell-corrections. In particular, all type of inner-shell effects are built into the model through the kinematically restricted integrals over the Bethe surface. The net contribution of higher-order corrections is found to be minimal over most of the present range. Thus, within the uncertainty of the dielectric model (few %) the present calculations are 'exact' down to approximately 100 keV.

Monte-Carlo study of energy deposition by heavy charged particles in sub-cellular volumes.

Detailed-history Monte-Carlo code is used to study the energy deposition from proton and alpha particle tracks at the sub-cellular level. Inelastic cross sections for both the vapour and liquid phases of water have been implemented into the code in order to explore the influence of non-linear density effects associated with the condensed-phase cellular environment. Results of energy deposition and its straggling for 0.5 to 5 MeV amu(-1) protons and alpha particles traversing or passing near spherical volumes of 2-200 nm in diameter relevant to DNA- and chromosome-size targets are presented. It is shown that the explicit account of delta-ray transport reduces the dose by as much as 10-60%, whereas stochastic fluctuations lead to a relative uncertainty ranging from 20% to more than 100%. Protons and alpha particles of the same velocity exhibit a similar delta-ray effect, whereas the relative uncertainty of the alphas is almost half that of protons. The effect of the phase is noticeable (10-15%) mainly through differences on the transport of delta-rays, which in liquid water have higher penetration distances. It is expected that the implementation of such results into multi-scale biophysical models of radiation effects will lead to a more realistic predictions on the efficacy of new radiotherapeutic modalities that employ either external proton beam irradiation or internal alpha-emitting radionuclides.

Accurate electron inelastic cross sections and stopping powers for liquid water over the 0.1-10 keV range based on an improved dielectric description of the Bethe surface.

Electron inelastic cross sections and stopping powers for liquid water over the 0.1-10 keV range are presented based on a recently developed dielectric response model for liquid water (D. Emfietzoglou, F. Cucinotta and H. Nikjoo, Radiat. Res. 164, 202-211, 2005) that is consistent with the experimental data over the whole energy-momentum plane. Both exchange and second-order Born corrections are included in a material-specific way using the dielectric functions of liquid water. The numerical results are fitted by simple analytic functions to facilitate their further use. Compared to previous studies, differential cross sections are shifted toward smaller energy losses resulting in smaller inelastic and stopping cross sections with differences reaching, on average, the approximately 20% and approximately 50% level, respectively. Contrary to higher energies, it is shown that the dispersion model for the momentum dependence of the dielectric functions (Bethe ridge) is as important as the optical model used. Within the accuracy of the experimental data (a few percent) upon which our dielectric model is based, the calculations are "exact" to first order, while the uncertainty of the results beyond first order is estimated at the 5-10% level. The present work overcomes the limitations of Bethe's theory at low energies by a self-consistent account of inner-shell effects and may serve to extend the ICRU electron stopping power database for liquid water down to 100 eV with a level of uncertainty similar to that for the higher-energy values.

A Monte-Carlo code for the detailed simulation of electron and light-ion tracks in condensed matter.

In an effort to understand the basic mechanism of the action of charged particles in solid radiation dosimeters, we extend our Monte-Carlo code (MC4) to condensed media (liquids/solids) and present new track-structure calculations for electrons and protons. Modeling the energy dissipation process is based on a model dielectric function, which accounts in a semi-empirical and self-consistent way for condensed-phase effects which are computationally intractable. Importantly, these effects mostly influence track-structure characteristics at the nanometer scale, which is the focus of radiation action models. Since the event-by-event scheme for electron transport is impractical above several kilo-electron volts, a condensed-history random-walk scheme has been implemented to transport the energetic delta rays produced by energetic ions. Based on the above developments, new track-structure calculations are presented for two representative dosimetric materials, namely, liquid water and silicon. Results include radial dose distributions in cylindrical and spherical geometries, as well as, clustering distributions, which, among other things, are important in predicting irreparable damage in biological systems and prompt electric-fields in microelectronics.

A comparative study of dielectric response function models for liquid water.

Various methodologies that aim at an analytic representation of the dielectric response function (DRF) of liquid water with emphasis on the Bethe ridge region are compared. The use of optical data is a common feature to all models presented providing an empirical ground for modelling the valence energy losses where many-body (and phase) effects are expected to be most prevalent. The dispersion models used for describing the momentum dependence of the DRF are evaluated against the recent inelastic X-ray scattering (IXS) spectroscopy data. Recent developments along the lines of Ritchie's extended-Drude scheme for an improved representation of the experimental Bethe ridge are presented.

Raman and AFM studies of swift heavy ion irradiated InGaAs/GaAs heterostructures.

The effect of swift heavy ion (SHI) irradiation on InGaAs/GaAs heterostructures is studied using Raman spectroscopy and atomic force microscopy (AFM). The structures consist of molecular beam epitaxy (MBE) grown InGaAs layers on GaAs(001), having layer thicknesses of 12, 36, 60 and 96 nm. After irradiation, the GaAs type longitudinal optical (LO) mode blue shifted to higher frequency in thin samples and red shifted towards lower frequency in thick samples. These results are discussed invoking the penetration depth of the probe radiation (λ = 514.5 nm) in InGaAs. Deconvoluting the Raman spectra of thin samples indicates a compressive strain developed in the substrate, close to the interface upon irradiation. This modification and diffusion of indium across the interface results in an increase of strain and reduction of the defect densities in the InGaAs layer. The variations in FWHM of the Raman modes are discussed in detail. The surface morphology of these heterostructures has been studied by AFM before and after SHI irradiation. These studies, combined with Raman results, help to identify different relaxation regimes.

Monte-Carlo calculations of radial dose and restricted-let for protons in water.

A new Monte-Carlo code for event-by-event simulation of the transport of energetic non-relativistic protons (approximately 0.5-10 MeV) and all their secondary electrons (down to 1 Ry) in both the vapour and liquid phases of water is presented. A unified particle-water inelastic model for both phases of water has been developed based on experimental optical data and elements of the Bethe theory. The model applies to both electrons and heavy-charged particles and is particularly suitable for extension to other media of biological relevance (organic polymers, DNA, etc.). Condensed-phase effects are included in the liquid version (MC4L) by means of the dielectric functions which, essentially, substitute the oscillator-strength used in the vapour version (MC4V). The results in the form of radial dose distributions and spatially restricted linear energy transfer are presented and compared with the literature.

Monte Carlo simulation of the energy loss of low-energy electrons in liquid water.

A Monte Carlo code that performs detailed (i.e. event-by-event) simulation of the transport and energy loss of low-energy electrons (approximately 50-10 000 eV) in water in the liquid phase is presented. The inelastic model for energy loss is based on a semi-empirical dielectric-response function for the valence-shells of the liquid whereas an exchange corrected semi-classical formula was used for K-shell ionization. Following a methodology widely used for the vapour phase, we succeeded in parametrizing the dielectric cross-sections of the liquid in accordance with the Bethe asymptote, thus providing a unified approach for both phases of water and greatly facilitating the computations. Born-corrections at lower energies have been implemented in terms of a second-order perturbation term with a simple Coulomb-field correction and the use of a Mott-type exchange modification. Angular deflections were determined by empirical schemes established from vapour data. Electron tracks generated by the code were used to calculate energy- and interaction-point-kernel distributions at low electron energies in liquid water. The effect of various model assumptions (e.g., dispersion, Born-corrections, phase) on both the single-collision and slowing-down distributions is examined.