Ionization yields in hydrocarbons under electron irradiation

Ionization yields and W-values in several hydrocarbon gases under electron irradiation have been calculated using Inokuti's solution of the Fowler equation, i.e., incorporating a linear dependence of ionization yield on source electron energy. Collision stopping powers of hydrocarbons were evaluated using the Bethe formula with mean excitation energies determined using the additivity rule with modification based on molecular bond strengths. Contributions to the collision stopping powers from discrete level excitations were estimated by multiplying collision stopping powers by the excitation fractions constructed from atomic calculations. Average energy transfers for ionizing collisions producing subionization electrons were calculated using differential ionization cross sections proposed by Khare and co-workers. The calculated W-values are in good agreement with those recommended by ICRU.     

Cross section calculations for electron scattering from DNA and RNA bases

Differential and integral cross sections for elastic electron collisions with uracil, cytosine, guanine, adenine and thymine have been calculated using the independent atom method with a static-polarization model potential for incident energies ranging from 50 to 4000 eV. Total cross sections for single electron-impact ionization of selected DNA and RNA bases have also been calculated with the binary-encounter-Bethe model from the ionization threshold up to 5000 eV. Cross sections within the investigated energy range, can be related to the molecular symmetry, the number of target electrons and molecular size; elastic and ionization processes are most efficient for guanine and adenine molecules, while the lowest cross sections were obtained for the uracil molecule. The ionization cross sections for cytosine, thymine, adenine and guanine are compared with those recently obtained with a semi-classical and binary-encounter-Bethe formalisms. No theoretical and experimental data for elastic electron scattering from DNA and RNA bases are available, but comparisons with calculations for molecules of similar size and geometry allows the validity of the theoretical approach to be verified.     

Calculation of the proximity function of electrons

A new semianalytical method to calculate the proximity function for electrons is proposed. An integral equation for the proximity function that can be solved by using information on the spatial dose distributions is obtained. The proximity function for electrons in the energy range from 10 eV to 10 keV is calculated by solving the equation numerically, using a set of electron collision cross sections for water vapor. The results are in good agreement with those obtained using the Monte Carlo method. The proposed method can be used for electrons of high energies much more efficiently than the Monte Carlo method.     

Comparison and assessment of electron cross sections for Monte Carlo track structure codes.

The purpose of this study was to make an intercomparison and assessment of cross sections for electrons in water used in electron track structure codes. This study is intended to shed light on the extent to which the differences between the input data and physical and chemical assumptions influence the outcome in biophysical modeling of radiation effects. Ionization cross sections and spectra of secondary electrons were calculated by various theories. The analyses were carried out for water vapor cross sections, as these are more abundant and readily available. All suitable published experimental total ionization cross sections were fitted by an appropriate function and used for generation of electron tracks. Three sets of compiled data were used for comparison of total excitation cross sections and mean excitation energy. The tracks generated by a Monte Carlo track code, using various combinations of cross sections, were compared in terms of radial distributions of interactions and point kernels. The spectrum of secondary electrons emitted by the ionization process was found to be the factor that has the most influence on these quantities. A different set of cross sections for excitation and elastic scattering did not affect the electron track structure as much as did ionization cross sections. It is concluded that all codes, using different cross sections and in different phase, currently used for biophysical modeling exhibit close similarities for energy deposition in larger size targets while appreciable differences are observed in B-DNA-size targets. We recommend fitted functions to all available suitable experimental data for the total ionization and elastic cross sections. We conclude that most codes produce tracks in reasonable agreement with the macroscopic quantities such as total stopping power and total yield of strand breaks. However, we predict differences in frequencies of clustering in tracks from the different models.     

Cross sections for low-energy (10-50 eV) electron damage to DNA

We report direct measurements of the formation of single-, double- and multiple strand breaks in pure plasmid DNA as a function of exposure to 10-50 eV electrons. The effective cross sections to produce these different types of DNA strand breaks were determined and were found to range from approximately 10(-17) to 3 x 10(-15) cm(2). The total effective cross section and the effective range for destruction of supercoiled DNA extend from 3.4 to 4.4 x 10(-15) cm(2) and 12 to 14 nm, respectively, over the range 10-50 eV. The variation of the effective cross sections with electron energy is discussed in terms of the electron's inelastic mean free path, penetration depth, and dissociation mechanisms, including resonant electron capture; the latter is found to dominate the effective cross sections for single- and double-strand breaks at 10 eV. The most striking observations are that (1) supercoiled DNA is approximately one order of magnitude more sensitive to the formation of double-strand breaks by low-energy electrons than is relaxed circular DNA, and (2) the dependence of the effective cross sections on the incident electron energy is unrelated to the corresponding ionization cross sections. This finding suggests that the traditional notion that radiobiological damage is related to the number of ionization events would not apply at very low energies.     

Cross sections for low-energy (1-100 eV) electron elastic and inelastic scattering in amorphous ice

We report the integral cross sections per scatterer (i.e. elastic collision, phonon excitations, vibrational excitations, electronic excitations and ionization) for 1-100 eV electron scattering in an amorphous film of ice condensed at a temperature of 14 K. The integral cross sections are determined relative to the total from a two-stream multiple-scattering analysis of the electron energy distribution backscattered from the film. Their energy dependence is obtained from both the analysis of the elastic electron reflectivity as a function of the film thickness and the vibrational electron energy-loss spectra measured for several incident energies and large film thickness. The magnitude and various features found in the energy dependence of the cross sections are discussed, whenever possible, by comparison with data and with scattering mechanisms available in the gas phase. Microcospic effects, which are implicitly included in cross sections determined in this way, are discussed in terms of interference and coherent multiple-scattering contributions among the scattering sites as well as interactions of the scattering sites with their neighbors in the condensed phase.     

Monte Carlo transport of swift protons and light ions in water: The influence of excitation cross sections,relativistic effects,and Auger electron emission in w-values

PurposeTo develop a particle transport code to compute w-values and stopping power of swift ions in liquid water and gases of interest for reference dosimetry in hadrontherapy. To analyze the relevance of inelastic and post-collisional processes considered.MethodsThe Monte Carlo code MDM was extended to the case of swift ion impact on liquid water (MDM-Ion). Relativistic corrections in the inelastic cross sections and the post-collisional Auger emission were considered. The effects of introducing different electronic excitation cross sections were also studied.ResultsThe stopping power of swift ions on liquid water, calculated with MDM-Ion, are in excellent agreement with recommended data. The w-values show a strong dependence on the electronic excitation cross sections and on the Auger electron emission. Comparisons with other Monte Carlo codes show the relevance of both the processes considered and of the cross sections employed. W and w-values for swift electron, proton, and carbon ions calculated with the MDM and MDM-Ion codes are in very close agreement with each other and with the 20.8 eV experimental value.ConclusionWe found that w-values in liquid water are independent of ion charge and energy, as assumed in reference dosimetry for hadrontherapy from sparse experimental results for electron and ion impact on gases. Excitation cross sections and Auger emission included in Monte Carlo codes are critical in w-values calculations. The computation of this physical parameter should be used as a benchmark for micro-dosimetry investigations, to assess the reliability of the cross sections employed.     

Low-energy electron penetration range in liquid water

Monte Carlo simulations of electron tracks in liquid water are performed to calculate the energy dependence of the electron penetration range at initial electron energies between 0.2 eV and 150 keV, including the subexcitation electron region (<7.3 eV). Our calculated electron penetration distances are compared with available experimental data and earlier calculations as well as with the results of simulations using newly reported amorphous ice electron scattering cross sections in the range approximately 1-100 eV.     

Role of secondary electrons and metastable atoms in the electron-beam activation of argon-silane mixtures

The energy and spatial degradation of the primary beam electrons and the production of high-energy secondary electrons in ionizing collisions are analyzed by solving the Boltzmann integral equation for the electron distribution function. The effect of the primary and secondary electrons on the direct ionization of an Ar-SiH₄ mixture, the production of metastable argon atoms, and the dissociation of monosilane molecules is investigated over a wide range of the beam electron energies, argon pressures, and monosilane concentrations. The influence of metastable Ar* atoms on the dissociation of SiH₄ is studied by using the balance equation for metastable argon atoms and the equation for the ambipolar diffusion of ions and low-energy secondary (plasma) electrons in the beam plasma. It is shown that the main contribution to the activation of an Ar-SiH₄ mixture in an electron-beam plasma is provided by secondary electrons with energies higher than the excitation threshold for argon and the dissociation threshold for monosilane, whereas the contribution from metastable argon atoms, though potentially being comparable with that from secondary electrons, is less than in gas-discharge plasmas.     

Energy spectra of secondary electrons in water vapour

The purpose of this work is to present a method for the calculation of secondary electron spectra generated by photons in water vapour in the energy region from 10 eV to 10 MeV. The cross sections below and above 1 keV have been treated separately. Examples are given for secondary electron spectra for low-energy photons, <100 eV, in which all electrons are photoelectrons, and at higher energy regions, such as for ⁶⁰Co photons. The spectrum of the first generation of secondary electrons, produced by ⁶⁰Co photons, which are mainly due to incoherent scattering, was fitted with a set of polynomial functions which can be used as input for electron radiation action calculations.     

Monte Carlo calculations of energy deposition distributions of electrons below 20 keV in protein

The distributions of energy depositions of electrons in semi-infinite bulk protein and the radial dose distributions of point-isotropic mono-energetic electron sources [i.e., the so-called dose point kernel (DPK)] in protein have been systematically calculated in the energy range below 20 keV, based on Monte Carlo methods. The ranges of electrons have been evaluated by extrapolating two calculated distributions, respectively, and the evaluated ranges of electrons are compared with the electron mean path length in protein which has been calculated by using electron inelastic cross sections described in this work in the continuous-slowing-down approximation. It has been found that for a given energy, the electron mean path length is smaller than the electron range evaluated from DPK, but it is large compared to the electron range obtained from the energy deposition distributions of electrons in semi-infinite bulk protein. The energy dependences of the extrapolated electron ranges based on the two investigated distributions are given, respectively, in a power-law form. In addition, the DPK in protein has also been compared with that in liquid water. An evident difference between the two DPKs is observed. The calculations presented in this work may be useful in studies of radiation effects on proteins.     

Effective cross sections for production of single-strand breaks in plasmid DNA by 0.1 to 4.7 eV electrons

We determined effective cross sections for production of single-strand breaks (SSBs) in plasmid DNA [pGEM 3Zf(-)] by electrons of 10 eV and energies between 0.1 and 4.7 eV. After purification and lyophilization on a chemically clean tantalum foil, dry plasmid DNA samples were transferred into a high-vacuum chamber and bombarded by a monoenergetic electron beam. The amount of the circular relaxed DNA in the samples was separated from undamaged molecules and quantified using agarose gel electrophoresis. The effective cross sections were derived from the slope of the yield as a function of exposure and had values in the range of 10(-15)- 10(-14) cm2, giving an effective cross section of the order of 10(-18) cm2 per nucleotide. Their strong variation with incident electron energy and the resonant enhancement at 1 eV suggest that considerable damage is inflicted by very low-energy electrons to DNA, and it indicates the important role of pi* shape resonances in the bond-breaking process. Furthermore, the fact that the energy threshold for SSB production is practically zero implies that the sensitivity of DNA to electron impact is universal and is not limited to any particular energy range.     

Calculations of heavy-ion track structure

A Monte Carlo model is presented to study details of the energy deposition inside tracks of heavy charged particles in water vapor. The input data for most of the calculations based on the binary encounter approximation are double-differential cross sections for electron emission after heavy-ion impact. The paths of the liberated electrons are simulated, taking into account elastic scattering, ionization, and excitation. Each basic interaction of an electron or heavy ion is treated individually. Radial dose distributions and specific energy deposition are calculated for projectiles from protons to uranium in the energy range from one to several hundred megaelectron volts per unified atomic mass unit. Good agreement with measurements in tissue-equivalent gas and propane is obtained for light and medium-heavy projectiles, whereas for heavy projectiles such as uranium, deviations around a factor of 2–3 are observed.     

The effect of model approximations on single-collision distributions of low-energy electrons in liquid water

The development of cross sections for the inelastic interaction of low-energy electrons with condensed tissue-like media is best accomplished within the framework of the dielectric theory. In this work we investigate the degree to which various model approximations, used in the above methodology, influence electron single-collision distributions. These distributions are of major importance to Monte Carlo track structure codes, namely, the energy-loss spectrum, the inelastic inverse mean free path, and the ionization efficiency. In particular, we make quantitative assessment of the influence of (1) the optical data set, (2) the dispersion algorithm, and (3) the perturbation and exchange Born corrections. It is shown that, although the shape and position of the energy-loss spectrum remains almost fixed, its peak height may vary by up to a factor of 1.5. Discrepancies in the calculated inelastic inverse mean free path are largely within 20-30% above 100 eV; they increase drastically, though, at lower energies. Exchange and perturbation Born corrections increase gradually below 1 keV leading to a approximately 30 to 40% reduction of the inverse mean free path at 100 eV. The perturbation effect contributes more than the exchange effect to this reduction. Similar to the dispersion situation, the effect of Born corrections at lower energies is also unclear since the models examined disagree strongly below 100 eV. In comparison, the vapor data are higher than the liquid calculations by 20 to 50% as the energy decreases from 1 to 0.1 keV, respectively. The excitation contribution is the main cause of this difference, since the ionization efficiency in the liquid levels off at approximately 90%, whereas the plateau value for the vapor is approximately 70%. It is concluded that electron inelastic distributions for liquid water, although in some respects distinctively different from the vapor phase, have associated uncertainties that are comparable in magnitude to the phase differences. The situation below 100 eV is uncertain.     

Method of simplified kinetic equation for simulating the electron kinetics in dense gases in strong electric fields

A method for calculating the electron kinetics in dense gases in strong electric fields is developed. The method differs from the forward-backward approximation proposed by Ra?zer and Shne?der for “high-energy” electrons in that it introduces the effective cosines of the scattering angles with respect to the electric force, μ⁺(?, E) and μ^?(?, E), which are different from +1 and ?1, as in the forward-backward approximation. The method was implemented numerically for atmospheric-pressure helium and molecular nitrogen for fields in the ranges 10–200 and 50–800 kV/cm, respectively. The cosines μ⁺(?, E) and μ^?(?, E), the frequency of “fatal” collisions making high-energy electrons to pass from an acceleration regime to a deceleration one, and the rate at which the electrons leave the low-energy reservoir with energies of ≤15 eV for nitrogen and of ≤20 eV for helium are calculated.     

Possibility of using a low-energy proton beam for particle-induced X-ray emission microanalysis.

The present analysis concentrates on the utilization of low-energy proton accelerators of several hundred kilovolts for particle-induced X-ray emission microanalysis. Experiments on stainless-steel and carbon matrices for thick target conditions have been carried out at several proton energies. The ionization cross sections for some elements are calculated using the ECPSSR theory. The effective cross section and minimum detection limits are calculated for the two matrices. With the availability of ultra LE-Ge detectors low-Z elemental detection is discussed.     

Diffuse and constricted modes of a dc discharge in neon: Simulation of the hysteresis transition

Results are presented from theoretical studies of high-pressure (～100 Torr) dc discharges in neon. The diffuse and constricted discharge modes are studied using a model including the equation of balance for charged and excited particles, heat conduction equations for the neutral gas and plasma electrons, and Poisson’s equation for the radial electric field at a fixed total discharge current. A specific feature of the constricted mode in the investigated range of low fields and high degrees of ionization is that the excitation and ionization rates in the center of the discharge tube and at the periphery differ by several orders of magnitude. This implies that, in the constricted mode, the region where the electron energy distribution function is Maxwellian due to electron-electron collisions may adjoin the region (beyond the constriction zone) where the high-energy part of the distribution function is depleted. The hysteresis transition between the diffuse and constricted modes is analyzed. A transition from the constricted to the diffuse mode can be regarded as a manifestation of the nonlocal character of the formation of the electron distribution function, specifically, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region toward the periphery. The nonlocal formation of the distribution function is described by a nonlocal kinetic equation accounting for electron-electron collisions and electron transport along the radius of the discharge tube. Since only high-energy electrons produce gas ionization, the effect of the nonlocal formation of the electron distribution function is taken into account by introducing the effective temperature of the high-energy part of the distribution function and solving the equation for the radial profile of the high-energy part of the distribution function. This approach allows one to approximately take into account the nonlocal character of the electron distribution function without substantial expenditure of computer resources. The nonlocal model makes it possible to numerically simulate the hysteresis transition between the diffuse and constricted modes, which is impossible in the local approximation.     

A Monte Carlo code for the simulation of heavy-ion tracks in water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.     

Analysis of low-energy electron track structure in liquid water

An implementation is presented of interaction cross sections for non-relativistic electron track structure simulations. The model, incorporating liquid-phase cross sections for inelastic interactions and improved algorithms for elastic scattering, is applied to Monte Carlo simulation of the track structure of low-energy electrons. Benchmark distributions and mean values are presented for several measures of penetration distances that characterize the general physical extent of the track structure. The results indicate that, except for the last approximately 500 eV of energy loss, electron tracks have a quasi-linear character; this suggests that a major part of an electron track may be reasonably described by a lineal-energy-like characterization.