Differential and integral W-values for ionization in gaseous water under electron and proton irradiation: consistency of inelastic collision cross sections.

Differential and integral W-values for ionization in gaseous water for electron and proton irradiation have been analyzed from the theoretical point of view for consistency between ionization and total inelastic collision cross sections. For low-energy electrons, which are ubiquitous for all primary radiations, the experimental or compiled cross sections from different sources are sometimes not consistent with one another. A practical, self-consistent procedure is outlined in such cases. The high-energy asymptotic W-values for differential and integral ionization are calculated to be 33.7 and 34.7 eV, respectively, for electron irradiation and 34.6 and 32.5 eV, respectively, for proton irradiation. The computed variations of the W-values with energy are generally in good agreement with experiment. Integral primary W-values due only to the interactions between the incident particle and the water vapor are calculated to be 43.5 and 45.0 eV for electrons and protons, respectively, in the high-energy asymptotic limit.     

High-energy electron irradiation of proteins and nucleic acids: collisional stopping power and average energy loss

Inactivation of proteins due to the direct action of ionizing radiation and the electron energy loss spectra of organic materials indicate that an average of 60–66 eV of energy is lost from high energy electrons in each inelastic collision with target molecules. The average energy loss per inelastic collision with high energy electrons in solid, carbon-based materials, proteins and nucleic acids is calculated from mass collisional stopping powers and empirical total inelastic cross-sections. Bragg’s Additivity Law is used for the calculation of the mean excitation energy of molecules. For simple organic compounds, the calculated average energy loss is close to that obtained by direct observation of the energy loss suffered by electrons as they pass through thin films of organic material. The density effect correction for the rate of energy loss, important in the more complex case of proteins irradiated with 10 MeV electrons, is determined using the comparable mass collisional stopping power of water and proteins. In this manner, a value is obtained for the average energy per inelastic collision of high energy electrons with proteins, which is similar to the average energy per inactivating event of proteins. Analogous calculations for nucleic acids are also presented.     

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.     

Simulation of the passage of fast electrons and the early stage of water radiolysis by the Monte Carlo method

A numerical computer simulation of the processes of the interaction of electrons with liquid water and vapor was performed, beginning with the absorption of the energy of ionizing radiation and including the chemical changes in the medium. The specific features of the liquid phase compared with the gaseous phase were taken into account. Among them are the decrease of the ionization potential and collective excitations of the plasmon type. The mass stopping powers and ranges of electrons in liquid water and vapor were calculated. Within the frames of the stochastic model the kinetics of water radiolysis in the picosecond range of radiolysis was calculated by the Monte Carlo method. The mechanism of water radiolysis was found with the electron-ion recombination and the reactions of quasi-free and solvated electrons taken into account.     

Aspects of fast-ion dosimetry

A first step in the dosimetry of fast-ion beams is the determination of accurate Bragg (ionization) functions. Bragg functions for several substances have been measured and calculated for 3480 MeV carbon ions. In the measurements, the ions first traverse an absorber in which the energy is reduced to either 1900 or 1200 MeV, then a "range gauge" followed by a thin ionization chamber. Functions are calculated with an analytical method using convolutions of straggling functions. This approach gives results without the stochastic variations implicit in Monte Carlo methods. The comparison of measured and calculated functions shows how reliable the calculations are. An important part of the calculations is the determination of the total range of the ions. The range can be determined from the Bragg function. The measured range is given by the sum of the thickness of the absorber and the residual range measured with the range gauge. For water, the range is about 150 mm, and the precision of the measurements is +/-0.05 mm. Because the ion energy at the surface of the absorber fluctuates with time, measurements with water are used to define this energy. Thus the ranges (or average stopping powers) in absorbers are obtained relative to those in water. Measured ranges R(m) are compared with ranges R(0) calculated with a current version of the Bethe theory. For light absorbers (atomic number Z < 20), differences between R(m) and R(0) are less than +/-0.3 mm; for Z > 20 differences are between 0 and +/-0.6 mm. This agreement between calculated and measured ranges confirms the value I = 80 eV for water measured earlier for protons. The ionization by nuclear fragments is obtained from the difference between measured and calculated ionization functions, and has little influence on the ranges of the primary ions.     

Energy loss of hydrogen- and helium-ion beams in DNA: calculations based on a realistic energy-loss function of the target

We have calculated the electronic energy loss of proton and α-particle beams in dry DNA using the dielectric formalism. The electronic response of DNA is described by the MELF-GOS model, in which the outer electron excitations of the target are accounted for by a linear combination of Mermin-type energy-loss functions that accurately matches the available experimental data for DNA obtained from optical measurements, whereas the inner-shell electron excitations are modeled by the generalized oscillator strengths of the constituent atoms. Using this procedure we have calculated the stopping power and the energy-loss straggling of DNA for hydrogen- and helium-ion beams at incident energies ranging from 10 keV/nucleon to 10 MeV/nucleon. The mean excitation energy of dry DNA is found to be I = 81.5 eV. Our present results are compared with available calculations for liquid water showing noticeable differences between these important biological materials. We have also evaluated the electron excitation probability of DNA as a function of the transferred energy by the swift projectile as well as the average energy of the target electronic excitations as a function of the projectile energy. Our results show that projectiles with energy ?100 keV/nucleon (i.e., around the stopping-power maximum) are more suitable for producing low-energy secondary electrons in DNA, which could be very effective for the biological damage of malignant cells.     

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.     

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.     

Negative-polarity fast ionization wave in molecular gases: Electric field, electron density, and energy branching

The charge density per unit length, the longitudinal component of the electric field, and the electron density behind the front of a fast ionization wave initiated by a nanosecond negative voltage pulse in air, N₂, and H₂ in the 1-to 24-torr pressure range are reconstructed from the experimental data. It is shown that the electron density behind the wave front depends weakly on the sort of gas used and, at relatively high pressures (8–24 torr), is (2–3)×10¹² cm^?3. The energy deposited in the internal degrees of freedom is analyzed. It is shown that, for all gases used, most of the deposited energy (40–60%) is spent on the excitation of the electron degrees of freedom. The fraction of the energy deposited in the high-energy degrees of freedom (ionization and dissociation) monotonically decreases with increasing the pressure, whereas the fraction of the energy spent on the excitation of the low-energy degrees of freedom (rotational and vibrational) monotonically increases.     

Effect of the shape of the electron energy distribution function on the dust grain charge and its screening in glow discharge plasmas

The dust grain charge in the plasma of a glow discharge in noble gases and nitrogen is calculated in the orbit motion limited model for reduced fields in the range of E/N = 1–20 Td. The calculations were performed using the electron energy distribution functions (EEDFs) obtained by solving the Boltzmann equation numerically with allowance for elastic and inelastic electron scattering and analytically with allowance for only elastic scattering and (for nitrogen) excitation of rotational levels, as well as using a Maxwellian EEDF. In the latter case, either the characteristic electron energy or mean electron energy multiplied by two thirds was used as the electron temperature. It is shown that the calculations with the use of a Maxwellian EEDF yield larger values of the grain charge as compared to those calculated with EEDFs obtained by solving the Boltzmann equation. The range of E/N values is determined in which analytical expressions for the EEDF obtained with allowance for elastic scattering and excitation of rotational levels are applicable to calculating the grain charge. The effect of the EEDF shape on the screening of the dust grain charge in plasma is investigated. The Debye screening length in case of a Maxwellian EEDF is shown to be shorter than that obtained with EEDFs calculated by numerically solving the Boltzmann equation.     

Experimental and theoretical study of the near IR emission of xenon excited by a fast electron beam

Emission of xenon excited by a 120-keV electron beam at gas pressures of 100, 200, 500, and 760 Torr nm was studied experimentally and theoretically. More than 30 spectral lines were identified in the wavelength range of 750–1000 nm. A self-consistent kinetic model is developed to calculate the emission intensity of xenon atoms in the near IR range. The model includes balance equations for the number densities of electrons, ions and excimer molecules; equations for the populations of electron levels; and the Boltzmann equation for the low-energy part of the electron energy distribution function with a source of slow electrons. Excitation and ionization rates of xenon by the beam electrons and the energy spectrum of slow electrons are calculated by the Monte Carlo method. It is shown that, under these conditions, the main mechanism of xenon atom excitation is dissociative recombination of Xe₃ ⁺ ions.     

Modeling of Coulomb collisions in a kinetic description of the electron cyclotron resonance plasma heating

The electron distribution function is modeled numerically with allowance for Coulomb collisions and quasilinear effects under cyclotron resonance conditions by solving a two-dimensional kinetic equation containing the quasilinear diffusion operator and the Coulomb collision operator in the Landau form. Two simplified model collision integrals that make it possible to describe electron heating by microwave radiation are considered. The first model collision operator is obtained by introducing the parametric time dependence of the temperature of the background Maxwellian electrons into the linear collision integral. It is shown that the heating of the bulk electrons can be described in a noncontradictory way if the temperature dynamics of the background electrons is calculated from the equation of energy balance, which is governed by the amount of the microwave power absorbed by the resonant electrons with the distribution function modified due to quasilinear effects. This conclusion is confirmed in a more rigorous fashion by comparing the solutions obtained using the first model Coulomb collision integral with those obtained using the second model integral, namely, the nonlinear operator derived by averaging the distribution function of the scattering electrons over pitch angles. The time-dependent linear collision integral is used to obtain analytic solutions describing quasi-steady electron heating with allowance for the quasilinear degradation of microwave power absorption.     

Transverse glow discharges in supersonic air and methane flows

Transverse glow discharges in supersonic air and methane flows are studied both experimentally and theoretically. The experiments show that a diffuse volume discharge filling the whole cross section of the flow can easily be initiated in air, whereas a diffuse discharge in a methane flow shows a tendency to transition into a constricted mode. The electron transport coefficients (mobility and drift velocity) and the kinetic coefficients (such as collisional excitation rates of the vibrational levels of a methane molecule, as well as dissociation and ionization rates) are calculated by numerically solving the Boltzmann equation for the electron energy distribution function. The calculated coefficients are used to estimate the parameters of the plasma and the electric field in the positive column of a discharge in methane.     

Lateral diffusion as a rate-limiting step in ubiquinone-mediated mitochondrial electron transport

Data are presented which indicate that the diffusion-based collisions of ubiquinone with its redox partners in the mitochondrial inner membrane are a rate-limiting step for maximum (uncoupled) rates of succinate-linked electron transport. Data were obtained from experimental analysis of a comparison of the apparent activation energies of lateral diffusion rates, collision frequencies, and electron transport rates in native and protein-diluted (phospholipid-enriched) inner membranes. Diffusion coefficients for Complex III (ubiquinol:cytochrome c oxidoreductase) and ubiquinone redox components were determined as a function of temperature using fluorescence recovery after photobleaching, and collision frequencies of appropriate redox partners were subsequently calculated. The data reveal that 1) the apparent activation energies for both diffusion and electron transport were highest in the native inner membrane and decreased with decreasing protein density, 2) the apparent activation energy for the diffusion step of ubiquinone made up the most significant portion of the activation energy for the overall kinetic activity, i.e. electron transport steps plus the diffusion steps, 3) the apparent activation energies for both diffusion and electron transport decreased in a proportionate manner as the membrane protein density was decreased, and 4) Arrhenius plots of the ratio of experimental electron transport productive collisions (turnovers) to calculated theoretically predicted, diffusion-based collisions for ubiquinone with its redox partners had little or no temperature dependence, indicating that as temperature increases, increases in electron transport rate are accounted for by the increases in diffusion-based collisions. These data support the Random Collision Model of mitochondrial electron transport in which the rates of diffusion and appropriate concentrations of redox components limit the maximum rates of electron transport in the inner membrane.     

Oxygen diffusion-concentration product in rhodopsin as observed by a pulse ESR spin labeling method.

Permeation of molecular oxygen in rhodopsin, an integral membrane protein, has been investigated by monitoring the bimolecular collision rate between molecular oxygen and the nitroxide spin label using a pulse electron spin resonance (ESR) T1 method. Rhodopsin was labeled by regeneration with the spin-labeled 9-cis retinal analogue in which the beta-ionone ring of retinal is replaced by the nitroxide tetramethyl-oxypyrrolidine ring. The bimolecular collision rate was evaluated in terms of an experimental parameter W(x), defined as T1(-1)(air,x)--T1(-1)(N2,x) where T1's are the spin-lattice relaxation times of the nitroxide in samples equilibrated with atmospheric air and nitrogen respectively, which is proportional to the product of local oxygen concentration and local diffusion coefficient (transport). W-values at the beta-ionone binding site in spin-labeled rhodopsin are in the range of 0.02-0.13 microseconds-1, which are 10-60 times smaller than W's in water and 1.1-20 times smaller than in model membranes in the gel phase, indicating that membrane proteins create significant permeation resistance to transport of molecular oxygen inside and across the membrane. W(thereby the oxygen diffusion-concentration product) is larger in the meta II-enriched sample than in rhodopsin, indicating light-induced conformational changes of opsin around the beta-ionone binding site. W decreases with increase of temperature for both rhodopsin and meta II-enriched samples, suggesting that temperature-induced conformational changes take place in both samples. These changes were not observable using conventional ESR spectroscopy. It is concluded that W is a sensitive monitor of conformational changes of proteins.     

Electron stopping power and inelastic mean free path in amino acids and protein over the energy range of 20–20,000 eV

Systematic calculations of stopping power (SPs) and inelastic mean free path (IMFP) values for 20–20,000 eV electrons in a group of 15 amino acids and a simple protein have been performed. The calculations are based on the dielectric response model and take into account the exchange effect between the incident electron and target electrons. The optical energy-loss functions for the 15 investigated amino acids and the protein are evaluated by using an empirical approach, because of the lack of experimental optical data. For all the considered materials, the calculated mean ionization potentials are in good agreement with those given by Bragg’s rule, and the evaluated SP values at 20 keV converge well to the Bethe–Bloch predictions. The data shown represent the first results of SP and IMFP, for these 15 amino acids and the protein in the energy range below 20 keV, and might be useful for studies of various radiation effects in these materials. In addition, the average energy deposited by inelastic scattering of the electrons on this group of 15 amino acids, on the protein, on Formvar and on DNA, respectively, has been estimated for energies below 20 keV. The dependences of the average energy deposition on the electron energy are given. These results are important for any detailed studies of radiation-induced inactivation of proteins and the DNA.     

Electron Transport and Nonlinear Optical Properties of Substituted Aryldimesityl Boranes: A DFT Study

A comprehensive theoretical study was carried out on a series of aryldimesityl borane (DMB) derivatives using Density Functional theory. Optimized geometries and electronic parameters like electron affinity, reorganization energy, frontiers molecular contours, polarizability and hyperpolarizability have been calculated by employing B3PW91/6-311++G (d, p) level of theory. Our results show that the Hammett function and geometrical parameters correlates well with the reorganization energies and hyperpolarizability for the series of DMB derivatives studied in this work. The orbital energy study reveals that the electron releasing substituents increase the LUMO energies and electron withdrawing substituents decrease the LUMO energies, reflecting the electron transport character of aryldimesityl borane derivatives. From frontier molecular orbitals diagram it is evident that mesityl rings act as the donor, while the phenylene and Boron atom appear as acceptors in these systems. The calculated hyperpolarizability of secondary amine derivative of DMB is 40 times higher than DMB (1). The electronic excitation contributions to the hyperpolarizability studied by using TDDFT calculation shows that hyperpolarizability correlates well with dipole moment in ground and excited state and excitation energy in terms of the two-level model. Thus the results of these calculations can be helpful in designing the DMB derivatives for efficient electron transport and nonlinear optical material by appropriate substitution with electron releasing or withdrawing substituents on phenyl ring of DMB system.     

Probe measurements of the electron distribution function in an electron-beam-produced ytterbium plasma

A nonequilibrium anisotropic plasma produced by an electron beam in the residual air with a low content of ytterbium vapor was investigated by the probe method. It is found that a minor (at a level of a few ppm) admixture of ytterbium to low-pressure air substantially modifies the electron energy distribution function (EEDF): the main peak corresponding to thermal electrons broadens, and new peaks appear. It is shown that the observed change in the EEDF is caused by the low ionization energy of ytterbium, due to which one beam electron can ionize several ytterbium atoms. The new peaks in the EEDF correspond to the final energies of a beam electron after each subsequent ionizing collision with ytterbium atoms.     

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.