Simple stopping power formula for low and intermediate energy electrons

Electron interaction with DNA constituents in aqueous phase

Electron driven chemistry of biomolecules in aqueous phase presents the realistic picture to study molecular processes. In this study we have investigated the interactions of electrons with the DNA constituents in their aqueous phase in order to obtain the quantities useful for DNA damage assessment. We have computed the inelastic mean free path (IMFP), mass stopping power (MSP) and absorbed dose (D) for the DNA constituents (Adenine, Cytosine, Guanine, Thymine and Uracil) in the aqueous medium from ionisation threshold to 5000 eV. We have modified complex optical potential formalism to include band gap of the systems to calculate inelastic cross sections which are used to estimate these entities. This is the maiden attempt to report these important quantities for the aqueous DNA constituents. We have compared our results with available data in gas and other phase and have observed explicable accord for IMFP and MSP. Since these are the first results of absorbed dose (D) for these compounds, we have explored present results vis-a-vis dose absorption in water.

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.

Intercomparison of nanodosimetric distributions in nitrogen simulated with Geant4 and PTra track structure codes

To facilitate the use of Geant4-DNA for radiation transport simulations in micro- and nanodosimeters, which are physically operated with tissue-equivalent gases such as nitrogen (and propane), this work aims to extend the cross section data available in Geant4-DNA to include those of nitrogen for electron energies ranging from 1 MeV down to the ionisation threshold. To achieve this, interaction cross section data for nitrogen that have been used with the in-house PTB PTra track structure code have been implemented in the current state-of-the-art Geant4-DNA simulation toolkit. An intercomparison has been performed between the two codes to validate this implementation. To quantify the agreement between the cross section models for nitrogen adopted in PTra and those implemented in Geant4-DNA, the simulation results of both codes were analysed using three physical parameters describing the ionisation cluster size distribution (ICSD): mean ionisation cluster size, variance of the cluster size and the probability to obtain a single ionisation within the target. Statistical analysis of the results indicates that the interaction cross section models for nitrogen used in PTra (elastic scattering, impact ionisations and electronic excitations) have been successfully implemented in Geant4-DNA. In addition, simulated ICSDs were compared to those measured with the Jet Counter nanodosimeter for energies between 100 and 2000 eV. For greater energies, the ICRP data for LET and particle range were used as a reference. The modified Geant4-DNA code and data successfully passed all these benchmarks fulfilling the requirement for their public release in the next version of the Geant4 toolkit.

Dose-mean lineal energy values for electrons by different Monte Carlo codes: Consequences for estimates of radiation quality in photon beams

BACKGROUND

The microdosimetric quantity lineal energy and its mean values have proven useful for quantifying radiation quality in many situations. The ratio of dose-mean lineal energies is perhaps the simplest quantity for quantifying differences between two radiation qualities. However, published dose-mean lineal energy values from different codes may differ significantly with potential influence on radiation quality estimates.

PURPOSE

The purpose was to compare dose-mean lineal energy values from different track-structure data sets for condensed water vapor and liquid water, and to evaluate the influence on radiation quality estimations for some photon sources.

METHODS

Published dose-mean lineal energy values for 0.1 keV to 1 MeV electrons in spheres with diameters 2 nm to 1 μm, calculated with water vapor and liquid water track structure codes and proximity functions, were collected, analyzed, and compared. Data for cylinders were converted to spheres using a theoretical transformation published by Kellerer. A new set of dose-mean lineal energy values was calculated to cover the whole range of volumes of interest here using the GEANT4-DNA code. The influence from the differences between codes on radiation quality calculations was estimated using dose-mean lineal energy ratios for the photon sources ¹²⁵ I, ¹⁶⁹ Yb, and ¹⁹² Ir relative to ⁶⁰ Co.

RESULTS

The theoretical relation for converting the dose-mean lineal energy between different geometrical volumes, results in differences up to 10% between cylinders and spheres depending on electron energy and target size, in agreement with published simulated results. For spheres with diameter above 100 nm, dose-mean lineal energy values for condensed water vapor and liquid water are with few exceptions within ±10%. Below 100 nm, the difference increases with decreasing diameter reaching a factor of two at 2 nm. The values from water vapor codes are in general larger than from liquid water codes. If the dose-mean lineal energy ratio is based on condensed water vapor instead of liquid water, the ratio differs less than 9% for the nuclides ¹²⁵ I, ¹⁶⁹ Yb, and ¹⁹² Ir relative to ⁶⁰ Co independent of the volume simulated. However, a specific value of the dose-mean lineal energy ratio, is found at a larger target diameter in liquid water than in condensed water vapor.

CONCLUSIONS

When ratios of the dose-mean lineal energy are used as a measure of the radiation quality it is important to compare values for geometrically equal target shapes. A practical method of converting values for cylinders of equal diameter and height to spheres was demonstrated. Although dose-mean lineal energy values calculated with water vapor and liquid water codes may differ significantly, the radiation quality, in terms of ratios of dose-mean lineal energy, for the three photon sources ¹⁹² Ir, ¹⁶⁹ Yb, and ¹²⁵ I relative to ⁶⁰ Co, agree within 9%. The same ratio appears at a larger diameter when a liquid water code is used. It is therefore important to use the same code in radiation quality investigations. The present findings may be of special interest in studies related to the relative biological effectiveness (RBE).

Stopping power and CSDA range calculations of electrons and positrons over the 20 eV-1 GeV energy range in some water equivalent polymer gel dosimeters

In this study, the stopping power, CSDA range and radiation yield calculations of electrons and positrons over the 20 eV-1 GeV energy range in some water equivalent polymer gel dosimeters were performed. For collision stopping power calculations of electrons and positrons the effective charge concept proposed by Sugiyama were considered. Here, both the effective charge of incident electrons and positrons (z*) and the effective charge (Z*) and the effective mean excitation energy (I*) of the target material were calculated. For the density effect correction the Fano model was selected. For the radiative stopping power analytical model based on the ratio between the collision and the radiative stopping power discribed by Attix was considered. For CSDA range and radition yield the continuous slowing down approximation (CSDA) was considered and the calculations were performed using numerical integral methods. Because of their water equivalent and 3D dose distribution properties, MAGIC and MAGAS polymer gels were selected as a target materials. The calculations were performed by programming all the equations discribed in this study as a computational code. The results of the stopping power, range and radiation yield were compared with those of ESTAR program and PENELOPE Monte Carlo modelling. Some deviations in low and high energy region between the calculated and reference data were observed. However, the similarity between calculated and reference data is remarkable. For the collision stopping power and CSDA range a good agreement between the calculated and reference data was observed for energies >1 keV. Whereas, for the radiative stopping power a good agreement was observed for energies >100 keV.

100th Anniversary of Macromolecular Science Viewpoint: Polymeric Materials by In Situ Liquid-Phase Transmission Electron Microscopy

A century ago, Hermann Staudinger proposed the macromolecular theory of polymers, and now, as we enter the second century of polymer science, we face a different set of opportunities and challenges for the development of functional soft matter. Indeed, many fundamental questions remain open, relating to physical structures and mechanisms of phase transformations at the molecular and nanoscale. In this Viewpoint, we describe efforts to develop a dynamic, in situ microscopy tool suited to the study of polymeric materials at the nanoscale that allows for direct observation of discrete structures and processes in solution, as a complement to light, neutron, and X-ray scattering methods. Liquid-phase transmission electron microscopy (LPTEM) is a nascent in situ imaging technique for characterizing and examining solvated nanomaterials in real time. Though still under development, LPTEM has been shown to be capable of several modes of imaging: (1) imaging static solvated materials analogous to cryo-TEM, (2) videography of nanomaterials in motion, (3) observing solutions or nanomaterials undergoing physical and chemical transformations, including synthesis, assembly, and phase transitions, and (4) observing electron beam-induced chemical-materials processes. Herein, we describe opportunities and limitations of LPTEM for polymer science. We review the basic experimental platform of LPTEM and describe the origin of electron beam effects that go hand in hand with the imaging process. These electron beam effects cause perturbation and damage to the sample and solvent that can manifest as artefacts in images and videos. We describe sample-specific experimental guidelines and outline approaches to mitigate, characterize, and quantify beam damaging effects. Altogether, we seek to provide an overview of this nascent field in the context of its potential to contribute to the advancement of polymer science.

Ensemble machine learning methods: predicting electron stopping powers from a small experimental database

Electron stopping power (SP) is of great importance in theoretical and applied research areas specifically for Monte Carlo simulation studies in many microanalysis and surface analysis techniques, radiation dosimetry, and the design of particle detectors. However, experimental data are available for a dozen elemental materials only. On the other hand, the Bethe analytical expression of the SP is applicable at high energies only whereas no generally accepted formula exists at lower energies. We employed ensemble machine learning (ML) methods with the available experimental database for the prediction of SPs of electrons with energies from 100 keV down to 1 eV, in elements over the entire periodic table. With a small training database for electron SPs, we applied various algorithms individually as well as their ensembles, which have the credibility to enhance the prediction accuracy in the case of a small training database. Based on the model's performance evaluation tests, we concluded that the stacked generalization is more accurate than the individual algorithms. Using this method, we were able to predict the electron SPs for 54 elements (in total) including 12 elements that were present in the training database as well as for 42 elements beyond the training database over a wide energy range (1 eV to 100 keV). Compared to other theoretical approaches, the ML predicted SPs show very good agreement with the available experimental data at all energies. Moreover, unlike other theoretical approaches, the ML model does not need dielectric function data and other physical parameters which involve complex calculations. Using our ML model, we have predicted SPs for a further 14 elements for which no theoretical SPs are available because of the lack of good dielectric function data.

Spatially dependent dose rate in liquid cell transmission electron microscopy

The use of liquid cell electron microscopy as a quantitative probe of nanomaterial structures and reactions requires an accurate understanding of how the sample is altered by the imaging electron beam. In particular, changes in the chemical environment due to beam-induced radiolysis can strongly affect processes such as solution-phase nanocrystal synthesis or electrochemical deposition. It is generally assumed that beam effects are uniform throughout the irradiated liquid. Here we show that for a liquid cell filled with water, the inevitable presence of interfaces between water and the surrounding surfaces causes a spatial variation in the energy absorbed by the water near the walls. The mechanism for this effect is that the walls act as a source of secondary and backscattered electrons which diffuse and deposit energy in the water nearby. This increased dose rate then changes the local concentrations of radiolysis species. We quantify and compare the effects for different materials used in practical liquid cells. We show that the dose rate can increase by several times within tens of nanometers of a water/Au interface, locally increasing the concentrations of species such as the hydrated electron. We discuss the implications for materials processes that are typically triggered at the solid-liquid interface.

Stopping power and CSDA range calculations for incident electrons and positrons in breast and brain tissues

The stopping power in some biological compounds for electrons and positrons was calculated over the energy range from 100 eV to 1 GeV. Total stopping power was obtained by summing the electronic (collisional) and radiative stopping power of the target materials and then employing the continuous slowing down approximation (CSDA) to calculate the path length of incident particles in the target. An effective charge approximation was used for the calculation of collisional stopping power, and an analytical expression for the radiation length was applied to obtain the radiative stopping power. Calculations of stopping power and CSDA range were based mostly on analytical expressions, to allow for an easy calculation of these parameters. The results were tabulated and compared with available data.

Hot electron dominated rapid transverse ionization growth in liquid water

Pump/probe optical-transmission measurements are used to monitor in space and time the ionization of a liquid column of water following impact of an 800-nm, 45-fs pump pulse. The pump pulse strikes the 53-μm-diameter column normal to its axis with intensities up to 2 × 10(15) W/cm2. After the initial photoinization and for probe delay times < 500 fs, the neutral water surrounding the beam is rapidly ionized in the transverse direction, presumably by hot electrons with initial velocities of 0.55 times the speed of light (relativistic kinetic energy of ~100 keV). Such velocities are unusual for condensed-matter excitation at the stated laser intensities.

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.

Electron inelastic mean free path formula and CSDA-range calculation in biological compounds for low and intermediate energies

In this study, for low atomic number targets and biological compounds, an inelastic mean free path (IMFP) formula and energy straggling parameter formula are presented, being valid for low and high electron energies. In addition, calculation of the continuous slowing down approximation-range (CSDA-range) from the stopping power is also made. The IMFP and the energy straggling parameter formulae are evaluated using the generalized oscillator strength (GOS) model and the exchange correction to the inelastic differential cross section (IDCS) given by Inokuti, M., [1978. Inelastic collisions of fast charged particles with atoms and molecules--the Bethe theory revisited. Rev. Mod. Phys. 50, 23-35]. The IMFP and CSDA-range for the biological compounds C5H5N5 (adenine), C5H5N5O (guanine), C4H5N3O (cytosine), C5H6N2O2 (thymine), C20H27N7O13P2 (cytosine-guanine) and C19H26N8O13P2 (thymine-adenine) have been introduced for incident electrons in the energy range 20 eV-1 MeV. The calculated results are compared with semi-empirical results and other theoretical results, good agreement being found with experimental data and Monte Carlo (PENELOPE code) predictions. All the IMFP versus energy curves exhibit minima around 80 eV.