Dynamics of low-energy electrons in liquid water with consideration of Coulomb interaction with positively charged water molecules induced by electron collision
Introduction
In order to explain the effects of low-dose radiation on living cells, it is essential to understand the energy-deposition process on bio-molecules along each radiation track in the system. It has been determined that low-energy electrons at the end of the track mimic high-linear energy transfer (LET) radiation that cause heavy ionizations or excitations (Michael and O’Neill, 2000). Monte Carlo computer simulations have been applied in many previous studies to analyze the radiation track-structure and bio-molecular damage, such as DNA damage. These studies have provided significant insights into radiation-induced DNA damage structures specific to the track-structure. In particular, multiple lesions arising in a DNA localized area, so-called clustered DNA damage (Goodhead, 1994, Ward, 1994), have been focused in terms of ionization density and resulting water radiolysis along the track of the low-energy electrons.
Free radicals are produced as a consequence of water radiolysis and diffuse to react with DNA with a known probability (Buxton et al., 1988). Monte Carlo methods have been shown to be of great advantage in estimating reactions of the diffusible water radicals with DNA (Nikjoo et al., 1997). In addition to the indirect action of the diffusible species (indirect effect), direct ionization or DNA excitation caused by inelastic electron collisions (direct effect) induce molecular damage. It has been reported that low-energy electrons below a few tens of electron volts are able to cause DNA single- (SSBs) and double-strand breaks (DSBs) (Boudaïffa et al., 2000) by the resonantly dissociative electron attachment (DEA) mechanism. On the other hand, it has been inferred that the electron re-capturing into the parent molecule reduces the positive charges. We previously reported that the DNA strand break yields and base lesions show an irregular reduction caused by K-shell phosphorus photoionization in the DNA backbone (Yokoya et al., 2009). At the ionization threshold, the low-energy photoelectron ejected from phosphorus K-shell is believed to be taken back to the positively tetravalent phosphorus ion produced by the Auger decay process, and then re-captured. We also report more experimental evidence of photoelectron re-capture in DNA using electron paramagnetic resonance spectroscopy (Oka et al., 2012). Dynamical calculation of an electron moving in a Coulomb field around a highly ionized molecule is required in this simulation. However, this Coulomb force effect on the electron trajectory has not been taken into account in our previous Monte Carlo simulations (Watanabe et al., 2004). Taking into account the electron re-capture frequencies of DNA, it should be necessary to perform the dynamical calculation of electrons induced by radiation.
We should address previous study for electron behavior in liquid and solid water, as well as the DNA damage by radiation to make needs for the dynamical calculation more clear. Experimental results of range for incident electrons were reported in the energy region above 10 keV (ICRU, 1984) and extremely lower energy region below 4 eV (Konovalov et al., 1988) so far. There have been scarce experimental results for the range in the energy region of hundreds of eV such as a track end of an electron. Paretzke (1987) reported results for the range of the incident electron in water using useful empirical formula obtained from the experimental data (ICRU, 1984) and Monte Carlo method in high-energy region. Goulet and Jay-Gerin (1988) reported the spatial probability-distribution of thermalized subexcitation electrons using Monte Carlo method in solid water.
In this study, we have developed an advanced Monte Carlo track-structure method that takes into account the Coulomb interaction between low-energy electrons and molecular ions. This method has been based partly on the molecular dynamics (MD) proposed by Moribayashi (2011) to simulate the temporal evolution of electron collisional processes in pure water. By solving a Newtonian equation, the trajectories of incident and secondary ejected electrons moving in a Coulomb field around ionized water molecules were calculated. This was accomplished by considering not only the cross sections of the ionization, electronic and vibrational excitations but also the cross sections of rotational excitations, dissociative electron attachment, and elastic scattering. Near the track end of the electron whose energy is around hundreds of eV, the ionized electrons will intricately move because the ionized electrons and its parent ions are densely produced by the incident electron along its track. We reported that an Auger electron, whose kinetic energy is 500 eV, emitted from an Oxygen atom plays an important role in DNA damage induced by Soft X-ray (Fujii et al., 2009). The results mainly presented in this study include the number of collisional events by the impact of 500 eV incident electrons, and the dynamics of secondary electrons produced. We evaluate the contribution of the Coulomb interaction using acceleration and the re-capture of electrons in water from the comparisons of our results and previous results (Paretzke, 1987, Goulet and Jay-Gerin, 1988, Morbayashi, 2011).
Section snippets
Theory
In this paper, we focus on ionization and excitations of water molecules induced along the trajectory of incident electrons on 100 fs timescale. We assumed that water may be modeled as a uniform continuum with 1.0 g/cm3 density. We calculated the temporal evolution of the number of collisions, mean energy, and the range of the incident and secondary electrons with water molecules. Here, we define the incident electron as the primary electron and assume that it is generated at the origin at time t
Results and discussions
First, we compared our results with those from previous work. To test and verify our results of mean diffusion distance of primary electron, we compared our results with the previous results (Paretzke, 1987). As per Ref. (Paretzke, 1987), we calculated the range R (in nm) of the primary electron in water using the empirical formula obtained from the experimental data in the high-energy region (ICRU, 1984),where E is the primary electron energy (in keV). This formula is useful in
Conclusions
Most interesting results in our study were of electrons re-captured to water molecule ions within 100 fs. Those electrons re-captured within hundreds of fs would be recombined to some electronic excited states at some future time. Currently, LaVerne et al. (2005) reported experimental results of fast electron recombination within 5 ps for high-LET-ions irradiations in water. We would believe that the experimental evidence would support our calculated results for electrons re-captured because the
Acknowledgments
We wish to thank Drs. M. Pinak, N. B. Ouchi, E. Yabu, and A. Endo for their useful discussions.
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