Proton Impact Research Articles

Independent-atom-model description of multiple ionization of water, methane, and ammonia molecules by proton impact

We study multiple ionization in proton collisions with water, methane, and ammonia molecules using an independent-atom model. Previous work on total (net) capture and ionization cross sections is extended to treat the multiple-ionization channels explicitly. We present the theoretical framework to treat charge-state correlated processes within the independent-atom-model approach, which uses the geometric screening introduced for different molecular geometries and orientations. A comparison of results is made for the target molecules ${\text{H}}_{2}\text{O}, {\text{CH}}_{4}$, and ${\text{NH}}_{3}$ with an emphasis on $q$-fold electron removal. Coincident measurements of produced molecular fragments can be used to estimate this quantity. We find very good agreement for the model calculations for the water molecule, where data exist for $q=1--4$. For methane we observe reasonable agreement for $q=1,2$ and for ammonia only for $q=1$, i.e., the experimental data show little support for a direct multiple-ionization channel in the latter case.

L-shell ionisation and X-ray production cross-sections for some low Z-elements by proton impact

L-shell ionisation and x-ray production cross-sections of various targets are useful in many Proton Induced X-ray Emission (PIXE) applications. Generally, x-ray production cross sections are measured directly but ionisation cross sections are only evaluated using theoretical models. The use of ionisation models has been instrumental in the ion-atom description of the subshells which are then converted to x-ray production cross sections, however, certain limitations exist for currently available models. For instance, at extremely low energy and high energy of the incident particle, some modifications are made to these models to correctly obtain these values. While existing ionisation theory coupled with associated computed codes or data tables have been used successfully in determining cross-sections of medium Z and high Z-elements, targets of low atomic number have not been fully studied, especially when bombarded with proton energy less than 1 MeV. In this study, a revised model using computer codes and algorithm are used in obtaining cross-sections of some light elements (Neon, Magnesium and Argon) whose experimental values are difficult to measure. To verify the certainty of these values, a comparison was made with some experimental values.

Theoretical multiple-ionization cross sections of Ne-like molecules by light-ion impact: H2O

We present a simple theoretical model to calculate multiple-ionization cross sections (MICS) of Ne and Ne-like molecules (molecules with ten electrons as ${\mathrm{H}}_{2}\mathrm{O}, \mathrm{C}{\mathrm{H}}_{4}, \mathrm{N}{\mathrm{H}}_{3}$, and HF) for proton and light-ion impact, taking into account both direct and postcollisional emissions. In this paper, we tackle the case of water molecules, relevant to investigate the radiobiological effects of ion impact on living matter. The theory is developed in the framework of the independent electron model (IEM). To keep the model as simple as possible, we describe the impact parameter dependence of the single-particle ionization probabilities required by the IEM through decreasing exponential functions for each target orbital. We obtain the parameters of the exponential functions from the total net-ionization cross sections for each orbital by applying either the continuum distorted wave-eikonal initial-state (CDW-EIS) approximation or Rudd's model. We then calculate the contribution of Auger postcollisional electron emission to MICS by using the Ne postcollisional emission probabilities. This postcollisional treatment offers a very simple alternative to the much more complex molecular evaluation of postcollisional relaxation and provides results in close agreement with experimental data for proton and other light ions. We also demonstrate the relevance of considering postcollisional emission for water molecules after the $2{a}_{1}$ ($2s$ Ne-like) orbital direct ionization.

A theoretical study of fragmentation dynamics of water dimer by proton impact

To investigate the collision processes of proton with the water dimer (H2O)2 at 50 eV, the time-dependent density functional theory coupled with molecular dynamics nonadiabatically is applied. Six specific collision orientations with various impact parameters are considered. The reaction channels, the mass distribution and the fragmentation mass spectrum are explored. Among all launched samples, the probability of the channel of non-charge transfer scattering and charge transfer scattering is about 80%, hinting that the probability of fragmentation is about 20%. The reaction channel of proton exchange process 2 is taken as an example to exhibit the detailed microscopic dynamics of the collision process by inspecting the positions, the respective distance, the number of loss of electrons and the evolution of the electron density. The study of the mass distribution and the fragmentation mass spectrum shows that among all possible fragments, the fragment with mass 36 has the highest relative abundance of 65%. The relative abundances of fragments with masses 1, 35, and 34 are 20%, 13%, and 1.5%, respectively. For the total electron capture cross section, the present calculations agree with the available measurements and calculations over the energy range from 50 eV to 12 keV.

Electron emission from water vapor under the impact of 250-keV protons

Absolute double differential cross sections (DDCS) of low-energy electron emission from water molecule were measured upon collisions with 250-keV protons for emission angles between 30--150 degrees. The electrons having energies between 1 and 600 eV were detected by using hemispherical electrostatic analyzer. The single differential (SDCS) and total cross section (TCS) were calculated by integrating the DDCS and SDCS, respectively. The measured DDCS, SDCS, and TCS were compared with the classical trajectory Monte Carlo (CTMC) model, using a dynamical approach in which a time-dependent screening is considered. The continuum-distorted-wave eikonal-initial state (CDW-EIS) theoretical model has also been used to explain the energy and angular distribution data. The angular distribution of the DDCS are very well reproduced by the CTMC approach. The TCS calculated by the CTMC model matches better with the measured values as compared to the CDW-EIS estimation. The forward-backward angular asymmetry parameter was also estimated to test the validity of the state-of-the-art theoretical models used. Finally the recently developed CDW-EIS calculations considering a residual target dynamic charge (DC-CDW-EIS) is shown to provide an improved agreement with the experiments compared to the CDW-EIS. The present data and interpretation should provide inputs towards energy loss calculations required for the radiobiology involved in the hadron therapy of cancer.

Parabolic quasi-Sturmian approach to proton-impact ionization of helium

A method for calculating ion-atom ionizing collisions is formulated and applied to single ionization of helium induced by energetic proton impact. Within the frozen-core model for the residual helium ion, the four-body problem in the exit channel is recast as an inhomogeneous Schr\"odinger equation for the Coulomb three-body system $({e}^{\ensuremath{-}},{\text{He}}^{+},{p}^{+})$. The asymptotic behavior of its solution contains the transition amplitude. We suggest to solve the driven equation in the representation of so-called parabolic convoluted quasi-Sturmian (CQS) basis functions which are constructed using quasi-Sturmians (QSs) for the $({e}^{\ensuremath{-}},{\text{He}}^{+})$ and $({p}^{+},{\text{He}}^{+})$ subsystems. By applying the corresponding Coulomb Green's function operators, these QSs are generated from orthogonal complements to square-integrable (${L}^{2}$) Sturmian functions in parabolic coordinates. In the proposed parabolic CQS approach explicit asymptotic expressions for the basis functions provide an expansion of the transition amplitude in terms of ``basis amplitudes,'' which we express analytically. The proton-electron interaction is treated as a perturbation and is approximated by a truncated Sturmian basis-set expansion. It is found that, at least in the high-energy limit, the ionization amplitude converges pretty fast as the number of terms in the separable expansion for the proton-electron potential is increased. The calculated fully differential cross sections for singly ionizing 1-MeV $p$-He collisions in several kinematical regimes in the scattering plane are found to be in reasonable agreement with experimental data and with the theoretical results obtained using the first Born approximation, the 3C model, and the wave-packet convergent close-coupling method. The theory-experiment discrepancy over the binary peak position observed by other authors remains unexplained.

Measurements of charge transfer and target-electron-loss cross sections forH+,D+, andHe+impact on lithium at low energies

Experimental cross section measurements for charge transfer and for electron loss from lithium via charge transfer and direct ionization are reported for collisions between light ions and lithium atoms. Beams of protons, deuterium ions, and helium ions intersect a lithium atom beam, and collision cross sections are inferred by measuring the number of lithium ions produced in the collisions. The collision energy ranges studied are 0.13--3.5 keV for proton impact, 0.13--0.83 keV for deuterium ion impact, and 0.28--3 keV for helium ion impact. At proton collision energies below 0.7 keV our charge transfer cross sections are in excellent agreement with the theoretical predictions, resolving a long-standing discrepancy between theory and experiment in this energy range. Cross sections for proton and for deuterium ion impact on lithium are measured to be identical when scaled to the same collision velocity, indicating that quantum effects are not significant in the energy range studied. Comparison between our cross section measurements for lithium electron loss due to helium ion impact and previously measured charge transfer cross sections show that ionization is a negligible process in ${\mathrm{He}}^{+}+\mathrm{Li}$ collisions at energies below 3 keV. Undulations in the measured collision cross sections at low energy are observed for both proton and helium ion impact and are compared to molecular orbital close-coupling calculations.

Peculiarities of matrix-element calculations with few Coulomb functions for particles' scattering processes

We present ultra high resolution data on single ionization of helium under impact of 1-MeV protons in comparison with theoretical calculations. Good agreement between theory and experiment [1] is obtained. Three initial trial helium wave functions are employed: a weakly correlated Roothaan-Hartree-Fock function, a simple Silverman-Platas-Matsen function ofthe configuration interaction family, and a strongly correlated function [2,3]. Multidimensional singular integrals which defining differential cross sections are calculated using special transform for each above trial function. Results of some calculations arepresented in Figure 1.

Single Ionization of He by Energetic Protons in a Parabolic Quasi-Sturmians Approach

A fully differential cross section for single ionization of helium induced by 1 MeV proton impact is calculated using the parabolic convoluted quasi-Sturmian (CQS) method. In the framework of this approach the transition amplitude is extracted directly from the asymptotic behavior of the solution of an inhomogeneous Schrödinger equation for the Coulomb three-body system (e−,He+,p+). The driven equation is solved numerically by expanding in convolutions of quasi-Sturmians for the two-body proton-He+ and electron-He+ systems. It is found, at least in the high energy limit, that the calculated cross sections within the proposed CQS method converge quickly as the number of terms in the expansions is increased, and are in reasonable agreement with experimental data and other theoretical results.

Electron-impact-like feature in triple fragmentation of CO23+ under slow proton impact

We have studied the three-body breakup of ${\mathrm{CO}}_{2}^{3+}$ created by the impact of slow ($v<1$ a.u.) protons on ${\mathrm{CO}}_{2}$. Employing the coincidence momentum imaging technique, we have obtained the correlated momenta of the three fragments, ${\mathrm{O}}^{+}+{\mathrm{C}}^{+}+{\mathrm{O}}^{+}$, and thence the kinetic energy release (KER) distribution. By examining the Dalitz plots for the three-body breakup, we separate the sequential and concerted breakup events and analyze the corresponding KER distributions. Based on the potential energy curves reported in the literature, we identify the possible transient states of ${\mathrm{CO}}_{2}^{3+}$ that lead to the different features in the KER distribution. We find that under ${\mathrm{H}}^{+}$ impact, the KER distribution shows a low-energy feature, which is seen in the case of electron impact, but not under the impact of slow or fast highly charged ions. This feature is identified as arising via the low-lying ${}^{2}\mathrm{\ensuremath{\Pi}}$ and ${}^{4}\mathrm{\ensuremath{\Pi}}$ states of the transient molecular ion. We further note that slow protons, which are the simplest of projectiles, are able to excite the ${\mathrm{CO}}_{2}$ molecule to a broad range of triply ionized transient states, spanning those accessed by the impact of slow highly charged ions and also those accessed by electron impact, but with varying probabilities.

Differential cross sections for ionization of hydrogen-like atoms by proton and antiproton impact

Differential cross sections for ionization of hydrogen-like atoms by proton and antiproton impact

A Review, Tabulation, and Parameterization of M-Series X-Ray Production Cross Sections for Proton and Helium Ion Impact

In the present work, the experimental total and line resolved M-series x-ray production cross sections (XRPCSs) for different elements with Z = 59–92 for 0.05–39.34 MeV proton and 0.2–6.0 MeV He ion (3He/4He) impact reported by different research groups until December 2020 have been compiled in tabular form. A status of different physical parameters, namely, the ionization cross sections, x-ray emission rates, fluorescence yields, and Coster–Kronig and super Coster–Kronig yields, required to calculate the theoretical M-series XRPCSs have been reviewed. The tabulated experimental total M-series XRPCSs for different elements are found to exhibit universal scaling similar to that shown by the theoretical cross sections. These tabulated experimental cross sections for different elements have been parameterized in order to provide empirical cross sections for use in different applications.

Te L-shell X-ray production cross section induced by lower energy H+ and He2+ ions

The L-shell x-rays of Te have been measured for the impact of protons with energies from 100 to 300 keV, and He2+ ions in the energy range of 300–600 keV. The new experimental data of Te for individual L-subshell and total L x-ray production cross sections were extracted from the thick-target analysis of x-ray yields. This is significant for updating the existing database. The cross sections were also compared with theoretical calculations of BEA, PWBA, ECPSSR and ECUSAR along with various atomic parameter databases and including modification of multiple ionization. On the whole, The ECUSAR-MI predictions using Campbell’s atomic parameters present a best agreement to the experimental data.

Handling of beam spectra in training and application of proton RBE models

Published data from cell survival experiments are frequently used as training data for models of proton relative biological effectiveness (RBE). The publications rarely provide full information about the primary particle spectrum of the used beam, or its content of heavy secondary particles. The purpose of this paper is to assess to what extent heavy secondary particles may have been present in published cell survival experiments, and to investigate the impact of non-primary protons for RBE calculations in treatment planning. We used the Monte Carlo code Geant4 to calculate the occurrence of non-primary protons and heavier secondary particles for clinical protons beams in water for four incident energies in the [100, 250] MeV interval. We used the resulting spectra together with a conservative RBE parameterization and an RBE model to map both the rise of RBE at the beam entry surface due to heavy secondary particle buildup, and the difference in estimated RBE if non-primary protons are included or not in the beam quality metric. If included, non-primary protons cause a difference of 2% of the RBE in the plateau region of an spread out Bragg peak and 1% in the Bragg peak. Including non-primary protons specifically for RBE calculations will consequently have a negligible impact and can be ignored. A buildup distance in water of one millimeter was sufficient to reach an equilibrium state of RBE for the four incident energies selected. For the investigated experimental data, 83 out of the 86 data points were found to have been determined with at least that amount of buildup material. Hence, RBE model training data should be interpreted to include the contribution of heavy secondaries.

Ionization of H(2p) atom by 30 keV proton and antiproton impact

Ionization process of the hydrogen atom, being initially in the excited 2p-state, projected by 30 keV proton and antiproton impact has been investigated. The second-Born approximation (SBA) is used to measure the triple differential cross sections (TDCSs). The closure relation is employed on the second-Born term to come over consideration of the intermediate states. The triple differential cross-sections are represented graphically against the ejection angle, for two scattering angles and ejected energies into both scattering and perpendicular geometric planes. The single differential cross-section (SDCS) is calculated in the framework of the first-Born approximation.

Collision dynamics of cytosine under proton irradiation

In the framework of the time-dependent density-functional theory, applied to valence electrons, coupled non-adiabatically to molecular dynamics of ions, the collision dynamics of cytosine impacted by proton is studied. We especially focus on the effect of the collision orientations on the damage of cytosine by choosing two collision orientations taking the oxygen atom on the double bond CO as the collision site with the incident energy of proton ranging from 150 eV to 1000 eV. First, two collision dynamical processes are explored by analyzing the molecular ionization, the ionic position and the kinetic energy, the energy loss of proton and the electronic density evolution. The results show that the damage process of cytosine induced by proton impact is mainly the capture of electrons by proton, the departments of ions and groups as well as the opening of ring. It is found that the orientation has little effect on the loss of the kinetic energy of proton, which is about 21.5[Formula: see text] of the incident energy of proton. Although the scattering angle [Formula: see text] has a polynomial relationship with [Formula: see text] in both cases, it is greatly affected by the orientation. When [Formula: see text] eV, the scattering angle of proton colliding with O along the [Formula: see text]-axis is greater than that of proton colliding with O along the [Formula: see text]-axis. The orientation also has a great effect on the mass distribution of the fragments and the fragmentation route. When proton moves along the [Formula: see text]-axis, the fragmentation route is that O leaves the cytosine and the rest keeps on vibration, while products are not only related to the incident kinetic energy, but also show diversity when proton moves along the [Formula: see text]-axis.

Double differential cross section for the single ionization of methane molecule by swift proton projectile

In the present work, single ionization of the methane molecule is studied. The double differential cross section for the ejected electron is considered. The target is ionized by the effect of perturbation created by proton impact with high incident velocity. In our theoretical formalism, the one Coulomb wave model is employed in the framework of the first Born approximation, which means that the final state is considered as a product of a plane wave function for the scattered heavy particle and a Coulomb wave function for the ejected electron. The initial state is a product of a plane wave function for the fast incident charge and wave functions centered over the heavy nuclei to describe the active electron. In our formalism, the one Coulomb wave model is corrected by Salin factor to take into account the effect of the electron transfer to the continuum. The obtained results are compared to the available experimental data.

Fully differential cross sections for single ionization of helium by proton impact

Fully differential cross sections for single ionization of helium by proton impact

Ionization of Hydrogen-Like Atoms by Proton Impact

Direct ionization processes of hydrogen-like atoms by proton impact are investigated by Born theory. The triple differential cross sections (TDCSs) and the quantities of physical interest in the process are calculated for ionization of H, He+, Li2+, and Be3+ ground-state atoms, using the first- and second-Born approximations. The closure relation is employed to come over the consideration of the intermediate states. The calculations are carried for fixed scattering angles and ejected electron energies at the impact energies 75, 200, and 500 keV. The influence of each of the incidence energy and the atomic number of the target atom on the TDCSs is studied. The contribution of the second-Born term to the cross section is illustrated.

Using a post-version continuum distorted wave formalism for calculation of the fully differential cross section of helium atom single ionization by proton impact

In the present work, the fully differential cross section of single ionization of helium atom is calculated by fast proton impact. The calculations are done as a four-body formalism and by using a post-version continuum distorted wave theory with considering symmetric wave functions in the both initial and final channels. The ionization is considered from the ground and $$2^{1}S$$ excited states of helium atom. In order to investigate the role of the static electronic correlations, the calculations are performed by single-parameter Hylleraas and two-parameter Silverman as the ground state of helium atom wave functions. The results of the present theory are compared with the experiment in 1MeV proton impact energy and various values of the ejected electron energy and momentum transfer in the scattering and azimuthal planes. The results show that the present theory is able to predict the binary and recoil peaks as well as the experiment for ejected electron energies and momentum transfers are discussed in this manuscript.