Electron Loss Cross Sections Research Articles

Calculations of positron scattering from F, F2, HF, and various fluorocarbons

Abstract Single center convergent close-coupling (CCC) calculations have been completed for positron scattering from atomic fluorine. Total, electron-loss, positronium-formation, direct ionization, momentum transfer, elastic, bound-state excitation, and stopping power cross sections have been determined for energies between threshold and 5000 eV. Past calculations for this scattering system exist only for elastic and momentum-transfer cross sections. For high energies, good agreement is found between current and past results. At low energies, however, large differences are found between the current calculations and previous results. The atomic fluorine results are then used in a modified independent atom approach to calculate cross sections for positron scattering on F2, HF, CF4, C2F6, C3F6, C3F8, and C6F6. The current molecular results are typically higher than previous positron experiments across the calculated energy range, however, these experiments were not corrected for the forward angle scattering effect and likely underestimate the true result. Good agreement is found between the current positron results and previous electron experiments and calculations at high energies.

Experimental cross sections for electron loss from 0.1 to 1.0 MeV O+ and 0.2-1.5 MeV O2+ and electron capture to 0.05-1.0 MeV O+ and 0.1-1.5 O2+ in SF6

Experimentally determined single and double-electron-capture and single and double projectile stripping cross sections are presented for intermediate and low projectile energies (0.1 – 1.5 MeV) Oq+ (q = 1,2) on SF6 gaseous target. These cross-section data are useful for the simulation of ion–neutral processes in Earth's atmosphere and to improve existing theoretical models.

Prediction of charge-changing cross sections of low-charged 88Sr, 138Ba and 142Nd ions in a He-gas target at collision energies 50 eV/u–10 GeV/u

Electron-loss (EL) and electron-capture (EC) cross sections of neutral and low-charged heavy Srq+, Baq+ and Ndq+ ions with charges q = 0, 1 and 2 in collisions with He atoms are predicted in the energy range E = 50 eV/u–10 GeV/u. Experimental data on EL and EC cross sections of these particles colliding with He atoms are practically absent. At relatively low energies E = 8–30 keV, EL cross sections σ12 of Sr1+, Ba1+ and Nd1+ ions are predicted from new experimental equilibrium charge-state fractions F1 and F2 and calculated EC cross sections. Predicted value for Ba1+ ions, σ12=6.8⋅10−18cm2, is in a good agreement with the one available experimental point σ12exp=5.7⋅10−18cm2 at E = 20 keV (Fedorenko, 1954). Calculations of EL and EC cross sections are performed by available computer codes shortly described in the paper. Theoretically estimated neutral-atom fractions F0 are found much smaller than the measured F1, F2, and F3 charge-state fractions.

Comparing different charge-state models with experimental data of ion beams penetrating fully and partially ionized plasmas

In the present work, we have conducted a study to investigate the validity of three different charge-state models of ion beams penetrating plasma targets through a comparison with a total of five experiments from the literature. We have applied two alternative theoretical approaches. On the one hand, we have used a further extension of our cross-sectional model (CSM) code based on projectile electron loss and capture cross sections (rate equations) that was developed previously [Morales et al., Phys. Plasmas 24, 042703 (2017); R. Morales, Ph.D. thesis (Universidad de Castilla-La Mancha, 2019)]. On the other hand, we also used two charge-state models based on a semi-empirical formalism adapted to the plasma case: the Kreussler model [Kreussler et al., Phys. Rev. B 23, 82 (1981)] and the Gus'kov model [Guskov et al., Plasma Phys. Rep. 35, 709 (2009)]. Specifically, we present the predictions and the interpretation of the charge state of light to heavier ions at high, intermediate, and low velocities in Z-pinch and laser-produced partially and fully ionized plasmas. We are showing that experimental data support our new CSM code based on the cross-sectional formalism. In contrast, the framework based on semi-empirical formulas is less accurate for a precise charge-state prediction, but it can be applied for a reasonable stopping power calculation. Overall, results denote that the Gus'kov model is better suited to stopping power calculations at low projectile velocities and the Kreussler model fits better the energy loss data at intermediate velocities. Additionally, we propose a simple non-equilibrium charge model, derived from the semi-empirical framework, as a function of the ion path and equilibrium charge state.

Projectile electron loss, excitation and de-excitation cross section database in a collision between two hydrogen atoms in the impact energy range between 50 keV–5.0 MeV, Part I: Target is in ground state

We present projectile electron loss, excitation, and de-excitation cross-sections database for H(nl)+H(1s) collision system. A four-body classical trajectory Monte Carlo (CTMC) and a quasi-classical trajectory Monte Carlo (QCTMC) methods were employed in the projectile energy range between 50 keV to 5.0 MeV.

Empirical relations for heavy-ion equilibrated charges and charge-changing cross sections in diluted $$\hbox {H}_{{2}}$$ with application

Highly ionized heavy evaporation residues (ERs) resulting from heavy-ion (HI) fusion–evaporation reactions are knocked out from solid targets to rarefied gas of gas-filled recoil separators. In gas, these ERs undergo charge-changing collisions on their way to a detection system. An equilibrium between the loss of charge (electron capture) and the gain of charge (electron loss) for ionized ERs allows one to use equilibrated charge-state distributions in trajectory calculations for ERs moving through a magnetic field. The distance from a target to the point where the ER charge-state distributions become to be the equilibrated one is essential for such calculations. This distance can be estimated in simulations based on electron capture and loss cross sections for energetic HIs. Reasonable approximations of available experimental data have provided these cross sections, which were applied to the Monte Carlo simulations of the ionic charge evolution for highly ionized heavy ERs. The results of these simulations demonstrate the setting of charge equilibration close to the target.

Absolute cross sections for electron capture and loss of O+ in water molecule

SynopsisAbsolute cross sections for single and double electron loss and single and double electron capture for O+ projectiles colliding with water vapor have been measured. In addition, we have performed many-body clas-sical trajectory Monte Carlo calculations, where the O+ projectile was either one or more particle, depending on the model used. The water target is modeled as two virtual particles. The calculated cross sections are in agree-ment with the experimental data.

Dynamics of Charge States of Relativistic Gold Ion Beams Passing through Cu and Au Foils in the NICA Project

In order to study the properties of dense baryonic matter, an accelerator complex is under development at the Joint Institute for Nuclear Research (Dubna, Russia) within the new NICA project. The NICA project assumes the use of accelerated ion beams ranging from protons to gold ions with relativistic energies up to 4.5 GeV/nucleon. To design experiments, it is necessary to have information on the efficiency of the yield of bare gold nuclei formed at the passage of a gold ion beam with energies of about several hundreds of MeV per nucleon through a foil of a specialized stripping station at the output of the booster of the accelerator. In this work, the optimal conditions (material and thickness of the foil and the energy of the ion) for the formation of fractions of bare gold nuclei with a probability of 80–90% have been determined by calculating electron loss and capture cross sections, as well as the dynamics of charge states of gold ions colliding with copper and gold foils at energies of 400 and 600 MeV/nucleon,

Formation of the charge distribution of fast multicharged ions passing through a carbon target

The equilibrium and nonequilibrium charge distributions of ions with nuclear charges from 10 to 18 are analyzed by evaluating ion charge-exchange cross sections with the density effect taken into account. It is shown that the increase in the cross section for electron loss and the decrease in the cross section for electron capture by ions in a solid target (carbon) compared with gases is maximum in the region of 0.1–0.2MeV/nucleon. It is also shown that, in the case of a solid target, the energy by ion cross section for electron loss by an ion becomes maximum decreases, which is explained by a decrease in the binding energy of the active electron in the ion because of the presence of excited states. This leads to an increase in the average equilibrium ion charge in solid targets compared with the value in gases. The results of calculations agree with the experimental data in the entire considered energy region. The proposed method for calculating the ion charge-exchange cross sections in solid targets also makes it possible to qualitatively describe the dependence of the average ion charge on the target thickness and calculate the thickness (required to determine the equilibrium charge distribution) for different energies and charges of the ion nucleus.

Disordering of ultra thin WO3 films by high-energy ions

We have studied disordering or atomic structure modification of ultra thin WO3 films under impact of high-energy ions with non-equilibrium and equilibrium charge incidence, by means of X-ray diffraction (XRD). WO3 films were prepared by thermal oxidation of W deposited on MgO substrate. Film thickness obtained by Rutherford backscattering spectrometry (RBS) is as low as 2nm. Smoothness of film surface was observed by atomic force microscopy. It is found that the ratio of XRD intensity degradation per 90MeV Ni+10 ion (the incident charge is lower than the equilibrium charge) to that per 90MeV Ni ion with the equilibrium charge depends on the film thickness. Also, film thickness dependence is observed for 100MeV Xe+14. By comparison of the experimental result with a simple model calculation based on the assumption that the mean charge of ions along the depth follows a saturation curve with power-law approximation to the charge dependent electronic stopping power, the characteristic length attaining the equilibrium charge is obtained to be ∼7nm for 90MeV Ni+10 ion incidence or the electron loss cross section of ∼1016cm2, demonstrating that disordering of ultra WO3 films has been observed and a fundamental quantity can be derived through material modification.

H+−H2Ocollisions studied by time-dependent density-functional theory combined with the molecular dynamics method

${\mathrm{H}}^{+}\ensuremath{-}{\mathrm{H}}_{2}\mathrm{O}$ collisions are investigated using the time-dependent density-functional theory combined with the molecular dynamics method, in which the electrons are described quantum mechanically within the framework of time-dependent density-functional theory and the ionic cores are described classically by Newton's equations. The feedback between quantum electrons and classical ions is self-consistently coupled by Ehrenfest's method. The electron capture, electron loss, and ionization cross sections are obtained in the energy range of 1--1000 keV and excellent agreements are achieved with available experimental and theoretical data. The orientation effects of the ${\mathrm{H}}_{2}\mathrm{O}$ target are found to be significant in the collision processes, especially in low-energy collisions.

Multiple-electron losses in uranium ion beams in heavy ion synchrotrons

Charge changing processes as the result of collisions with residual gas particles are the main cause of beam loss in high energy medium charge state heavy ion beams. To investigate the magnitude of this effect for heavy ion synchrotrons like the planned SIS100 at GSI, the multiple-electron and the total electron-loss cross sections are calculated for Uq+ ions, q=10, 28, 40, 73, colliding with typical gas components H2, He, C, N2, O2, and Ar at ion energies E=1MeV/u–10GeV/u. The total electron-capture cross sections for U28+ and U73+ ions interacting with these gases are also calculated. Most of these cross sections are new and presented for the first time. Calculated charge-changing cross sections are used to determine the ion-beam lifetimes τ for U28+ ions which agree well with the recently measured values at SIS18/GSI in the energy range E=10–200MeV/u.Using simulations made by the StrahlSim code with the reference ion U28+, it is found that in SIS100 the beam loss caused by single and multiple electron losses has only little impact on the residual gas density due to the high efficiency of the ion catcher system.

Accurate solution of the proton–hydrogen three-body scattering problem

An accurate solution to the fundamental three-body problem of proton–hydrogen scattering including direct scattering and ionization, electron capture and electron capture into the continuum (ECC) is presented. The problem has been addressed using a quantum-mechanical two-center convergent close-coupling approach. At each energy the internal consistency of the solution is demonstrated with the help of single-center calculations, with both approaches converging independently to the same electron-loss cross section. This is the sum of the electron capture, ECC and direct ionization cross sections, which are only obtainable separately in the solution of the problem using the two-center expansion. Agreement with experiment for the electron-capture cross section is excellent. However, for the ionization cross sections some discrepancy exists. Given the demonstrated internal consistency we remain confident in the provided theoretical solution.

Total projectile electron loss cross sections ofU28+ions in collisions with gaseous targets ranging from hydrogen to krypton

Beam lifetimes of stored ${\mathrm{U}}^{28+}$ ions with kinetic energies of 30 and $50\text{ }\mathrm{MeV}/\mathrm{u}$, respectively, were measured in the experimental storage ring of the GSI accelerator facility. By using the internal gas target station of the experimental storage ring, it was possible to obtain total projectile electron loss cross sections for collisions with several gaseous targets ranging from hydrogen to krypton from the beam lifetime data. The resulting experimental cross sections are compared to predictions by two theoretical approaches, namely the CTMC method and a combination of the DEPOSIT code and the RICODE program.

Estimation of the average charges of light ions during their penetration through thin carbon films

The equilibrium and nonequilibrium average charges of boron, carbon, and nitrogen ions are calculated as functions of the carbon-target thickness in a broad projectile energy range of 0.01 to 10 MeV/nucleon. The calculations are based on a method for determining the electron loss and capture cross sections in solids. The equilibrium target thickness is estimated for different energies of projectile ions.

Measurement of 181 MeV H− ions stripping cross-sections by carbon stripper foil

The stripping cross-sections of 181MeV H− (negative hydrogen) ions by the carbon stripper foil are measured with good accuracy. The present experiment was carried out at the 3-GeV RCS (Rapid Cycling Synchrotron) of J-PARC (Japan Proton Accelerator Research Complex). The stripping cross-sections for different charge states, also known as electron loss cross-sections of H− ion, are denoted as σ−11, σ−10 and σ01, for both electrons stripping (H−→H+), one-electron stripping (H−→H0) and the 2nd-electron stripping (H0→H+) proceeding σ−10, respectively. We have established very unique and precise techniques for such measurements so as also to determine a foil stripping efficiency very accurately. The cross-sections σ−11, σ−10 and σ01 are obtained to be (0.002±0.001)×10−18cm2, (1.580±0.034)×10−18cm2 and (0.648±0.014)×10−18cm2, respectively. The presently given cross-sections are newly available experimental results for an incident H− energy below 200MeV and they are also shown to be consistent with recently proposed energy (1/β2) scaled cross-sections calculated from the previously measured data at 200 and 800MeV. The present results have a great importance not only at J-PARC for the upgraded H− beam energy of 400MeV but also for many new and upgrading similar accelerators, where H− beam energies in most cases are considered to be lower than 200MeV.

Cross sections for electron capture and loss by H+ and H impact on O and O2

AbstractProjectile‐charge‐changing cross sections for electron capture by H+ and H collisions with O atoms and electron loss by H collisions with O atoms have been determined. The H+ and H energies ranged from 2.0 down to 0.125 keV. The cross‐beam technique involved measuring the cross‐section ratios for reactions with O‐atom targets to those for O2 targets. The O‐atom‐target cross sections were then obtained by normalizing these ratios to previously measured O2‐target cross sections. The experimental apparatus employed is described, and the measured results are compared with other available data.

Influence of relativistic effects on electron-loss cross sections of heavy and superheavy ions colliding with neutral atoms

The influence of relativistic effects, such as relativistic interaction and relativistic wave functions, on the electron-loss cross sections of heavy and superheavy atoms and ions (atomic number Z ≳ 92) colliding with neutral atoms is investigated using a newly created RICODE-M computer program. It is found that the use of relativistic wave functions changes the electron-loss cross section values by about 20–30% around the cross-section maximum compared to those calculated with nonrelativistic wave functions. At relativistic energies E ≥ 200 MeV/u, the relativistic interaction between colliding particles leads to a quasiconstant behavior of the loss cross sections σELrel ∼ const, to be compared with the Born asymptotic law σELB ∼ lnE/E.

The DEPOSIT computer code based on the low rank approximations

We present a new version of the DEPOSIT computer code based on the low rank approximations. This approach is based on the two dimensional cross decomposition of matrices and separated representations of analytical functions. The cross algorithm is available in the distributed package and can be used independently. All integration routines related to the computation of the deposited energy T(b) are implemented in a new way (low rank separated representation format on homogeneous meshes). By using this approach a bug in integration routines of previous version of the code was found and fixed in the current version. The total computational time was significantly accelerated and is about several minutes. New version program summaryProgram title: DEPOSIT 2014Catalogue identifier: AENP_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENP_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 182103No. of bytes in distributed program, including test data, etc.: 1163484Distribution format: tar.gzProgramming language: C++, Fortran.Computer: Any computer that can run C++ and Fortran compilers.Operating system: Any operating system with installed compilers mentioned above. Tested on Mac OS X 10.9 and Ubuntu 12.04.Has the code been vectorized or parallelized?: Due to the fast computation in the current implementation only a single-threaded version has been developed.Classification: 2.6, 4.10, 4.11, 19.1.External routines: BLAS, LAPACK and ALGLIB. The last one is included in the distribution.Catalogue identifier of previous version: AENP_v1_0Journal reference of previous version: Comput. Phys. Comm. 184(2013) 432Does the new version supersede the previous version?: YesNature of problem:For a given impact parameter b to calculate the deposited energy T(b) as a 3D integral over a coordinate space, and ionization probabilities Pm(b). For a given energy of the projectile to calculate the total and m-fold electron-loss cross sections using T(b) values on the whole b-mesh.Solution method:Calculation of the 3D-integral T(b) in all points of the b-mesh based on the low rank separated representations of matrices and tensors. For details, please see Ref. [1]Reasons for new version:The computation of the deposited energy T(b) integral is the slowest part of the program and should be done as fast as possible. To accelerate the program a new approach based on the low rank approximations was applied. It made computational scheme more stable and decreased the computational time by a factor of ∼103. By means of this approach a bug in the integration routines was found and fixed for a special case of the energy gain.Summary of revisions:A two dimensional cross decomposition algorithm was developed as an independent module and was integrated with the energy gain ΔE. For the Slater density ρ(r) a separated representation via a sum of Gaussians was implemented. The calculation of three dimensional integrals T(b) was totally rewritten by using quadrature schemes based on the cross decomposition for energy gain and separated representations for Slater density. Details are reported in Ref. [1].Running time:For a given energy the total and m-fold cross sections are calculated within about several minutes on a single-core.

Absolute cross sections for electron loss, electron capture, and multiple ionization in collisions of Li2+ with argon

Exclusive absolute cross sections for the electron loss and capture processes, accompanied by target multiple ionization and pure target multiple ionization, as well as total electron loss and capture cross sections, in collisions of Li2+ with Ar have been measured in the 0.5–3.5 MeV energy range. The experimental data of the total electron loss cross section are compared with theoretical results based on the plane-wave Born approximation and the free-collision model, and with the available experimental data. Some discrepancies are observed when comparing the experimental data with the theoretical models, which can be attributed to the competitive mechanisms that lead to electron loss. The dependences of the single-capture and transfer-ionization processes on the projectile charge state are similar to those observed for collisions between other low-charged light ions and noble-gas targets. The same behaviour is observed when one compares the present data for the single- and double-ionization cross sections with those for He2+ projectiles on Ar. These facts indicate that the dynamics of the collision does not seem to depend on the projectile species, so that few-electron projectiles may act as structureless point charges in the intermediate- to high-velocity regime.