Total Electron-loss Cross Sections Research Articles

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.

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.

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.

Multiple-electron losses of highly charged ions colliding with neutral atoms

We present calculations of the total and m-fold electron-loss cross sections using the DEPOSIT code for highly charged Uq+ ions (q = 10,31,33) colliding with Ne and Ar targets at projectile energies E = 1.4 and 3.5 MeV u−1. Typical examples of the deposited energy T(b) and m-fold ionization probabilities Pm(b) used for the cross-section calculations as a function of the impact parameter b are given. Calculated m-fold electron-loss cross sections are in good agreement with available experimental data. Although the projectile charge is rather high, the contribution of multiple-electron-loss cross sections to the total electron-loss cross sections is high: about 65% for the cases mentioned.

Free-collision model calculations for projectile electron loss by the H2 molecule

An extended version of the free-collision model was employed for the calculation of the electron-loss cross sections of projectiles carrying one to five electrons in collisions with the H2 molecule in the low- to intermediate-velocity regime (0.2–12 au). The model presented by Sigaud (2008 J. Phys. B: At. Mol. Opt. Phys. 41 015205) has been modified in order to calculate total electron-loss cross sections of projectiles with two or more electrons in the same subshell. The electron–electron contribution to the projectile electron loss was included within the independent particle model. The comparison of the calculated cross sections with the available experimental data shows very good agreement in almost all cases.

Theoretical interpretation of equilibrium charge-state distributions of 4He ions backscattered from metallic foils using extended Bohr theory

Equilibrium charge-state distributions (ECSD’s) for He0, He+, and He++ backscattered by the foils made of silver have been measured using a post-acceleration system, and simulated by the extended Bohr theory. The kinematics behavior of the backscattered ions is understood from Rutherford backscattering spectrometry (RBS). The results from these measurements have been integrated with the data available in the literature to cover a wide energy range of the incident singly charged helium ion He+. The detected charge states increase from 0 to +Z with the incident ion energy. A formula for calculating He0 distribution, for the studied energy range, has been proposed. The ratio of singly to doubly ionized helium ions backscattered from thin Ag-foils, F(He\(^+)\)/F(He\(^{++})\), has been measured as a function of incident ion velocity. The use of a semi-classical approach, based on the theory of Bohr, allows a satisfactory theoretical description of F(He\(^+)\)/F(He\(^{++})\) ratios. It has been found that the measured and simulated ratios are strongly decreased with the incident velocity. The present study has demonstrated that the satisfactory fits of ECSD’s and the ratio of the fractions are mainly accounted to the contribution of both free valance electrons of the target and screened target nucleus in the calculation of total electron loss cross section.

Theoretical Interpretation of Atomic Charge Exchange between Singly Charged Helium Ions and Aluminum Foils

An experimental method for determining the equilibrium charge state of fast helium ions backscattered by solid Al-foils has been conducted using single Silicon Surface Barrier Detector (SBD) in a post acceleration system (PAS). The charge state measurements have been conducted to cover a wide energy range of the incident singly charged helium ion He+. The detected charge states increases from 0 to +Z with the incident ion's velocity. The method consists of measuring the charge states of ions after backscattering from the Al-foil as a function of projectile velocity and also finding the charge state distributions as a function of Al-foil thickness. The measurements are conducted for two types of Al-foil, one of which is thinner (2.5, 4.0, 5.4 ?g/cm2) and the other of which is of the order of an equilibrium foil thickness, where thicknesses of 6.8, 8.1, 9.5, and 10.8 were used. Ratios of equilibrium charge state yields for singly to doubly ionized He ions; He+1 and He+2, were also measured. The kinematics behavior of the measured He0, He+ and He+2 fractions is understood by the well-known Rutherford Backscattering Spectrometry technique (RBS). It has been shown that the dominant processes occurring to a fast He+ ions traversing Al-foil are the capture of the electron from the Al-atom to vacant state in the ion and the stripping of the bound electron from the He+ ion. The charge composition of the ion beams changes when it backscatters Al-foil, which thick enough for multiple atomic collisions, leading eventually to an equilibrium charge state distribution (ECSD). It was found that the theoretical calculations for electron-capture and loss ratios, based of semi-classical approach of Bianconi, are successful in describing the measured He ions. The satisfactory fits of the measured equilibrium charge state fractions (ECSF's) are mainly accounted to the contribution of both free valance electrons of the target and screened target nucleus in the calculation of total electron-loss cross sections. Bianconi approach is also applied to describe the measured mean equilibrium charges (MEC). The agreement between experiment and theory in this investigation is accounted to the reliability of the used post-acceleration system where all the backscattering charge-states, at certain incident ion's velocity, are separated and collected in one measurement.

Single- and multiple-electron loss cross-sections for fast heavy ions colliding with neutrals: Semi-classical calculations

Extensive calculations of single, multiple and total electron-loss cross-sections of fast heavy ions in collisions with neutral atoms are performed in the semi-classical approximation using the DEPOSIT code based on the energy deposition model and statistical distributions for ionization probabilities. The results are presented for Ar 1+, Ar 2+, Kr 7+, Xe 3+, Xe 18+, Pb 25+ and U q+ ( q = 10, 28, 39, 62) ions colliding with H, N, Ne, Ar, Kr, Xe and U atoms at energies E > 1 MeV/u and compared with available experimental data and the n-particle classical-trajectory Monte Carlo ( nCTMC) calculations. The results show that the present semi-classical model can be applied for estimation of multiple and total electron-loss cross-sections within accuracies of a factor of 2. From calculated data for the total electron-loss cross-sections σ tot , their dependencies on relative velocity v, the first ionization potential I 1 of the projectile and the target atomic number Z A are found and a semi-empirical formula for σ tot is suggested. The velocity range, where the semi-classical approximation can be used, is discussed.

Electron loss of fast many-electron ions colliding with neutral atoms: possible scaling rules for the total cross sections

General features of the total electron-loss (projectile ionization) cross sections, σtot, for fast many-electron ions colliding with neutral atoms are investigated. Two independent scaling laws for σtot are obtained: one follows from the experimental data and another one from the classical calculations based on the n-particle classical trajectory Monte Carlo (nCTMC) and semi-classical treatments. The semi-classical method has recently been developed based upon the energy deposition model and the statistical ionization probabilities. Both scaling relations are expressed in terms of the projectile velocity v, its first ionization potential I1 and the nuclear charge ZA of the target atom. The accuracy of the scaling relations suggested is a factor of 2–3. At the high-velocity region (v2 ≫ I1), experimental data are found to decrease approximately as σtot ∼ v−2, i.e., close to the Born ionization cross section. At low energies, the σtot values are better described by the classical approximation which accounts for multi-electron-loss processes. These scaling laws obtained are compared with a known scaling law for the Ar target and are used for the prediction of the total electron-loss cross sections in a wide range of the collision parameters. The predicted cross sections σtot can be approximately evaluated as a minimum cross section obtained from two scaling formulae.

Charge transfer and ionisation by intermediate-energy heavy ions

The use of heavy ion beams for microbeam studies of mammalian cell response leads to a need to better understand interaction cross sections for collisions of heavy ions with tissue constituents. For ion energies of a few MeV u(-1) or less, ions capture electrons from the media in which they travel and undergo subsequent interactions as partially 'dressed' ions. For example, 16 MeV fluorine ions have an equilibrium charge of 7(+), 32 MeV sulphur ions have an equilibrium charge of approximately 11(+), and as the ion energies decrease the equilibrium charge decreases dramatically. Data for interactions of partially dressed ions are extremely rare, making it difficult to estimate microscopic patterns of energy deposition leading to damage to cellular components. Such estimates, normally obtained by Monte Carlo track structure simulations, require a comprehensive database of differential and total ionisation cross sections as well as charge transfer cross sections. To provide information for track simulation, measurement of total ionisation cross sections have been initiated at East Carolina University using the recoil ion time-of-flight method that also yields cross sections for multiple ionisation processes and charge transfer cross sections; multiple ionisation is prevalent for heavy ion interactions. In addition, measurements of differential ionisation cross sections needed for Monte Carlo simulation of detailed event-by-event particle tracks are under way. Differential, total and multiple ionisation cross sections and electron capture and loss cross sections measured for C(+) ions with energies of 100 and 200 keV u(-1) are described.

Formation of O 2+ in collisions between O + ions and N 2 molecules

We report measurements of the total and absolute differential electron loss cross sections of 2.0–5.0 keV O + ions in collisions by N 2 target at scattering angles between − 3.2 ° ≤ Θ ≤ 3.2 ° in the laboratory frame. The behavior of the absolute differential cross sections display an expected decreasing behavior with increasing angle. The measured total electron loss cross section show a monotonically increasing behavior as a function of the incident kinetic energy and found to be within the order of magnitude between 1 0 − 19 and 1 0 − 21 cm 2.

Static over-the-barrier model for electron transfer between metallic spherical objects

We present a static classical over-the-barrier model (OBM) for electron transfer between two isolated, infinitely conducting spheres with arbitrary and different electrical charges. This model is shown to be very useful for first estimates of single- and multiple-electron transfer cross sections in cluster-cluster collisions when the collision velocities are significantly lower than the typical target electron velocities. For faster collisions, more advanced models such as the dynamical OBM, or the time-dependent local density approximation (TDLDA) or the solutions of their semiclassical counterparts---the Vlasov equations have to be used. The latter two methods clearly provide the most detailed information on the electronic response, but they are also computationally very demanding and have, so far, only been used for collisions involving one cluster (and an atomic ion). We compare our static OBM results (in the limit in which one of the sphere radii approaches zero) with TDLDA and Vlasov calculations of cluster charging in ${\mathrm{Ar}}^{8+}\ensuremath{-}{\mathrm{Na}}_{40}$ collisions at different velocities to demonstrate that the present static OBM is valid at sufficiently low velocities. The static OBM is then used in a comparison with experimental target charge state distributions in ${\mathrm{C}}_{60}^{q+}\ensuremath{-}{\mathrm{C}}_{60}$ and ${\mathrm{C}}^{q+}\ensuremath{-}{\mathrm{C}}_{60}$ collisions at $0.01\sqrt{q}$ and $0.06\sqrt{q}{v}_{0},$ respectively. Calculated electronic excitation of the projectile after two-electron transfer in ${\mathrm{C}}_{60}^{4+}\ensuremath{-}{\mathrm{C}}_{60}$ collisions readily explains the recently observed suppression of the transfer ionization channel in this reaction. Finally, we model the total projectile electron loss and dissociation cross section in highly protonated Lysozyme-oxygen $(\mathrm{Lys}\ensuremath{-}{\mathrm{H}}_{9}^{9+}\ensuremath{-}{\mathrm{O}}_{2})$ collisions and make comparisons with recent experimental results at $0.01{v}_{0}.$

Total electron loss, charge transfer, and ionization in proton-hydrogen collisions at 10–100 keV

A three-dimensional lattice solution of the time-dependent Schr{umlt o}dinger equation for low quantum states (n{le}3) is combined with classical trajectory Monte Carlo results for high quantum states (n{ge}4) to predict total electron loss and total charge-transfer cross sections for proton collisions with atomic hydrogen at intermediate energies. The total charge-transfer cross sections range from 5{percent} above to 10{percent} below the furnace target measurements of McClure [Phys. Rev. {bold 148}, 47 (1966)], while the total electron-loss cross sections range from 5{percent} to 15{percent} above the pulsed crossed-beams measurements of Shah, Elliot, and Gilbody [J. Phys. B {bold 20}, 3501 (1987)]. The calculation of ionization as a difference between electron loss and charge transfer leads to theoretical ionization cross sections that are 10{percent} to 35{percent} larger than the crossed-beams measurements of Shah and Gilbody [J. Phys. B {bold 14}, 2361 (1981)] and Shah, Elliott, and Gilbody [J. Phys. B {bold 20}, 2481 (1987)]. {copyright} {ital 1999} {ital The American Physical Society}

Saturation Effects in Charge-changing Collisions with Multiply-charged C and O Ions

The electron loss of multiply-charged dressed ions by heavy neutral atoms can have a significant contribution from collisions with small impact parameters. This can render one of the two competing mechanisms which govern the electron loss, i.e. the screening, highly non-perturbative. The other mechanism (antiscreening) is due to electron-electron interactions and its contribution can be treated perturbatively. The dependence of the total electron loss cross sections on the target atomic number, Z2, presents a strong saturation as the value of Z2 increases. Calculations based on the Plane Wave Born Approximation present such a behavior for the antiscreening but not for the screening, since this saturation is related to a non-perturbative regime. In this work we compare data for the total electron loss cross sections of C3+ and O5+ ions by H, He, Ne, Ar, Kr and Xe targets, with energies ranging from 1.0 to 3.5 MeV, with calculations for the screening contribution based on the free-collision model. This comparison shows that, for highly-charged ions, the electron capture and direct target ionization channels play a major role in the description of experimental electron loss data.

Saturation effects in projectile electron loss

The behavior of the projectile electron-loss cross sections with the target atomic number, Z 2, presents a saturation as the value of Z 2 increases. This fact, which had elready been observed for the excitation of highly charged projectiles, appears in the first-order calculations for the contribution of the projectile electron-target electron interaction but not for the projectile electron-target nucleus interaction. In this work, we compare total electron-loss cross sections with Electron Loss to the Continuum (ELC) yields, for 1.0 MeV He − projectile on various targets, with atomic numbers ranging from 2 to 54. Besides a similar saturation with Z 2 observed in both cases, some differences between the data appear, such as enhanced values of the total loss for all targets when compared to the ELC and a structure between the Ar and Xe targets also in the total loss data. These differences may be assigned to the contribution due to the interaction between the projectile active electron and the target electron cloud.

Extension of IMGO model to projectile velocities where electron-capture ∼ electron-loss cross sections

An intramolecular geometric outscattering (IMGO) model, developed to extract “atomic” total single electron capture σ 10 cross sections from σ 10 and σ 01 (electron loss) measurements on C-bearing molecules by including intramolecular secondary electron loss processes for projectiles with σ 10 ⋘ σ 01 , was extended to 100–2500 keV H + on C m H n data which reaches projectile velocities where σ 10 ∼ σ 01. Atomic C and H cross sections compare well with theoretical calculations over the entire energy range. Reasonable “atomic” σ 10 values for H, even when it contributed < 1% to the overall cross section, could be obtained from a sufficiently large set of C m H n data. An initial analysis of total electron loss cross sections is also presented.

Electron loss mechanisms in collisions of He + ions with various targets

The electron loss of high-velocity ions by neutral atoms is due to two different and competing mechanisms. In the screening mode, the electron loss is basically due to the nucleus-electron interaction, with the target electrons assuming the passive role of decreasing the Coulomb field of the target nucleus in the vicinity of the projectile active electron. For a fixed projectile velocity, this contribution is expected to give a non-linear dependence with the target atomic number Z 2 due to the incomplete screening at the impact parameter region where the projectile ionization is more likely to occur. Within first-order theories, if the screening is completely absent, the expected dependence would be Z 2 2; with screening, it should scale between Z 2 and Z 2 2. On the other hand, in the antiscreening mode, where the loss is due to the action of the target electrons and the target nucleus plays no active role, the expected dependence would be approximately linear with Z 2. Thus, for first-order theories, the expected overall dependence with Z 2 would be dominated by the screening mode as Z 2 increases. We have measured total electron-loss cross sections of He + ions impinging upon He, Ne, Ar, Kr and Xe targets in the energy range from 1.0 to 4.0 MeV to complement previous measurements and the results point towards a much smaller contribution from the screening mode than expected from first-order theories, possibly due to a saturation effect manifested only in the screening channel.

Electron-electron interaction in projectile electron loss.

In ion-atom collisions where the projectile is ionized, target electrons act not only coherently by screening the target nucleus but they may also act incoherently by directly ejecting a projectile electron. This electron-electron interaction should be relatively most important for targets that have a low nuclear charge, since the cross section for a neutral target is roughly proportional to ${\mathit{Z}}_{\mathit{t}}^{2}$+${\mathit{Z}}_{\mathit{t}}$, where ${\mathit{Z}}_{\mathit{t}}^{2}$ is the contribution due to the target nucleus and ${\mathit{Z}}_{\mathit{t}}$ comes from the target electrons. In order to investigate the electron-electron interaction, we have measured and calculated cross sections for ${\mathrm{Li}}^{2+}$, ${\mathrm{C}}^{5+}$, and ${\mathrm{O}}^{7+}$ on ${\mathrm{H}}_{2}$ and He, ${\mathrm{Au}}^{52+}$ on ${\mathrm{H}}_{2}$, He, C, and ${\mathrm{N}}_{2}$, ${\mathrm{Au}}^{75+}$ on ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$, ${\mathrm{U}}^{86+}$ on ${\mathrm{H}}_{2}$ and He, and ${\mathrm{U}}^{90+}$ on ${\mathrm{H}}_{2}$. The collision energies range from 0.75 to 405 MeV/nucleon. The calculations have been performed in the plane-wave Born approximation. We demonstrate that for energies where the target electrons have sufficient kinetic energy in the projectile frame to ionize the projectile, the electron-electron interaction can lead to a significant increase in the total electron-loss cross section.

Feq+ + H, H2 and He Electron Loss and He2+ + H(n = 1,2) Electron Capture Cross Sections: Processes of Interest in Fusion Plasmas

Cross sections have been calculated utilizing the classical trajectory Monte Carlo method for collisional processes of special interest to plasma fusion research. Specifically, H, H2 and He total electron loss cross sections for the impact by Feq+ (1 < q < 26) impurity ions, in the energy range of 50 to 500 keV/u, are presented. These results illustrate a clear departure for low charge states (q < 10) from scaling of the cross section with projectile charge (q). Further, cross sections for electron capture from both the ground and n = 2 states of H by 30 to 100 keV/u He2+ impact are tabulated as function of final n-level, yielding information for neutral beam heating models.

Experiments concerning electron capture and loss to the continuum and convoy electron production by highly ionized projectiles in the 0.7 - 8.5-MeV/u range transversing the rare gases, polycrystalline solids, and axial channels in gold

Velocity spectra of electrons emitted into the forward direction have been measured for 0.7--8.5-MeV/u projectile ions traversing He, Ne, and Ar targets, polycrystalline solids (C, Al, Ag, Au), and axial channels in gold. Spectral shapes and yields are compared and contrasted with one another and with theories which seek to account for the cusp-shaped peaks observed in terms of electron capture and loss to low-lying projectile-centered continuum states. We report the results of both singles and coincidence measurements, where the dependence of cusp shapes and yields on the emergent-ion charge state are examined. For electron capture to the continuum (ECC), variance is noted with respect to the simple, first-order theory of Dettmann, Harrison, and Lucas. The ECC yields are compared to experimental and theoretical studies of bound-state capture, especially to high Rydberg states. For electron loss to low-lying continuum states (ELC), variance is noted with respect to the corresponding theories of Briggs, Drepper, and Day, and ELC cross sections are compared to total electron-loss cross sections. For convoy electron production in solids, no known theory accounts for the results. As in ELC processes, convoy cusp widths are observed to be velocity independent. Convoy electron yields are also observed to bemore » independent of emergent-ion charge state.« less