Stopping Of Heavy Ions Research Articles

Limiting fragmentation in heavy-ion stopping?

Based on a nonequilibrium–statistical relativistic diffusion model that is consistent with quantum chromodynamics (QCD), we investigate baryon stopping in relativistic heavy-ion collisions at SPS, RHIC, and LHC energies. The net-proton rapidity distributions of the individual fragments exhibit a scaling behaviour similar to limiting fragmentation (LF) that is related to geometric scaling in the colour-glass condensate (CGC) and depends upon the gluon saturation scale. Forward-angle net-proton data at energies reached at the LHC are required to verify the prediction.

Bond-specific fragmentation of oligopeptides via electronic stopping of swift heavy ions in molecular films

Highly bond-specific fragmentation of oligopeptides induced by swift heavy ion (SHI) irradiation was investigated by means of mass spectrometry. In pronounced contrast to measurements of samples irradiated with keV ions, oligopeptides which were exposed to 946 MeV Au ions show a high abundance of specific fragments. The highly bond-specific nature of SHI-induced fragmentation is attributed to electronic stopping as the most relevant energy loss mechanism for SHI in the oligopeptide samples in combination with the subsequent coupling between the excited electronic and the atomic subsystem. Fragmentation induced by SHI is observed to be further influenced by the structure of the oligopeptides, suggesting that electronic excitation and/or the electronic-vibrational coupling depend on the details of the molecular structure.

The Bloch correction, key to heavy-ion stopping

The Bloch correction is known as the link between Bethe’s quantum theory of the stopping of charged particles in matter and Bohr’s classical theory. Less well-known and underestimated in the literature, is its role as the link between the energy loss of heavy vs light ions. At the same time, the role of another key parameter, the ion charge, has been unclear until a few years ago, not the least due to the almost universal use of the competing effective-charge concept. We show that proper account of the Bloch correction and the ion charge forms the key to a qualitative and quantitative description of the electronic energy loss of heavy ions. In the standard textbook versions, neither Bohr nor Bethe stopping provide a valid description below the Bragg maximum, since logarithmic dependencies on the velocity cause the stopping cross section to become negative. Although this obstacle can easily be repaired by more accurate evaluation of the underlying integrals, we found the Bloch correction to be more tightly connected with these logarithms than expected. This requires caution in practical applications.

Nuclear versus electronic energy loss in slow Ar ion scattering on a Cu (100) surface: Experiment and simulations

In the scattering and stopping of heavy ions on a few surface layers in solids, contributions of the electronic and nuclear energy losses can become comparable. In this work we present a study of 0.6--5-keV Ar ion scattering on a Cu (100) surface. Energy-loss spectra were measured and displayed some changes as the incident ion energy changes. Thus, a structured spectrum is observed at the higher energies. We analyze the characteristics of the spectra and contributions from the nuclear and electronic energy-loss components using both a Monte Carlo kinetics simulation assuming an averaged electron density and a semiclassical deterministic simulation with an inhomogeneous electron density in the solid. The general features of the experimental spectra were well reproduced, and semiclassical simulations allow us to identify contributions from trajectories coming from below and on top of the surface atomic layer. The relative contribution of nuclear energy loss and electronic energy loss (EEL) were delineated and a more refined analysis of the EEL for different trajectories is presented.

Is electronic stopping of ions velocity-proportional in the velocity-proportional regime?

We have studied systematic deviations of reported electronic stopping cross sections from velocity proportionality predicted by Lindhard and Scharff. Most pronounced is an apparent drop-off at beam energies below ∼0.01 MeV/u. In the frequently-used transmission technique, only a narrow cone of the beam is analysed in order to minimize the contribution from nuclear stopping. This has the consequence that a reduced instead of the full electronic energy loss is recorded. The magnitude of this effect has been computed on the basis of a recently developed extension of the scheme of Fastrup et al. to correct for nuclear stopping. In a detailed study of the C-Ar system based on our PASS code we find close agreement between the derived reduced electronic stopping cross section and the experimental result reported by Ormrod. Results are reported for eight ions on argon, for O in C and Cl in C and for Ni in Ag. For Ni in Ag as well as for one set of reported stopping cross sections for N in Ar a particularly sharp drop-off is shown to be caused by an inadequate nuclear-stopping correction. Our findings do not support Paul’s assertion of a gas-solid difference in electronic stopping of low-energy heavy ions.

Core Electrons in the Electronic Stopping of Heavy Ions.

Electronic stopping power in the keV/Å range is accurately calculated from first principles for high atomic-number projectiles and the effect of core states is carefully assessed. The energy loss to electrons in self-irradiated nickel is studied using real-time time-dependent density functional theory. Different core states are explicitly included in the simulations to understand their involvement in the dissipation mechanism. The core electrons of the projectile are found to open additional dissipation channels as the projectile velocity increases. Almost all of the energy loss is accounted for, even for high projectile velocities, when core electrons as deep as 2s^{2}2p^{6} are explicitly treated. In addition to their expected excitation at high velocities, a flapping dynamical response of the projectile core electrons is observed at intermediate velocities. The empirical reference data are well reproduced in the projectile velocity range of 1.0-12.0a.u. (1.5-210MeV).

Progress in understanding heavy-ion stopping

We report some highlights of our work with heavy-ion stopping in the energy range where Bethe stopping theory breaks down. Main tools are our binary stopping theory (PASS code), the reciprocity principle, and Paul’s data base. Comparisons are made between PASS and three alternative theoretical schemes (CasP, HISTOP and SLPA). In addition to equilibrium stopping we discuss frozen-charge stopping, deviations from linear velocity dependence below the Bragg peak, application of the reciprocity principle in low-velocity stopping, modeling of equilibrium charges, and the significance of the so-called effective charge.

Determination of molecular stopping cross section of 12C, 16O, 28Si, 35Cl, 58Ni, 79Br, and 127I in silicon nitride

Silicon nitride is a technologically important material in a range of applications due to a combination of important properties. Ion beam analysis techniques, and in particular, heavy ion elastic recoil detection analysis can be used to determine the stoichiometry of silicon nitride films, which often deviates from the ideal Si3N4, as well as the content of impurities such as hydrogen, even in the presence of other materials or in a matrix containing heavier elements. Accurate quantification of IBA results depends on the basic data used in the data analysis. Quantitative depth profiling relies on the knowledge of the stopping power cross sections of the materials studied for the ions involved, which in the case of HI-ERDA is both the primary beam, and the recoiled species. We measured the stopping cross section of 12C, 16O, 28Si, 35Cl, 58Ni, 79Br, and 127I in a well-characterised silicon nitride membrane. The measurements were made by independent groups utilising different experimental setups and methods. In some cases there is extensive overlap of the energy range in different experiments, allowing a comparison of the different results. The four independent data sets reported in this work are in excellent agreement with each other, in the cases where similar energy ranges were measured. On the other hand, the data are in most cases higher than calculations made with the interpolative schemes SRIM and MSTAR together with the Bragg rule. Better agreement is found with MSTAR in some of the cases studied. This work is a significant extension of the heavy ion stopping power data base for silicon nitride.

The hydrodynamic and radiative properties of low-density foams heated by x-rays

An advanced type of hydrodynamic stable plasma targets with homogeneous distribution of plasma parameters has been proposed for application in experiments on heavy ion stopping in plasmas and relativistic laser based particle acceleration. Plasma was created via x-ray heating of polymer aerogels with a mean density 103 times lower than that of solid matter. Hydrodynamic and radiation properties of low-density polymer aerogels heated by x-rays, which were generated due to laser interaction with a gold hohlraum, have been investigated experimentally and numerically. In experiments carried out at the PALS laser facility in Prague, the parameters of the hohlraum based soft x-ray source and the fraction of x-ray energy absorbed by foam layers have been measured. The results of these experiments and numerical simulations show that the x-ray heat process occurs via propagation of supersonic radiation driven heat waves. The measured heat wave velocity of 107 cm s−1 allows one to estimate the plasma temperature reached as 25 eV. The hydrodynamic stability of x-ray heated plasma layers has been demonstrated by means of an optical streak camera viewing the plasma expansion process. Simulations of the foam heating process denote rather homogeneous distribution of the plasma temperature and density in the x-ray heated plasma layer and sharp plasma boundaries. The investigated features of such plasma targets are a great advantage for experiments with heavy ion and relativistic laser beams.

Velocity dependence of heavy-ion stopping below the maximum

In the slowing-down of heavy ions in materials, the standard description by Lindhard and Scharff assumes the electronic stopping cross section to be proportional to the projectile speed v up to close to a stopping maximum, which is related to the Thomas–Fermi speed vTF. It is well known that strict proportionality with v is rarely observed, but little is known about the systematics of observed deviations. In this study we try to identify factors that determine positive or negative curvature of stopping cross sections on the basis of experimental data and of binary stopping theory. We estimate the influence of shell structure of the target and of the equilibrium charge of the ion and comment the role of dynamic screening.

Notes on Barkas-Andersen effect

Stimulated by recent statements in the literature on electronic stopping of heavy ions in matter, we try to clarify some central theoretical aspects of the Barkas-Andersen effect, about which there does not seem to be unanimous agreement in the community. We address the role of inner versus outer target shells, of projectile screening by bound electrons, the interference between Lindhard’s description and perturbation theory, as well as the equivalence between a single-electron versus Fermi-gas description of the effect.

The stopping of heavy ions in the low-to-intermediate energy range: The apparent velocity threshold

We present a non-linear study of the energy loss of heavy ions in solids, which is based on the transport cross section (TCS) and the extension of the Friedel sum rule (EFSR) for moving ions. We apply this approach to study the velocity dependence of the energy loss of heavy ions in the energy region below the stopping power maximum. With this formulation we are able to explain some striking effects in the energy loss of heavy ions which have been experimentally observed long time ago (Brown and Moak (1972) [14]), but have not been explained so far by the existing theoretical models: the deviations from the proportionality with ion velocity (predicted by alternative models in the low energy range), and the “apparent velocity threshold”.

Numerical study of heavy-ion stopping in foam targets with one-dimensional subcell-scale hydrodynamic motions

Heavy-ion stopping in foam targets with subcell-scale hydro motions was numerically investigated in relation to ion-driven warm dense matter experiments. To simulate porous foam targets, we employed a simple 1D periodic multilayer model consisting of thin solid slabs and gaps between them. The averaged pore diameter and cell-wall thickness of the foam were represented by the gap width between the slabs and the slab thickness, respectively. The density- and temperature-dependent projectile stopping cross-sections were evaluated using a binary encounter model taking into account the electronic state of target atoms during heating and expansion. We employed a combination of 11Na projectiles and subrange 13Al foam targets with ρ=0.05ρsolid. The hydrodynamic motion of the target was calculated with a 1D code. During homogenization, hot dense spots appeared at the original gap positions, owing to stagnation of the jets. As a result, even after the pores were filled with blow-off materials, the initial inhomogeneity was not completely smeared out, and the total energy loss was still not equal to that in the homogeneous equivalent, especially for large pore sizes.

Stopping power of 11B in Si and TiO2 measured with a bulk sample method and Bayesian inference data analysis

Abstract The popular stopping power interpolative schemes require experimental data to be developed. Where the data bases are sparse, with few experiments available, interpolations can be more inaccurate. This is the case for the stopping of heavy ions, where even for important targets such as Si there is a need for more measurements. For compounds, the situation is even worse with very few measurements available. In particular, the stopping in oxides and nitrides often deviates significantly from what would be expected using the Bragg’s rule. We apply a method that uses bulk or thick film samples to determine the stopping power of 11B in Si and TiO2. The method, which relies on Bayesian inference analysis of RBS spectra obtained at different energies, has been previously validated by verifying the results obtained in the well-known system 4He in Si.

Experimental stopping powers of Al, Mg, F and O ions in ZrO2 in the 0.1–0.6MeV/u energy range

The study of the stopping and range of heavy ions (Z > 3) in matter isdsc cfddc of both fundamental and practical interest as heavy ions find increasing usage in a wide range of ion beam based techniques. While semi-empirical formulations like the widely used SRIM code can predict the stopping powers of hydrogen and helium in many elemental and compound targets over a wide range of energies quite well, their predictive accuracy for heavy ions is not as good. This is mainly due to the lack of heavy ion experimental stopping power data on which such codes are based. We present results of measurements performed using a Time of Flight–Energy spectrometer to determine the stopping powers of O, F, Mg and Al ions in the oxide ceramic ZrO2 within the 0.1–0.6 MeV/u energy range. Possible SRIM correction (or correlation) factors for F, Mg and Al ions were extracted from quantitative comparisons of experimental and predicted stopping power values.

SRIM – The stopping and range of ions in matter (2010)

SRIM is a software package concerning the Stopping and Range of Ions in Matter. Since its introduction in 1985, major upgrades are made about every six years. Currently, more than 700 scientific citations are made to SRIM every year. For SRIM-2010, the following major improvements have been made: (1) About 2800 new experimental stopping powers were added to the database, increasing it to over 28,000 stopping values. (2) Improved corrections were made for the stopping of ions in compounds. (3) New heavy ion stopping calculations have led to significant improvements on SRIM stopping accuracy. (4) A self-contained SRIM module has been included to allow SRIM stopping and range values to be controlled and read by other software applications. (5) Individual interatomic potentials have been included for all ion/atom collisions, and these potentials are now included in the SRIM package. A full catalog of stopping power plots can be downloaded at www.SRIM.org. Over 500 plots show the accuracy of the stopping and ranges produced by SRIM along with 27,000 experimental data points. References to the citations which reported the experimental data are included.

Theory and simulation of heavy ion stopping in plasma

AbstractThe theoretical description of the energy loss of heavy ions in fully ionized matter is considered, where we focus on the many–body and plasma physics aspects of the stopping of point like projectiles with a fixed charge by free electrons, disregarding the atomic physics of the projectile and the target ions. This starts by identifying different coupling regimes for a heavy ion which passes through an electron plasma, and continues with a discussion of the available and appropriate analytical and numerical treatments of the energy loss and their applicability in these various regimes. Special attention is given to a nonlinear coupling regime with significant strong coupling effects on the projectile-target energy transfer where standard perturbative approaches cease to be valid. More advanced theoretical treatments, which are required for this regime, are presented, discussed and evaluated by comparison with simulation results.

Response of strontium titanate to ion and electron irradiation

The response of strontium titanate (SrTiO 3) to ion and electron irradiation is studied at room temperature. For an accurate energy to depth conversion and a better determination of ion-induced disorder profile from Rutherford backscattering spectrometry measurement, a detailed iterative procedure is described and applied to ion channeling spectra to determine the dechanneling yield and the disorder profiles for the Sr and Ti sublattices. The result shows a large underestimation in disorder depth, ∼40% at the damage peak, which indicates a large overestimation of the electronic stopping power for 1.0 MeV Au ions in SrTiO 3 predicted by the SRIM (Stopping and Range of Ions in Matter) code. Overestimation of heavy ion stopping power may lead to an overestimation of the critical dose for amorphization. The current study also demonstrates possible ionization effects in SrTiO 3 under ion and electron irradiation. Pre-amorphized SrTiO 3 exhibits strong ionization-induced epitaxial recovery at the amorphous/crystalline interface under electron irradiation.

Time-resolved measurement of energy loss of low-energy heavy ions in a plasma using a surface-barrier charged-particle detector

We tested an experimental setup for measurement of non-linear stopping of low-energy heavy ions in non-ideal plasmas. In this setup, we used a silicon surface-barrier charged-particle detector (SSBD), which could measure the energy of single ions. For synchronization between the plasma production and the injection of single projectiles, a fast beam kicker was installed in front of the plasma target. In order to test this setup, we used a laser-produced polyethylene plasma target instead of a shock-driven plasma device, which is under R&D process. Results of a preliminary energy loss measurement for low-speed heavy ions in the laser plasma are reported. Performance on the time resolution evaluated by using a carbon-foil target is also presented.

Experimental apparatus for the measurement of non-linear stopping of low-energy heavy ions

We developed an experimental apparatus for the study of non-linear stopping of low-energy heavy ions in non-ideal plasmas. The target plasma was produced by an electromagnetically driven shock tube. A pair of 50- μ m -diameter beam apertures was attached to the shock tube wall. These apertures confined hydrogen gas of ≈ 5 Torr in the tube and sustained the pressure difference ( ∼ 10 5 – 10 6 ) between the tube and the beam line. In order to measure the energy loss in the plasma in the tube, we used a semiconductor charged-particle detector, which could directly measure the kinetic energy of single particles, since the beam transmission through these apertures was very small. To synchronize the plasma production in the shock tube and the injection of projectiles, a fast beam kicker was installed in front of the plasma target. Results of preliminary experiments using thin carbon foil targets showed that the measured energy loss of single projectiles after passing through the target was in agreement with other data. The time resolution of the energy-loss measurement system was ≈ 150 ns , which is enough to measure the projectile energy loss during the life time of the target plasma.