Stopping Of Heavy Ions Research Articles

Firsov approach to heavy-ion stopping in warm matter using a finite-temperature Thomas–Fermi model

Low-velocity (< c/137) heavy-ion stopping in warm ( kT<10 eV) matter was investigated by means of a Firsov model, in which the projectile energy loss was evaluated from the drag force due to the exchange of electrons between the projectile and the target. A finite-temperature Thomas–Fermi model was applied in order to calculate the density and momentum distribution of electrons around the nuclei of the collision partners. We have found that the stopping cross-section depends only weakly on the target temperature, whereas the density dependence is rather strong.

On the correlation between nuclear and electronic stopping of heavy ions in light targets

Interatomic potentials for Au–C system, calculated with density-functional theory (DFT) method, have been used to obtain the range parameters of gold in carbon at energies of about 1–1000keV and for the inverse implantation of carbon in gold between 5 and 40keV. The range parameters have been evaluated by the standard transport theory and by Monte–Carlo simulations. Good agreement between the computed range parameters and available experimental data does not confirm the existence of correlation effects between the nuclear and electronic stopping in the studied interval of energies.

Microstructural modifications of Ni–Ti shape memory alloy thin films induced by electronic stopping of high-energy heavy ions

The current study is part of an overarching goal to develop an ion implantation process for producing cyclic actuating elements used in microelectromechanical systems. The damage produced by high-energy ions can be used as a means to selectively suppress the martensitic transformation and bias the motion of shape memory alloy thin films Ni–Ti. In order to optimize the performance of these devices, detailed knowledge of the influence of ion implantation on the microstructure is needed. Recent experiments have shown that complex microstructures are formed after 5 MeV Ni ion implantation. In particular, the extensive surface amorphization and the depth distributions of the irradiation induced phase transformations, which were more prominent at shallower depths than expected, did not correlate with ion transport theories involving nuclear stopping damage distributions. Although electronic stopping effects are normally neglected in metals in these energy regimes, they may explain the unexpected surface amorphization since electronic stopping is the prevalent mode of ion energy transfer at shallow depths. Therefore, swift ion irradiation experiments were conducted to assess the effects of electronic stopping on the damage production. Microstructural observations showed that significant damage was produced from ions possessing low electronic stopping powers (<9 keV/nm) near those of 5 MeV Ni ions (3 keV/nm), confirming, in part, that electronic stopping effects contribute to the damage processes.

Study of Resonance Crossing in FFAG

Measurements of heavy-ion slowing down in matter differ in many aspects from experiments with light particles like protons and α-particles. An overview of the special experimental requirements, methods, data analysis and interpretation is presented for heavy-ion stopping powers, energy- and angular-straggling and ranges in the energy domain from keV/u up to GeV/u. Characteristic experimental results are presented and compared with theory and semiempirical predictions. New applications are outlined, which represent a challenge to continuously improve the knowledge of heavy-ion slowing down.

Stopping of high-Z ions at intermediate velocities

The stopping of heavy ions at intermediate velocities is influenced by projectile screening, shell corrections, Barkas–Andersen effect and charge exchange. These effects are accounted for in the binary theory of stopping and implemented in the PASS code. Previous applications of this scheme have focused on ions up to argon. The present work is a first attempt to apply the PASS code to very heavy projectiles. It is known that as the ion/target atomic-number ratio increases, the stopping force becomes increasingly sensitive to the ionic charge state. Therefore, care has been taken to incorporate realistic mean charges based on experimental data. Calculated stopping cross sections are found to agree well with experiment at energies above ∼2MeV/u, while a systematic overestimate of up to 20% is found at lower projectile speeds. Possible causes are studied. Charge-state averaging is shown to have a significant effect at low speed.

Heavy-ion stopping in solids: Energy transfer to the target or the dragging force due to the induced potential wake

There are two different approaches for describing the slowing down of charged particles in solids, commonly used in a separate way. Either one treats the energy transfer to the target or considers the dragging force due to the induced potential ('wake'). We herewith present a classical many-body calculation which intrinsically allows simultaneously both descriptions. For the first time, we can follow in detail the development of the stopping power, the projectile's charge and excitation state, as well as the formation of the wake, for ions entering into a solid. We further show that in nonequilibrium, stopping the development of the wake contributes much stronger to the change in stopping power than one could expect from the corresponding change of the projectile's charge or excitation state. This is exemplified by the explanation of an experimentally observed surface enhancement in the stopping power, which sheds new light on analysis tools with single atomic depth resolution. We underline our findings by simulating also anti-Ni ions, which are found to form a pressure wave in contrast to trailing wakes in the case of Ni ions.

Radiation dynamics of fast heavy ions interacting with matter

The study of heavy ion stopping dynamics using associated K-shell projectile and target radiation was the focus of the reported experiments. Ar, Ca, Ti, and Ni projectile ions with the initial energies of 5.9 and 11.4 MeV/u were slowed down in quartz and arogels. Characteristic radiation of projectiles and target atoms induced in close collisions was registered. The variation of the projectile ion line Doppler shift due to the ion deceleration measured along the ion beam trajectory was used to determine the ion velocity dynamics. The dependence of the ion velocity on the trajectory coordinate was measured over 70–90% of the ion beam path with a spatial resolution of 50–70 μm. The choice of SiO 2 aerogel with low mean densities of 0.04–0.15 g/cm 3 as a target material, made it possible to stretch the ion stopping range by more than 20–50 times in comparison with solid quartz. It allowed for resolving the dynamics of the ion stopping process. Experimentally, it has been proven that the fine porous nano-structure of aerogels does not affect the ion energy loss and charge state distribution. The strong increase of the ion stopping range in aerogels made it possible to resolve fast ion radiation dynamics. The analysis of the projectile Kα-satellites structure allows supposing that ions propagate in solid in highly exicted states. This can provide an experimental explanation for so called gas-solid effect.

A study of gas-stopping of intense energetic rare isotope beams

A scheme is proposed for the efficient thermalization of energetic and intense rare isotope beams. Simulation results indicate that gas stopping of heavy ions in a weakly focusing magnetic field can overcome the severe intensity limitation that exists in present systems and also provide a much faster ion extraction.

Stopping of Heavy Ions in Magnetized Strongly Coupled Plasmas: High‐Velocity Limit

AbstractThe energy loss of a heavy ion moving in a magnetized strongly coupled electron plasma is considered within the linear response treatment and in high‐velocity regime. The analytical expressions for the stopping power have been found for the arbitrary ion incidence angle. The obtained general expression for the stopping power is analyzed for the ion which moves parallel or perpendicular to the magnetic field. It is found that in general the magnetic field and the Coulomb coupling reduce the stopping power as well as the dynamical screening length at high velocities. The influence of the magnetic field and the Coulomb coupling on the high‐velocity stopping power is discussed. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Pair production and bremsstrahlung contributions to the stopping of relativistic heavy ions

We examine the energy loss to electron–positron pairs and bremsstrahlung for relativistic heavy ions penetrating matter. Pair production is the dominant source of loss at extreme projectile energies, and already at energies of a few hundred GeV/u it may add several per cent to the stopping power. An analytical formula for the pair-production contribution to the average energy loss is produced. In bremsstrahlung coherent action of the constituents of each collision partner is required in order to keep the nuclei from breaking up. This limits the emission substantially at high energies compared to the emission in collisions between pointlike non-composite but otherwise similar objects. A simple formula for the bremsstrahlung loss is presented. We conclude with remarks on the statistics of the energy-loss processes.

Pressure effects on the stopping and range of heavy ions

Pressure effects on the energy loss of heavy ions in compound target materials are analyzed through the cores and bonds (CAB) implementation of the kinetic theory of stopping for protons and the effective charge approximation. The effect of pressure on the target material is estimated through a model of molecular confinement whereby the changes in the molecular electronic properties are calculated selfconsistently. As pressure increases, a competing behavior between target density increase and reduction in the electronic stopping cross section is observed. As a consequence, total path ranges are decreased as compared with the corresponding pressure-free target. Range calculations are shown for He + ( E⩽1.6 MeV) and Li + ( E⩽2.6 MeV) projectiles on dense water and methane targets.

SRIM-2003

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 five years. For SRIM-2003, the following major improvements were made: (1) About 2200 new experimental stopping powers were added to the database, increasing it to over 25,000 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. A full catalog of stopping power plots has been published at www.SRIM.org. Over 500 plots show the accuracy of the stopping and ranges produced by SRIM along with 25,000 experimental data points. References to the citations which reported the experimental data are included.

Stopping of swift ions in compounds

Stopping of light and heavy ions in compounds has been studied on the basis of the binary theory of electronic stopping with the focus on limitations of Bragg's additivity rule. The case of LiF is analysed in detail because departures from Bragg additivity are expected to be particularly pronounced here, especially for penetrating antiprotons. A significant dependence on the atomic number and ionic charge of the projectile is predicted along with the more well-known velocity dependence of departures from Bragg additivity. Such departures are found to be affected by shell correction and Barkas effect in addition to the more well-known dependence on the I-value. Comparisons with experimental results include H 2O vapor, CH 4, CO 2, mylar and polycarbonate.

Validity of Bragg’s rule for heavy-ion stopping in silicon carbide

The stopping powers for O, Al, Cr, Mn, Co and Cu in a self-supported SiC film have been measured in transmission geometry over a continuous range of energies using a time of flight elastic recoil detection analysis (ToF-ERDA) system. These stopping data, along with the stopping data in Si and C obtained previously using the same ions and measurement technique, are used to assess the validity of the Bragg additivity rule for stopping powers in SiC over a range of ions and energies. Within the experimental uncertainties (±4%), the results indicate that Bragg's rule is valid in SiC for the ion species and energy region studied. The measured stopping powers in C, Si and SiC are also compared with the stopping power predictions of the two most recent versions of the SRIM (Stopping and Range of Ions in Matter) codes. While both versions of SRIM show varying degrees of agreement with the measured stopping data, there are significant deviations of the SRIM predictions for some ions and energy regions.

Interplay of charge exchange and projectile excitation in the stopping of swift heavy ions

The electronic energy loss of a dressed ion penetrating through matter is commonly considered as being synonymous with the sum of the excitation energies of the target and the projectile in atomic collisions undergone during the passage. We show that this is not justified in projectile-ionizing collisions and discuss some consequences.

Panel discussion on stopping of heavy ions

This is a condensed transscript of 90 minutes’ discussion session marking the end of the International Symposium on Stopping of Heavy Ions (STOP01) held in Odense, Denmark, 5–8 August 2001. The time was divided up about equally between introductory and concluding remarks by the panel, and a general discussion involving most of the participants. The session was moderated by A.H. S ørensen. We have kept the contributions in the chronological order.

Experimental studies of heavy-ion slowing down in matter

Measurements of heavy-ion slowing down in matter differ in many aspects from experiments with light particles like protons and α-particles. An overview of the special experimental requirements, methods, data analysis and interpretation is presented for heavy-ion stopping powers, energy- and angular-straggling and ranges in the energy domain from keV/u up to GeV/u. Characteristic experimental results are presented and compared with theory and semiempirical predictions. New applications are outlined, which represent a challenge to continuously improve the knowledge of heavy-ion slowing down.

Statistics of heavy-ion stopping

Energy-loss straggling of swift heavy ions penetrating through matter has been analysed on the basis of binary stopping theory as well as the modified Bohr model allowing for projectile screening. A program has been written which evaluates the generalized Bothe–Landau formula governing the energy-loss spectrum for penetration through a thin layer, allowing for charge exchange involving an arbitrary number of charge states. This program was generated on the basis of calculational schemes developed originally for swift light ions. Projectile screening and multiple-shell structure of target atoms are allowed for. Explicit energy-loss spectra are given for oxygen in carbon for charge states 6–8 and foil thickness 2, 10 and 50 μg/cm 2. It is also demonstrated that frozen-charge straggling depends only weakly on charge state.

Effective stopping of relativistic composite heavy ions colliding with atoms

A nonperturbative theory of energy loss by relativistic composite heavy highly charged ions colliding with atoms is developed. A simple formula for effective stopping is derived. By composite ions, we mean partially ionized atoms of heavy elements consisting of the ion core and several bound electrons that incompletely neutralize the ion core charge. Such ions, which have, as a rule, a high charge (for example, partly stripped uranium atoms), are used in many experiments performed with modern heavy ion accelerators.

A systematic study of the pulse height deficit in propane-filled gas ionization detectors

The response of gas ionization detectors to heavy ions is species dependent. Relative to a linear calibration based on the response to light ions, heavy ions show a pulse height deficit. Detailed knowledge of this deficit is essential for accurate energy spectroscopy of heavy ions. Precise measurements of the response of a propane-filled gas ionization detector have been performed for a large selection of ions in the ranges Z=6–79 and E=0.4–2.6 MeV/amu. Pulse height deficits were determined with respect to the response to carbon ions, and found to be as large as 25% of the incident energy. The deficit was found to depend on ion energy and atomic number. Isotopic effects were also observed. Care was taken to obtain a reliable estimate of the energy loss of the ions in the detector window. This included measurements of the window thickness and shape, and measurements of heavy ion stopping powers for Mylar. Monte-Carlo simulations were carried out using the code TRIM to evaluate the contribution of elastic collisions of the ions in the detector gas. It was found that after accounting for both window energy loss and elastic collisions, a significant residual pulse height deficit remains. An empirical formula was developed to predict the magnitude of the pulse height deficit, and aid in the accurate energy calibration of gas ionization detectors.