The stopping and range of ions in matter is physically very complex, and there are few simple approximations which are accurate. However, if modern calculations are performed, the ion distributions can be calculated with good accuracy, typically better than 10%. This review will be in several sections: 

a)

A brief exposition of what can be determined by modern calculations.




b)

A review of existing widely-cited tables of ion stopping and ranges.




c)

A review of the calculation of accurate ion stopping powers.

The stopping and range of ions in solids

SRIM is a software package concerning the S topping and R ange of I ons in M atter. 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.

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

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SRIM : the stopping and range of ions in matter

Phase transitions to quantum condensed phases—such as Bose–Einstein condensation (BEC), superfluidity, and superconductivity—have long fascinated scientists, as they bring pure quantum effects to a macroscopic scale. BEC has, for example, famously been demonstrated in dilute atom gas of rubidium atoms at temperatures below 200 nanokelvin. Much effort has been devoted to finding a solid-state system in which BEC can take place. Promising candidate systems are semiconductor microcavities, in which photons are confined and strongly coupled to electronic excitations, leading to the creation of exciton polaritons. These bosonic quasi-particles are 109 times lighter than rubidium atoms, thus theoretically permitting BEC to occur at standard cryogenic temperatures. Here we detail a comprehensive set of experiments giving compelling evidence for BEC of polaritons. Above a critical density, we observe massive occupation of the ground state developing from a polariton gas at thermal equilibrium at 19 K, an increase of temporal coherence, and the build-up of long-range spatial coherence and linear polarization, all of which indicate the spontaneous onset of a macroscopic quantum phase. Bose–Einstein condensation (BEC), a form of matter first postulated in 1924, has famously been demonstrated in dilute atomic gases at ultra-low temperatures. Much effort is now being devoted to exploring solid-state systems in which BEC can occur. In theory semiconductor microcavities, where photons are confined and coupled to electronic excitations leading to the creation of polaritons, could allow BEC at standard cryogenic temperatures. Kasprzak et al. now present experiments in which polaritons are excited in such a microcavity. Above a critical polariton density, spontaneous onset of a macroscopic quantum phase occurs, indicating a solid-state BEC. BEC should also be possible at higher temperatures if coupling of light with solid excitations is sufficiently strong. Demokritov et al. have achieved just that, BEC at room temperature in a gas of magnons, which are a type of magnetic excitation. This paper presents a comprehensive set of experiments in which polaritons are excited in a semiconductor microcavity. Above a critical density of polaritons, massive occupation of the ground state at 19 K is observed and various pieces of experimental evidence point to a spontaneous onset of a macroscopic quantum phase.

Bose-Einstein condensation of exciton polaritons

Geant4 is a software toolkit for the simulation of the passage of particles through matter. It is used by a large number of experiments and projects in a variety of application domains, including high energy physics, astrophysics and space science, medical physics and radiation protection. Over the past several years, major changes have been made to the toolkit in order to accommodate the needs of these user communities, and to efficiently exploit the growth of computing power made available by advances in technology. The adaptation of Geant4 to multithreading, advances in physics, detector modeling and visualization, extensions to the toolkit, including biasing and reverse Monte Carlo, and tools for physics and release validation are discussed here.

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Recent developments in GEANT4

The influence of the energy loss of slow projectiles during inelastic collisions on the inner-shell ionization cross sections is treated analytically. The result agrees with available experimental cross sections for $K$-shell ionization by protons. Residual trends in the data may gauge the quality of wave functions employed in calculations of Coulomb ionization cross sections.

Energy-loss effect in inner-shell Coulomb ionization by heavy charged particles

The effective charge of energetic ions as it pertains to the stopping power of solids is calculated in a dielectric-response approximation. The density distribution of $N$ electrons bound in an ion of atomic number ${Z}_{1}$ is given by a variational statistical approximation. The effective charge $Z_{1}^{}{}_{}{}^{*}e$ is always larger than the ionic charge ${Q}_{1}=({Z}_{1}\ensuremath{-}N)e$, because of close collisions. A comprehensive low-velocity formula predicts $Z_{1}^{}{}_{}{}^{*}e$ for given $Q$ as a function of the ratio between the ion size and the mean electron spacing in the medium. At high velocities one obtains a partition rule of stopping powers for the effective charge of ionic projectiles. The results are compared with new precision stopping-power measurements on C, Al, and Au with $_{7}\mathrm{N}$ ions.

Effective stopping-power charges of swift ions in condensed matter

Experimental $K$-shell ionization cross sections are reported for low-velocity heavy projectiles of atomic number small compared to the target atomic number. For such projectile-target combinations, the Coulomb interaction between the projectile nucleus and the $K$-shell electrons dominates the $K$-shell ionization process at all projectile velocities. The data can disagree by orders of magnitude with the primary predictions of the nonrelativistic quantum theory in the plane-wave Born approximation. Important physical processes are shown to be at the root of the discrepancies. They derive from the finite charge of the moving projectile, and thus do not contribute in the plane-wave Born approximation. They are the Coulomb deflection of the projectile in the field of the target nucleus and the perturbation of the target atomic states by the projectile. A theory for these processes is developed in an approximate manner. When incorporated with the theory in the plane-wave Born approximation, it accounts quantitatively for the data. A method results for reducing cross-section data in a comprehensive way. A universal graph of cross sections emerges which, in effect, constitutes an extrapolation of the data to the conditions of zero projectile charge. It comprises cross sections ranging over six orders of magnitude measured on different targets for various projectiles with a wide range of velocities, mostly below the mean $K$-shell velocities. The locus of this universal graph coincides with the prediction of the plane-wave Born approximation.

Universal Cross Sections for K -Shell Ionization by Heavy Charged Particles. I. Low Particle Velocities

The theory of Coulomb ionization of $L$ shells by low-velocity heavy charged particles whose atomic number is small compared to the atomic number of the target atom is extended to projectiles with velocities comparable to or larger than the $L$-shell orbital velocities. At large impact parameters projectiles polarize the shell, and at small impact parameters they increase the binding energies of the electrons to be excited. The polarization effect is incorporated in accordance with the perturbed stationary-state (PSS) approximation. The effect of the repulsion between the projectile and the target nucleus is accounted for by a Coulomb-deflection factor (C). This CPSS theory is developed further to include relativistic effects (R) of the target wave function through a procedure that reproduces the results of numerical calculations for heavy target atoms. With electron capture by the projectiles as an additional channel of ionization, the CPSSR theory is compared with experiment.

L-shell Coulomb ionization by heavy charged particles

This note discusses the question as to whether quasi-particles, such as excitons, i.e., nonlocalized excited states of solids, can fulfill necessary conditions for a Bose-Einstein condensation, and whether such condensation can be observed. Although uncertainties of present data on excitons preclude precise numerical predictions, it is concluded that under certain experimentally attainable circumstances excitons fulfill the necessary conditions, i.e., condensation is possible. Ways of detecting the condensation are considered, and a specific experiment is proposed.

Werner Brandt

Papers

Energy-loss effect in inner-shell Coulomb ionization by heavy charged particles

Effective stopping-power charges of swift ions in condensed matter

Universal Cross Sections for K -Shell Ionization by Heavy Charged Particles. I. Low Particle Velocities

L-shell Coulomb ionization by heavy charged particles

Bose-Einstein Condensation of Excitons