Energy Loss Of Charged Particles Research Articles

Energy loss of charged particles at large distances from metal surfaces

We present a theoretical study of the dissipative component of the force acting on a highly charged ion moving in front of a solid surface at large distances. The friction force (stopping power) of the surface is analyzed employing both the specular-reflection model and time-dependent density functional theory (TDDFT). Contributions from particle-hole and plasmon excitations are discussed. A simple method to include the correction due to the finite width of the plasmon resonance at large wavelength into the TDDFT description of the stopping power is suggested. We present applications to the energy loss of charged particles undergoing distant collisions at grazing incidence angles with the internal surface of the microcapillary. Our results indicate that the correlation between the angular distribution and the energy loss of transmitted ions can be used to probe the dielectric properties of the capillary material at large distances.

The contribution of stable isotopic tracing, narrow nuclear resonance depth profiling, and a simple stochastic theory of charged particle energy loss to studies of the dry thermal oxidation of SiC

We present the stochastic approach to calculating fast charged particle energy distributions when penetrating matter, and nuclear reaction yield curves obtained when the energy of a beam incident on a target is scanned about the energy of narrow nuclear resonances, such as 18O(p,α) 15N at 151 keV. In particular we present new calculations that show the insensitivity of the final calculations to the detailed form of the energy loss distribution assumed for independent single ion–atom collisions. We present application of narrow resonance profiling with 18O stable isotopic tracing to the study of the dry thermal oxidation mechanisms of silicon carbide, yielding insights into the process that cannot be obtained by other means.

Variation of the track etch rates of alpha-particle trajectory in PADC

The formation of etched tracks in solid-state nuclear track detectors is usually described by assuming an unequivocal correlation of the etch-rate ratio with the energy loss of charged particles. For alpha particles, this assumption could be verified within the scatter of the experimental data. In this article, the dependence of the depth (x) on the track etch rate (V T) was determined experimentally by track length measurement. It is found that the track etch rate as a function of the depth within the detector follows the Bragg curve. The track etch rate has been found to be described by a generalization of the restricted energy loss, in good approximation along the trajectories of alpha particles.

Charge determination of nuclei with the AMS-02 silicon tracker

The silicon tracker of the AMS-02 detector measures the trajectory in three dimensions of electrons, protons and nuclei to high precision in a dipole magnetic field and thus measures their rigidity (momentum over charge) and the sign of their charge. In addition, it measures the specific energy loss of charged particles to determine the charge magnitude. Ladders from the AMS-02 tracker have been exposed to ion beams at CERN and GSI to study their response to nuclei from helium up to the iron group. The longest ladder, 72 × 496 mm 2 , verified in the tests contains 12 sensors. Good charge resolution is observed up to iron.

Energy losses of charged particles moving parallel to the surface of an overlayer system

An energetic charged particle moving parallel to the surface of an overlayer system was studied. This system was composed of a thin film on the top of a semi-infinite substrate. Based on the dielectric response theory, the induced potential was formulated by solving the Poisson equation and matching the boundary conditions. The stopping force was built-up using the energy-momentum conservation relations and the extended Drude dielectric functions with spatial dispersion. Surface (vacuum–film) and interface (film–substrate) excitations were included in the formulations of the interaction between charged particles and the overlayer system. Results of the wake potential were presented for protons moving parallel to a vacuum–copper–silicon system. Dependences of the induced potential and the stopping force on film thickness, distance of the proton from surface, and proton velocity were investigated.

Surface effects on the electronic energy loss of charged particles entering a metal surface

Surface effects on the electronic energy loss of charged particles entering a metal surface are investigated within linear-response theory, in the framework of time-dependent density functional theory. Interesting phenomena occur in the loss spectra originated by the boundary (bregenzung) effect, which is as a consequence of the orthogonality of surface and bulk excitation modes. Our calculations indicate that the presence of a non-abrupt electron-density profile at the surface severely affects the nature of surface excitations, as deduced from comparison with simplified models.

Erratum: Energy loss of charged particles interacting with simple metal surfaces [Phys. Rev. B 64, 035423 (2001)

Received 10 December 2002DOI:https://doi.org/10.1103/PhysRevB.67.089902©2003 American Physical Society

Energy loss of charged particles moving in cylindrical tubules

The interactions of charged particles with cylindrical tubules are studied within the framework of the dielectric theory. Elementary excitations on a tubule are modeled by an infinitesimally thin layer of free-electron gas, uniformly distributed over the surface of the tubule. The dielectric function of such a system, obtained from the random-phase approximation, exhibits a dimensional crossover from two-dimensional to one-dimensional electron gas, when the radius of the tubule decreases. Energy loss of a charged particle, moving paraxially in a tubule, can be divided into a single-particle excitation part and a resonant excitation part. It is shown that the resonant excitation modes on a tubule, which dominate the energy loss in the high-velocity regime, are quite different from those in a cylindrical cavity in a solid, described by a bulk dielectric function of the surrounding three-dimensional electron gas.

Dependence of the etch rate ratio on the energy loss of light ions in CR-39

Mathematical simulation of the etch pit evolution requires the knowledge of the relationship between the etch rate ratio and the restricted energy loss of charged particles. Whereas a unique correlation of both quantities independent of the kind of particle and its initial energy was found for protons, deuterons and alpha particles the results of the depth-dependent track etch rates for 7 Li , 11 B and 12 C ions indicated a different behaviour for heavier ions. A detailed analysis of the etch rate ratio in dependence on the restricted energy loss confirmed the existence of specific relationships for ions of different kind and initial energy. The spread of the corresponding curves is explained by the gradual increase of the track etch rate over a certain distance from the detector surface. The speed of this increase is the higher the lower the restricted energy loss is.

Using secondary-proton spectra to study the compression and symmetry of deuterium-filled capsules at OMEGA

With new measurement techniques, high-resolution spectrometry of secondary fusion protons has been used to study compression and symmetry of imploded D2-filled capsules in direct-drive inertial-confinement-fusion experiments at the 60-beam OMEGA laser facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. Data from target capsules with ∼15 atmospheres of D2 fuel, in CH shells 19–27 μm thick, were acquired with a magnet-based, charged-particle spectrometer and with several new “wedge-range-filter”-based spectrometers incorporating special filters and CR39 nuclear track detectors. Capsules with 19-μm shells, imploded with similar laser energies (∼23 kJ) but different methods of single-beam laser smoothing, were studied and found to show different compression characteristics as indicated by the fuel areal density (determined by the ratio of secondary-proton yield to primary-neutron yield) and the total areal density (determined by the energy loss of protons due to slowing in the fuel and shell). In going from 0.3-THz SSD (smoothing by spectral dispersion) to 1-THz SSD and PS (polarization smoothing), the fuel areal density increased by at least 30%, while the total areal density increased by 40% (from ∼52 to ∼72 mg/cm2). In addition, significant low-mode-number spatial asymmetries in implosions were indicated by spectra measured at different angles with respect to the target. The mean energies of protons, measured at different angles during the same shot, varied by as much as 1 MeV, implying angular variations in areal density of order 30 mg/cm2. To the best of our knowledge, this is the first experimental demonstration that capsule symmetry can be sensitively studied by measuring the energy loss of charged particles.

A new approach to characterising the etch rate ratio in CR-39 using a function of two variables

The formation of etched tracks in solid-state nuclear track detectors is usually described assuming an unequivocal correlation of the etch rate ratio with the energy loss of charged particles. For protons, deuterons and alpha particles this assumption could be verified within the scatter of the experimental data. Experimental studies with 7 Li , 11 B and 12 C ions yielded, however, systematic deviations from the expected results. Analysing the complete experimental data set for CR-39, a dependence of the etch rate ratio was found not only on the particle's energy loss, but also on the depth within the detector where this energy loss occurs. Arranging the etch rate ratio as a function of both these variables all experimental results appear without inconsistencies. The etch rate ratio represented by a two-dimensional matrix can be used, then, for characterising the etch kinetics along the trajectories of charged particles of different kinds and initial energy.

Determining charged particle energy losses with the aid of transmutation isotopes

A new method is proposed for determining the energy losses of charged particles in solids, which is based on the comparison of profiles of the transmutation isotopes measured in the samples irradiated by particles of various energies.

Energy loss of relativistic heavy ions in matter

We have investigated the theory of energy loss of charged particles in matter due to ionization of the medium, integrating the work of other authors over several decades. We describe the most important corrections to standard energy-loss formulae. We compare our calculations to an improved measurement of the range of 1 A GeV U ions and to other codes and tabulations. We show that calculations based on the theory of ionization energy loss are at least as accurate as tabulations extrapolated from empirical data for the stopping of uranium ions in matter. We have made available the computer code resulting from our investigations.

Many-body approach to the nonlinear interaction of charged particles with an interacting free electron gas

We report various many-body theoretical approaches to the nonlinear decay rate and energy loss of charged particles moving in an interacting free electron gas. These include perturbative formulations of the scattering matrix, the self-energy, and the induced electron density. Explicit expressions for these quantities are obtained, with inclusion of exchange and correlation effects.

TAU DECAYS WITH CHARGED KAONS AT OPAL

From an analysis of the ionisation energy loss of charged particles selected from tau pair candidates recorded in the OPAL detector at centre-of-mass energies near the Z0 resonance, we determine competitive measurements of the τ-→ντ K -≥ 0h 0 branching ratio, where the h0 notation refers to a π0, an η, a [Formula: see text], or a [Formula: see text]. We also determine the τ-→ντ K -π- π+(π0) and τ-→ντ K -π- K +(π0) branching fractions, where the (π0) notation refers to decay modes with or without an accompanying π0. In addition, we examine the resonant structure of τ-→ντ K -π-π+ candidates, and find that the resonant structure is dominated by the K1(1270) resonance.

Thin-film effects on the surface stopping power of a free electron gas

The electronic properties of thin films present quantum-size effects (QSE), which are a consequence of the finite size of the system. Here we focus on the investigation of QSE on the electronic energy loss of charged particles moving parallel with metallic thin films. The energy loss is calculated within linear response theory, from the knowledge of the density-response function of the inhomogeneous system, which we evaluate either in the random-phase approximation or with the use of an adiabatic and local exchange-correlation kernel.

Energy loss of charged particles interacting with simple metal surfaces

Self-consistent calculations of the energy-loss spectra of charged particles moving near a plane-bounded free-electron gas are reported. Energy-loss probabilities are obtained, within linear-response theory, from the knowledge of the density-response function of the inhomogeneous electron system. Self-consistent single-particle wave functions and energies are obtained by solving the Kohn-Sham equation of density-functional theory, and the electronic response is then computed either in the random-phase approximation or with the use of an adiabatic local-density approximation. Special emphasis is placed on the various contributions from collective and electron-hole excitations to the energy loss of charged particles moving parallel with the surface. The effect of the electronic selvage at a metal surface on the energy-loss spectra is also discussed, by comparing our full self-consistent calculations with those obtained for electron densities that drop abruptly to zero at the surface.

Energy Loss of Charged Particles in Dense Nonideal Plasmas

The paper is devoted to theoretical investigations on the energy loss of charged particles in fully ionized, nonideal plasmas. Especially, the limiting behaviour for very low and high beam particle velocities is investigated. To give a consistent description for both limits, a combined model based on quantum kinetic theory is applied. For low beam velocities, a comparison with simulation data is given. The high beam velocity behaviour of our model is compared with the standard model of the stopping power given by the Bethe-formula and two correction terms, the Bloch term and a Z 3 b -correction (Barkas effect).

Energy Loss of Charged Particles in Dense Nonideal Plasmas

Energy Loss of Charged Particles in Dense Nonideal Plasmas

Ionization energy losses of fast charged particles produced in matter

1. Ionization energy losses of clusters formed by fast charged particles occurring at small distances from one another may differ significantly from the total ionization energy losses of the individual particles constituting the cluster if these particles are far from one another. This distinction is associated with the interference of the electromagnetic fields created by the particles of the cluster at distances that contribute significantly to ionization energy losses. Such a situation emerges, for example, when a high-energy electron‐ positron pair is produced in matter [1]. The point is that the characteristic angles of divergence of a high-energy pair produced in matter are very small. It follows that, over rather long a time interval, the transverse distance between the particles of the pair will be small in relation to the maximum impact-parameter values of ρ max ~ v / ω p , ( v is the particle velocity, and ω p is the plasmon frequency) that contribute significantly to the ionization energy losses of the individual particles of the pair. The electromagnetic fields of the electron and the positron of the product pair compensate each other partly at distances of v / ω p the from the pair in the transverse direction; therefore, the ionization energy losses of such a cluster are smaller than the ionization energy losses of the individual particles. By way of example, we indicate that, at photon energies of " ω ~ 100 GeV, characteristic angles of divergence of the particles forming the pair are