Particle Stopping Research Articles

Systematic study of Au–Au collisions with AGS experiment E917

The systematics of baryon stopping and strange particle production have been studied in Au+Au collisions at 6, 8, and 10.8 GeV per nucleon with AGS experiment E917. In particular, the systematic behavior of the proton yields, phi meson production, and the yields of antilambdas and antiprotons are examined as functions of beam energy and centrality.

Numerical simulation of tribo-electrification of particles in a gas–solids two-phase flow

Numerical simulation of tribo-electrification of particles in a gas–solids two-phase flow has been conducted. Under any injected conditions on the particle, normal component of impact velocity and number of impacts of a particle per unit length have, respectively, a constant value for the calculation beyond the particle stopping distance and impact charge increases linearly with the distance. Although gravity force changes particle motion dramatically, the impact charge increases about 10%. We have also investigated the effects of particle size, air velocity and pipe diameter on the particle motion and the impact charge, which revealed that both the normal component of impact velocity and the number of impacts of a particle decrease exponentially with increasing Stokes number. However, it was found that the effects of air velocity and pipe diameter on the impact charge are qualitatively different from those of the experimental results.

Semiclassical model of atomic collisions: Stopping and capture of heavy charged particles and exotic atom formation

The semiclassical approach to modeling atomic collision systems lies between the easy classical model, which is most useful for simple systems in which quantum effects can be neglected, and the full quantum mechanical description, which is generally too difficult for more than simple systems. By adding a mathematical model of quantum-mechanical effects to a classical Hamiltonian, the calculational simplicity of the manybodied classical model can be extended to the quantum realm; the validity of this approach can be measured by the degree to which the semiclassical model can replicate experimental data. Evolving from earlier work by Kirschbaum and Wilets, our model uses momentum-dependent pseudopotentials to exclude particles from quantum mechanically forbidden regions of phase space: a Heisenberg pseudopotential stabilizes the system by preventing atomic electrons from collapsing into the nucleus, while a Pauli pseudopotential holds identical electrons apart in phase space, structuring the electron configuration. This semiclassical model of an atom is then used as a target in collision simulations with a heavy projectile, which is itself treated classically. Collision cross sections are calculated from a series of simulation runs with Monte Carlo target orientations and impact parameters. The model is dialed in to match published experimental proton stopping powers, then applied to other systems of interest. Here, we present stopping and capture cross sections for antiprotons colliding with our semiclassical model of He. Antiproton stopping on He is compared with the results reported recently by the OBELIX group, and initial capture states are discussed in some detail, including a comparison with the quantum-mechanical calculations originally presented by Yamazaki and Ohtsuki and the later paper by Shimamura; among the differences: (1) In our calculations, the angular momentum of captured antiprotons obeys the classical limit l=n, and (2) the angular momentum distribution of our $$He^ + \bar p$$ states extends beyond that of the quantum calculations. It should be emphasized that our calculations are for times much shorter than the metastable lifetimes.

Heavy ion tumour therapy

Ion beams represent a promising radiotherapy modality for the treatment of deep seated tumours. Compared to conventional photon beams, in particular beams of heavier ions like e.g. carbon show several advantages which are related to their different physical and radiobiological properties: • The dose increases with penetration depth and shows a sharp distal fall off at the end of the particle range, i.e., the depth dose profile is inverted compared to photon beams. • They exhibit an increased biological effectiveness in particular at the end of their range and thus in the target volume. • The spatial distribution of stopping particles can be monitored by means of PET-techniques making use of the small amount of radioactive projectile fragments. Ion beams were first used for medical applications in 1954 in Berkeley. Since then, several treatment facilities for tumour therapy have been established worldwide, and approximately 25 000 patients have been treated with protons and 3000 patients with heavier ions successfully. As an example, the specific advantages of the heavy ion therapy facility at GSI Darmstadt established in cooperation with the Radiological Clinics and DKFZ Heidelberg and FZ Rossendorf will be described. In contrast to most existing facilities, it is based on an active beam delivery system, using magnetic deflection of a pencil beam (raster scan) and accelerator energy variation to adjust the penetration depth. Thus, an optimal conformation of the dose to the target volume is achieved. PET-measurements allow for a quasi on-line monitoring of the 3D distribution of stopping particles and in particular of the position of the distal edge of the dose distribution. Furthermore, in the treatment planning procedure the radiobiological properties of ion beams are taken into account in great detail. In December 1997, patient treatments started at GSI, and up to now 42 patients were treated with carbon ions alone or in a mixed carbon/photon beam regime.

Formation of an effective electric field in track regions during the stopping of fast heavy charged particles in materials

A microscopic approach is used to study the formation of an electric field near the trajectories of fast heavy charged particles propagating in various materials. The analysis is based on determining the space—time distribution function of the fast δ-electrons generated when heavy ions are stopped in materials and the electric current produced by them. The spatial dependence of the electric field strength is determined at various times. The results are used to analyze the process of electric field energy transfer to the ionic subsystem. The spatial distribution of the energy acquired by the ionic subsystem from the electric field is determined over its characteristic lifetime. A mechanism is proposed to explain the formation of track regions both as a result of the higher local heating of the ionic subsystem and as a result of the possible irreversible displacement of the atoms from nodal points.

Scaling properties of particle density fields formed in simulated turbulent flows.

Direct numerical simulations of particle concentrations in fully developed three-dimensional turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(lambda)) of 40, 80, and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large-scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parametrized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approximately 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70x10(6) particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum f(alpha), derived from measures obtained after binning particles into cells ranging from 2eta to 15eta in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self-similar across the scale range explored. However, spectra obtained at the 2eta, 4eta, and 8eta scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow independent. The singularity spectra found for 2eta-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(lambda)=110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(lambda) turbulent flows.

On the generation of radiation defects by accelerated ions in silicon

The introduction of centers of generation of charge carriers in pure Si is examined in the framework of the interaction of nonequilibrium defects and charge carriers directly in the track of an ion. An experiment on a particles with energies of 1.0–5.0 MeV is supplemented by the results of a numerical simulation of the stopping of such particles in Si. It is shown that the primary defects arising at the end of the track form a smaller number of generation centers. This is explained by the trapping of components of Frenkel pairs of charge carriers, the concentration of which in the track undergoes a 3-fold increase by the end of the range. Charge exchange between vacancies and interstitial atoms both accelerates recombination and lowers the number of primary defects participating in the subsequent complex-formation.

Stopping of charged particles in a magnetized classical plasma

The analytical and numerical investigations of the energy loss rate of the test particle in a magnetized electron plasma are developed on the basis of the Vlasov-Poisson equations, and the main results are presented. The Larmor rotation of a test particle in a magnetic field is taken into account. The analysis is based on the assumption that the energy variation of the test particle is much less than its kinetic energy. The obtained general expression for stopping power is analyzed for three cases: (i) the particle moves through a collisionless plasma in a strong homogeneous magnetic field; (ii) the fast particle moves through a magnetized collisionless plasma along the magnetic field; and (iii) the particle moves through a magnetized collisional plasma across a magnetic field. Calculations are carried out for the arbitrary test particle velocities in the first case, and for fast particles in the second and third cases. It is shown that the rate at which a fast test particle loses energy while moving across a magnetic field may be much higher than the loss in the case of motion through plasma without magnetic field.

Electroweak baryogenesis and Higgs and stop searches at LEP and the Tevatron

It has been recently shown that the observed baryon number may originate at the electroweak phase transition, provided that the Higgs boson and the lightest stop are sufficiently light. In this work, we perform a detailed analysis, including all dominant two-loop finite-temperature corrections to the Higgs effective potential, as well as the non-trivial effects proceeding from the mixing in the stop sector, to define the region of parameter space for which electroweak baryogenesis can happen. The limits on the stop and Higgs masses are obtained by taking into account the experimental bounds on these quantities, as well as those coming from the requirement of avoiding dangerous color breaking minima. We find for the Higgs mass m h ⪷ 105 GeV , while the stop mass may be close to the present experimental bound and must be smaller than, or of the order of, the top quark mass. These results provide a very strong motivation for further non-perturbative analysis of the electroweak phase transition, as well as for the search for Higgs and stop particles at the LEP and Tevatron colliders.

Stop production at hadron colliders

Stop particles are expected to be the lightest squarks in supersymmetric theories and the search for these particles is an important experimental task. We therefore present the cross sections for the production processes pp/pp → t̃1t̃1andt̃2t̃2 at Tevatron and LHC energies in next-to-leading order supersymmetric QCD. The corrections stabilize the theoretical predictions for the cross sections, and they are positive, thus raising the cross sections to values above the leading-order predictions. Mixed t̃1t̃2/t̃1t̃2 pairs can only be generated in higher orders at strongly suppressed rates.

The high-LET radiation component measured during the EUROMIR-94 mission

Stacks of CR-39 plastic nuclear track detectors were mounted inside the MIR-station during the EUROMIR-94-mission. We present LET-spectra determined separately for long range cosmic ray heavy ions and for short range target fragments produced in nuclear interactions of cosmic rays and measured charge distributions for relativistic and stopping particles.

Relative contribution of various factors to the formation of the energy spectrum of fast, medium-energy, charged particles and ions transmitted through a thin target with fluctuations of the target thickness

The characteristics of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil are investigated theoretically and experimentally as functions of the angle of incidence of the beam on the target. Analytical expressions for the average characteristics of the transmitted-particle energy spectrum are determined for the case of small-angle scattering. The combined influence of various factors affecting the formation of the energy spectra is taken into account: systematic stopping of particles in the medium, fluctuations of the particle energy losses in inelastic collisions, bending of the particle trajectories due to multiple elastic scattering, and fluctuations of the target thickness. It is shown that the contributions of these factors to the width of the transmitted-particle energy spectrum depend differently on the angle of incidence of the beam on the target surface. On the basis of this differentiation it is inferred from the experimental dependence of the width of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil on the angle of incidence of the beam that fluctuations of the particle energy losses in inelastic collisions are the predominant factor in the formation of the proton energy spectra.

A nonlinear theory of charged-particle stopping in non-ideal plasmas

The stopping power S=S1+SB for charged particles in non-ideal degenerate quantum plasmas is calculated with the help of the dielectric formalism in an approximation corresponding to taking account of the Barkas effect (the term SB; the term S1 corresponds to the Bethe formula). It is found that for a high projectile velocity vp>vF (where vF is the Fermi velocity) in non-ideal plasmas, SB∝e3pv−3p (where ep is the charge of the projectile), the well-known law for the Barkas effect, SB∝e3pv−5p being valid only for ideal plasmas. This relation explains a number of experiments on stopping of different charged particles (protons, muons and heavy ions) in metals without the introduction of fitted parameters. The possibility of extending of this theory to gaseous non-ideal plasmas arising in inertial-confinement fusion (ICF) experiments is also briefly discussed.

The strong interaction shift and width of the ground state of pionic hydrogen

The 3p-1s transition in pionic hydrogen was investigated with a high-resolution crystal spectrometer system. From the precisely measured transition energy, together with the (calculated) electromagnetic energy, the strong interaction shift of the 1s state was obtained as ϵ 1s = −7.127 ± 0.028(stat.)± 0.036(syst.) eV (attractive). From the natural line width, measured for the first time, we determine the decaywidth of the 1s state: Γ 1s (decay) = 0.97 ± 0.10(stat.)± 0.05(syst.) eV. With the recently calculated electromagnetic corrections the s-wave scattering lengths of an isospin symmetric strong interaction are deduced. The scattering length for elastic scattering of a negative pion on a proton is a π − p→ π − p h = 0.0885±0.00003(stat.)±0.0006(syst.) m π −1. The scattering lengthe for single charge exchange is found to be a π − p→ π 0 n h = −0.136 ± 0.007(stat.) ± 0.003(syst.) m π −1. The experiment was performed at the Paul Scherrer Institute (PSI) in Switzerland. A focussing crystal spectrometer with an array of bent crystals, the cyclotron trap (a magnetic system designed to increase the particle stop density) and a CCD (charge-coupled device) detector system were employed. The results from the pionic hydrogen experiment — together with those from the pionic deuterium experiment — were used to test the isospin symmetry of the strong interaction. The present data are still consistent with isospin sysmmetry.

Search for supersymmetric particles at [formula omitted] at LEP

A search for supersymmetric particles (charginos, neutralinos, sleptons and stop quarks) has been performed with data collected by the L3 detector during the November 1995 run of the LEP collider at centre of mass energies between 130 and 140 GeV with a total integrated luminosity of 5.1 pb −1. We observe no signal for supersymmetric particles and we set improved exclusion limits on their production cross sections and masses.

A Numerical Study of Dispersion and Local Exhaust Capture of Aerosols Generated from a Variety of Sources and Airflow Conditions

Focus is put on aerosol source parameters and their influence on aerosol dispersion and capture by a local exhaust. The studied parameters were particle diameter, density, and initial velocity. Included in the study was the influence of obstacles and airflow patterns. Direct capture efficiency of an exhaust above the contaminant source was used to compare the influence of the studied parameters. The study was based on a numerical model that computes the particle trajectories, taking inertia, drag forces, gravity, and turbulence into account. The relevance of particle relaxation time, aerodynamic diameter, and stopping distance is discussed. It is concluded that local exhaust capture of passively emitted particles can be described by particle relaxation time and the vertical air velocity at the emission point. The influence on direct capture efficiency from particle initial velocity is limited compared to imposed airflow patterns as jets and cross drafts. A table underneath the contaminant source may impro...

A trigger for the identification of pions stopped in an active target

The total cross sections of the π +p → π + π +n and π −p → π + π −n reactions near threshold can be used to obtain scattering lengths which are directly comparable to predictions of chiral perturbation theory. Data for these reactions were taken at TRIUMF using a segmented active scintillator target. The signature of a π + in an active target segment was a prompt pulse caused by the particle stopping, followed by a second pulse due to the π + to μ + decay. TRIUMF 500 Mhz transient digitisers were used to record the scintillator outputs in 2 ns steps so that the double pulses could be identified with high efficiency in off-line data analysis. A second level trigger able to reject events in less than 10 μs was necessary to avoid a prohibitively high deadtime due to the long read-out time of the digitisers. It was implemented with fast ECLine electronics and increased the useful event acquisition rate by a factor of more than forty.

Self-organized criticality in asymmetric exclusion model with noise for freeway traffic

The one-dimensional asymmetric simple-exclusion model with open boundaries for parallel update is extended to take into account temporary stopping of particles. The model presents the traffic flow on a highway with temporary deceleration of cars. Introducing temporary stopping into the asymmetric simple-exclusion model drives the system asymptotically into a steady state exhibiting a self-organized criticality. In the self-organized critical state, start-stop waves (or traffic jams) appear with various sizes (or lifetimes). The typical interval 〈 s〉between consecutive jams scales as 〈 s〉 ≃ L v with v = 0.51 ± 0.05 where L is the system size. It is shown that the cumulative jam-interval distribution N s ( L) satisfies the finite-size scaling form ( N s ( L) ≃ L − v f( s/ L v ). Also, the typical lifetime 〈m7rang; of traffic jams scales as 〈 m〉 ≃ L v ′ with v′ = 0.52 ± 0.05. The cumulative distribution N m ( L) of lifetimes satisfies the finite-size scaling form N m ( L)≃ L −1 g( m/ L v ′).

Charge-exchange and energy-loss statistics of swift penetrating ions

A general and powerful formalism has been developed for computation of energy-loss spectra of penetrating charged particles in the presence of charge exchange. Options on the input side are the cross sections for electron capture and loss, transition rates for radiative and nonradiative spontaneous processes and their associated energy losses or gains, and finally, cross sections for all processes that contribute to particle stopping but are not associated with charge exchange. The formalism generates an n × n transfer matrix, where n is the number of states needed for an adequate description of the projectile under consideration. This matrix delivers the joint distribution of energy loss and exit charge state for a given incident charge state and energy.The formalism can be used in principle as an alternative for Monte Carlo simulation, but until now we have concentrated on direct evaluation of key experimental parameters related to the energy-loss spectrum integrated over all exit charge states, in particular, mean energy loss, straggling, and skewness. Generally, valid analytic expressions have been found for these quantities, each of which can be separated into a stationary term representing chargestate equilibrium and a transient depending on the incident charge state. A brief survey is given of current analytic and numerical efforts addressing other experimental parameters.

Gluon radiation off scalar stop particles

We present the distributions for gluon radiation off stop-antistop particles produced in e + e − annihilation: e +e − → t ̃ t ̃ g . For high energies the splitting functions of the fragmentation processes t ̃ → t ̃ g and g → t ̃ t ̃ are derived; they are universal and apply also to high-energy stop particles produced at hadron colliders.