Individual Collisions Research Articles

Heavy ion damage in silicon and germanium

High resolution transmission electron microscopy techniques have been used to obtain information on the contrast, spatial distribution, size and annealing behaviour of the damaged regions produced within individual collision cascades by heavy ion bombardment of Si and Ge. Of particular interest was the dependence of the above features on the average deposited energy density θ ν within the collision cascade. Implants were performed at 35–50 K using monatomic and diatomic ions of 75 As, 121 Sb, 128 Te and 209 Bi, having incident energies of 10–120 keV, which meant that θ ν varied from 0.02 to 5.5 eV/atom. The bombarding ion fluences used covered the range 1.0 × 10 11 to 1.0 × 10 13 ions cm −2 . At high energy densities (θ gn 1.0 eV/atom), the visible damage produced in the main cascade consisted of a single, isolated damaged region. With decreasing values of θ ν (i.e. increasing ion implant energies), there was an increasing tendency for multiple damaged regions to be produced within the main cascade. Also, the fraction of the theoretical cascade volume occupied by a heavily damaged region steadily increased as θ ν increased. For high energy implants, at ion fluences > 5 × 10 11 ions cm- 2 , additional regions appeared which had lighter contrast than the multiple damaged regions formed in the initial stages. It is proposed that as overlap of the individual cascades occurs, the damage level in the peripheral regions becomes great enough to produce diffraction contrast in more extensive regions of the cascades. The annealing behaviour of the various damaged regions was also investigated at temperatures ranging from 300 to 775 K.

Collisions in aeolian saltation

Velocity vectors of saltating sand grains immediately before and after collision with a bed of mineralogically similar particles are looked at statistically. A cine-camera is used to film a controlled number of impacting grains in a wind tunnel. As a result, individual collisions can be examined.

Analytical treatment of high-energy nucleus-nucleus collisions including mean field effects: Boltzmann equation approach.

We study nucleus-nucleus collisions at high energy on the basis of Boltzmann's kinetic theory under the assumption that the incident energy per nucleon is high enough for nucleon-nucleon collisions to dominate the strength of the mean field so that the latter may be treated perturbatively. Then, by use of multiple collision expansion as well as linearization techniques and the eikonal approximation, we obtain the stationary distribution function from the Boltzmann equation with the nuclear mean field as external force. The distribution consists of an infinite sum over multiple collision components. Their momentum dependent parts obey a transport equation linear in the nuclear mean force field, and can be evaluated analytically. They differ from the solution of a Fokker-Planck-type equation without external forces, obtained previously, only by a shift in the momentum caused by the nuclear mean field. The present investigation confirms a recently developed phenomenological approach which has been successful in explaining the sideward kinetic energy flow of the particles emitted in individual nucleus-nucleus collision events.

Collisional ionisation and the atomic model

A consistent classical theory of atomic ionisation by charged particles is presented. The theory is consistent in the sense that not only individual collisions between the charged projectile and the atomic electron are described in a classical way (the theory is based on the binary-encounter approximation corrected for the collective field of the atom) but the entire atomic system considered as a classical structure with well defined electron orbits. The developed theory is applied to the analysis of atomic ionisation by heavy charged particles. The theoretical results appear to be sensitive to the atomic model used; in the case of the free-fall atomic model, they are found to be in good agreement with the experimental data.

High-energy gamma-ray emission in heavy-ion collisions.

Energy and angular distributions were measured for high-energy (E/sub ..gamma../>10 MeV) gamma rays from collisions of /sup 14/N on Pb, Zn, and C at beam energies of E/A = 20, 30, and 40 MeV. The gamma-ray energy spectrum was measured to about 120 MeV at E/A = 40 MeV and to about 80 MeV at E/A = 20 MeV. For E/sub ..gamma../>20 MeV the spectra are roughly exponential with characteristic slope parameters ranging from 10.0 MeV for /sup 14/N+Pb at E/A = 20 MeV to 14.2 MeV at E/A = 40 MeV. Although the mechanism responsible for high-energy gamma-ray emission is not well understood, reasonable agreement is obtained with a model employing bremsstrahlung from individual neutron-proton collisions in the heavy-ion collision.

Stochastic theory of equilibrium charge-state distributions of heavy ions in gases

A stochastic theory of equilibrium charge-state distributions is presented and its explicit relation to the underlying single ion-atom collision is shown. In this approach each individual collisions is regarded as a stochastic process in which either loss or capture of one or several electrons occurs. The result is a universal representation of charge-state distributions which reproduces the observed asymmetries in terms of a single energy-independent parameter. A statistical analysis shows that this parameter, which is related to a correlation function in single collisions, assumes essentially two values only, leading to the log normal and gamma distributions, respectively. Furthermore the theory predicts a scaling law for single collisions which was fulfilled by the recent cross section measurements of Astner and co-workers (1984).

Space-time correlation function representation of reactive scattering by large systems

Cross sections for atomic or molecular reactive scattering from a medium are expressed in terms of space-time correlation functions of the medium and transition amplitudes for individual reactive collisions. Among the physical effects included thereby are energy and momentum transfer to the medium. The relevant space-time correlation function for a reaction of type A + M → B + C is a one-particle Green's function describing creation and propagation of an “M hole”.

Ice conductivity restraints on the inductive theory of thunderstorm electrification

According to the inductive theory of thunderstorm electrification, a small ice crystal bouncing off the underside of a larger hydrometeor falling in the presence of an electric field should remove some of the field‐induced polarization charge from the surface of the larger particle; subsequent gravitational separation of the two particles should then result in a rapid growth of the electric field. However, because of the finite surface conductivity of the ice, it is not obvious that the polarization charges can flow along the ice surface in the short interaction time. We report laboratory experiments on the effect of an external electric field on the charge transferred during individual collisions of small (typically, 100‐μm) ice spheres with larger ice targets. When the surface conductivity of the ice was artificially increased by using 10−2 M NaCl, the full theoretical charge transfer was observed, but at 10−5 M NaCl, no field‐dependent charge transfer could be detected. Airborne measurements of cloud and precipitation purity have shown that 10−4 M NaCl is occasionally reached in low‐level stratiform clouds in polluted regions, but even with this degee of contamination the inductive mechanism operates at less than 20% of its potential efficiency at −10°C; at lower temperatures this fraction is reduced still further. We conclude that the inductive mechanism cannot account for the observed electrification of thunderstorms unless other contaminants are having an unexpectedly large effect on the conductivity.

Individual collision cascades in static bcc polycrystals.

Collision cascades induced by self-irradiation of polycrystalline tungsten are calculated with the simulation program marlowe. Component analysis is used to describe their spatial configuration. The method is explained and the concepts derived from it enable one to characterize the individual cascades. The influence of the primary energy on their configuration as well as on the point defect and energy densities is shown. Cascades generated by channeled primaries are markedly different from those which undergo no dominant aligned scattering. Subcascade formation in polycrystals results from the channeling of secondary recoils and the probability of its occurrence is found to be greater as the primary energy increases. This contrasts with cascades simulated in random targets where no subcascade formation is observed. In addition, the analysis method reveals strong fluctuations in local point-defect-density distributions. It is suggested that these fluctuations are associated with nonuniformities in the deposited energy-density distributions. Finally, isotropic recombination is shown to affect individual cascade configurations as well as vacancy and interstitial densities in the core of the cascades. The aspects of the individual cascade development studied concur to show that the component analysis brings out specific characteristics that do not appear when the usual statistical approaches are used.

Comparison of various Monte Carlo schemes for simulation of low-energy electron transport in matter

A detailed comparison of various characteristics obtained in an electron transport calculation by Monte Carlo methods with experimental data is given. Some restrictions on the use of the condensed random-walk scheme and the continuous slowing-down approximation are demonstrated. The individual collision scheme proposed provides the best agreement with the experiments for electron energies E 0 less than 50 keV.

Computer simulation of the geometrical effect on the stopping power of a very thin Cu foil for 7 MeV protons

The energy loss of 7 MeV protons has been found to increase with increasing emergence angle in both metallic and organic thin foils. Computer simulations were performed for thin Cu foils in order to investigate the origin of this phenomenon. The individual collisions which protons underwent within the foils were found to be restricted by the determination of detection angles. Such a restriction causes the dependence of the energy loss on the emergence angle. Recently, another series of experiments were performed to study the systematic behaviour of the geometrical effect. An interesting behaviour was observed for Be foils; the energy loss of protons did not show a continuous increase with increasing emergence angle but showed no increase or a slight decrease at large emergence angles where the yield of the angular distribution due to multiple scattering was extremely small. A computer simulation was performed to investigate this behaviour for a very thin Cu foil instead of Be foils and was found to give a good qualitative reproduction of the behaviour.

Particle production, chemical equilibrium, and the quasiergodic hypothesis in high energy collisions

Starting from kinetic theory, it is shown that particles heavier than the pion are not produced in chemical equilibrium. A new theory based on the degree of the reaction is then formulated. Pion induced reactions, following pion production from individual nucleon-nucleon collisions give the main mechanism for the production of strange particles, such as K/sup +/'s. ''Subthreshold'' production is a natural consequence of the theory.

Properties of the Collision Operators of the Electron Boltzmann Equation for a Weakly Ionized Plasma. II. Compactness Proof and Statements on the Spectrum

AbstractThe compactness has been proved of the inscattering operator covering elastic, exciting and deexciting processes between electrons and heavy neutral particles. Starting point is the proof of the boundedness of the different inscattering operators for the individual collision processes using certain assumptions on the structure of the corresponding differential cross sections. Then, under somewhat more confined conditions the proff of compactness could be performed with the aid of the square integrability of an eightfold iterated kernel. On the basis of this property it was possible to draw conclusions with regard to the spectrum of the total collision operator. They are related to the continuous as well as the discrete part of the spectrum and are discussed in detail. For elastic collisions additional statements can be deduced from our investigation.

Mg+(3p) excitation amplitudes in slow Mg+-Ar collisions

The probabilities and amplitudes for exciting the magnetic sublevels of Mg+(3p) in collisions between accelerated Mg+ ions and Ar atoms have been studied by means of the polarised-photon, scattered-ion coincidence technique. Selected collision energies and scattering angles within the ranges 1.2-11 keV and 0.9-9 degrees were chosen. The excitation probability for the Mg+(3p) configuration shows an apparent angular threshold. A special effort was made to determine the amplitudes in the region of this threshold. Strongly polarised charge distributions are formed in the individual collisions. The direction of this polarisation is parallel to the collision plane and in most cases nearly perpendicular to the beam direction. In the region of the apparent angular excitation threshold it starts turning within the collision plane. In close collisions at high energies some degree of circular polarisation is observed.

K+production in relativistic heavy-ion collisions

Recent experimental data on K/sup +/ production at 2.1 GeV/nucleon are not explained by either the cascade model or the fireball model. Here we introduce a hybrid model in which the total kaon yield is given by individual nucleon-nucleon collisions but its momentum distribution is determined by the temperature of the pion. The model is able to explain the data. The possibility of studying K/sup +/ yield as a signature for the pionic instability in heavy-ion collisions is indicated.

Charge transfer accompanying individual collisions between ice particles and its role in thunderstorm electrification

AbstractExperiments were conducted with a wind tunnel in a cold‐room in order to investigate the individual charges transferred when ice spheres collided with an artificial hailstone. The charge transferred to a sublimating hailstone was negative and had a magnitude proportional to the velocity of impact and to the diameter of the ice sphere to the power 1.7. The charge transferred when 100μm diameter ice spheres collided with the hailstone at a velocity of 8ms−1 was typically –15 fC. No variation of charging could be detected over the temperature range –5 to –25 °C, or when the ice was doped with impurities, or when hailstones of different surface roughness were prepared.Hailstones which were cooled below the ambient cold‐room temperature and subsequently grew by deposition, charged positively by typically 100 fC per collision. However, a hailstone which was cooled by the same amount but was maintained in a sublimating condition charged negatively. These experiments show that thermal effects did not play a direct role in the charge transfer process. Experiments were performed with a riming hailstone in order to simulate the conditions found in a natural cloud. The hailstone charged positively at temperatures of –5°C and –10°C and negatively at –15°C and –20°C with liquid water contents in the range 0.05 gm−3 to 0.85gm−3, the magnitudes of the charges being typically 30 fC.It is suggested that the charge transfer occurs from one ice surface to the other at the contact interface and that the driving force for the charge transfer at the contact interfaces is the different surface potentials and/or different charge carrier densities of ice surfaces formed in different ways. It is possible that the charge carriers may be surface ions of a liquid like layer on the ice surface.The results with the riming hailstone are consistent with thunderstorm observations that the negative charge centre is above the –10°C isotherm and that, although precipitation particles are predominantly negatively charged, a mixture of signs is usually present.

Charge transfer accompanying individual collisions between ice particles and its role in thunderstorm electrification

Charge transfer accompanying individual collisions between ice particles and its role in thunderstorm electrification

Monte‐Carlo Calculation of the Electron Transmission, Reflection, and Absorption in Solids in the Energy Range up to 10 keV

AbstractThe Monte‐Carlo model of individual collisions is applied for low energy electron transport calculations. The applicability of this model is analyzed in detail with theoretically calculated cross sections. Some semiempirical relations for the most important characteristics of the transmission, backscattering, and absorbed energy distributions for C, Mg, Al, Si, Ge, Bi solid targets are obtained.

Optogalvanic double-resonance spectroscopy

Optogalvanic double-resonance spectroscopy is proposed as a new method of state-selective spectroscopy in plasmas. It should be particularly valuable for molecular spectra in which individual vibrational progressions and collision- induced satellites can be observed.

Classical theory of transitions between degenerate states of excited hydrogen atoms in plasmas

The authors present a general classical theory of transitions between degenerate states of hydrogen-like atoms and ions, with particular application to multiple overlapping collisions with the charged particles of an isotropic plasma. They classify individual collisions as either Stark adiabatic or Stark sudden. The combined effects lead to a combination of diffusion and Poisson randomisation of the angular momentum, for which an explicit time-dependent solution is obtained in terms of elementary functions. The time constants, lambda D for the diffusion process and lambda P for the Poisson process, are given in terms of elementary functions of nuclear charge and principal quantum number, reduced mass, charge and density of incident particles and temperature. The equilibration rate for angular momentum, l, in the absence of other processes is equal to the sum over lambda D+ lambda P for all charged species.