Precise energy and angular distributions of 85.38 MeV/u Ar ions in solids are measured with the high-resolution spectrometer SPEG at GANIL. The nonuniformities of the target thickness were investigated with a laser-interferometric method. Stopping power, energy loss straggling, and angular scattering data are presented and compared with experimental data and theories.

We have examined zero-temperature metastable states of random-bond Ising models (random ferromagnets and spin glasses, in one, two, and three dimensions) for criticality (power-law sensitivity to single-spin-flip perturbations) and for limit cycles, with the following results. We found no evidence of criticality in metastable states obtained by quenches from high temperature. Near the metastability limit in a magnetic field, random ferromagnets in two and three dimensions are critical; the metastable states were generated by starting from a ground state and ramping a contrary field. Under a cycled magnetic field, both spin glasses and random ferromagnets quickly enter simple limit cycles.

A multiple-scattering distribution is calculated for angles larger than the maximum single-scattering angle. The small-angle Bothe formulation with appropriate modifications is used in the power-cross-section approximation. Although the distribution is asymptotically a Gaussian function multiplied by a series of Laguerre polynomials, a series expansion similar to those for the usual Bothe theory converges well out to large angles. The cutoff of the single-scattering kernel is ambiguous, so there is a free parameter. The alternative Goudsmit-Saunderson formalism is difficult to evaluate and is not easily summed to give asymptotic expansions, but with the aid of some tricks yields numerical results in good agreement with experiment.

The depth distribution of recoil daughter nuclei following the radioactive decay of implanted parent nuclei has been calculated. Moments of the depth distribution of the daughter nuclei are obtained from tabulated moments of the usual range distributions of the parent and daughter atoms. The daughter nuclei are nearly symmetrically distributed about the mean implantation depth with a variance slightly greater than a third of the square of the mean range of the daughter. The distribution may be represented by a Pearson Type II distribution or by the form exp(− a | x | p), with parameter p > 2. An example is given.

We have measured the increase in energy loss as a function of emergent angle for 1H and 4He ions traversing carbon foils. Our observations for energies E < 1 MeV are in agreement with theoretical predictions using the local density approximation for the impact parameter dependent inelastic energy loss.

Collision cascades in matter irradiated with heavy particles (ions, atoms, etc.) are seen to be approximate fractals, and their fractal dimension is calculated and discussed. Experimental and theoretical collision cascades are expected to be useful laboratories for the study of fractals. The fractal dimension of a cascade is calculated in three ways; the results agree whenever they may be expected to. High-energy cascades have low dimension, low-energy ones may become three-dimensional and space filling. Some other fractal aspects of atomic collisions in matter are commented on.

Recent measurements of the response of Si detectors to energetic light ions ( 1 H, 4 He) show evidence for nonlinearity. These data are in distinct contrast to previous investigations which assumed that the energy required to create an electron-hole pair depended only on atomic number and not on energy for a given ion. A summary of experimental results relating to this topic will be given, in order to search for inconsistencies in the data. Using this comparison, further experiments capable of yielding unambiguous results are suggested.

We have measured the increase in energy loss as a function of emergent angle for 1 H and 4 He ions traversing carbon foils. Our observations for energies E < 1 MeV are in agreement with theoretical predictions using the local density approximation for the impact parameter dependent inelastic energy loss.

A robust and conceptually simple numerical scheme for calculating moments of ion-implantation range distributions is presented. It allows calculation of moments to at least the fourth up to much higher energy than before, and inclusion of various complications, such as electronic straggling, charge-state-straggling, and nuclear-force scattering, only the first of which is discussed here. This scheme may be extended to calculate moments of damage and ionization distributions as well. Straggling in electronic stopping is incorporated in a simple approximation. A new method is used to construct two-dimensional distributions of implanted-ion density, illustrating at once both the longitudinal and transverse spreading of the beam.

We report measurements of the relative mean pulse height produced by 1H, 4He, 7Li and 16O ions in Si surface barrier detectors. The data are anomalous in that the pulse height for different ions of the same energy (after window and nonionizing losses are subtracted) increases with atomic number, contrary to observations for fission fragments. A simple model invoking a stopping power dependence of the energy required to create an electron-hole pair is consistent with all experimental data, suggesting that the response of Si detectors is nonlinear with particle energy.

The variance of the number of high-energy recoils produced in a cascade is calculated in the power-cross-section approximation. These' recoils have initial energy greater than some specified threshold value, which in turn is greater than a displacement energy. Displacement energy is neglected in this calculation. This distribution of high-energy-recoil number is wider than the Kinchin-Pease distribution but narrower than a Poisson distribution: the variance is (asymptotically) proportional to the number of recoils for all three, and the proportionality constant for the recoil number is greater than the Kinchin-Pease constant but less than unity. Both the asymptotic value of the variance and the energy dependence are obtained. These quantities should be of interest in the study of recoil implantation.

The angular distribution is calculated for a particle beam which has undergone both single scattering through a prescribed angle and multiple scattering. The usual assumptions are made: the target scatterers are immobile, and are homogeneously and randomly distributed, only binary collision events occur and the scattering has azimuthal symmetry, energy losses are negligible, and scattering angles are small in an absolute sense. The distributions are evaluated as power series for power-cross-section scattering, and in closed form for m = 12 and in the m = 1 (large-thickness or Gaussian) limit.

The energy loss spectrum of a beam of charged particles penetrating a layer of random material has been analyzed theoretically. A steepest-descent evaluation of the Bothe-Landau integral yields general expressions for the spectrum, the most probable energy loss, and the halfwidth, without reference to a particular collision cross section. The procedure has been tested against rigorous results for model cross sections as well as the Landau-Vavilov theory for free-Coulomb scattering.

The density of energy (LET) deposited in a lithium target by 100 MeV protons is estimated by two methods. The protons are slowed down by electronic stopping alone, nuclear stopping being negligible. Multiple scattering and transport of energy by recoil electrons (delta rays) are shown to be negligible.

A new method of solution is proposed for a Boltzmann equation describing the slowing down of charged particles in solids. It seems as if it would be more generally applicable. It can be considered as a multigroup method with the energy groups varying from point to point in a natural way dictated by the local spectrum. The energy moments of the density of moving particles are calculated at each point in the target, and at each point an extremal (in energy) density of particles is constructed. The extremal density allows for particles being stopped, and, hence, removed from the beam.

It is shown how one may calculate truncated multiple scattering distributions, in which any particles scattering beyond a specified limit, in angle or lateral spread, are immediately removed from the beam.

Type IV Pearson distributions have been used by several groups to represent ion implantation range distributions. It is pointed out here that these distributions are inappropriate, and type VI (or possibly type V) distributions should be used instead. It must be remembered that these distributions are only approximations to the true range distribution.

We try to understand the strangeness changing nonleptonic decays of kaons, hyperons, and the Ω− particle in terms of the modern, renormalized weak Hamiltonian expressed as a sum of four-quark Wilson operators, including the so-called penguin operators c5O5 and c6O6 arising from gluon radiative corrections. It is found that these decays, including the long-standing s-wave/p-wave puzzle in hyperon decays, can be understood if the Wilson coefficient [Formula: see text] has a sign opposite to that obtained from short-distance perturbative quantum chromodynamics calculations and has an effective value such that [Formula: see text].

The (vacancy) pair-separation function introduced by Dederichs and used by Sigmund et al. is examined in greater detail. Equations are given for finding moments of this quantity as functions of a recoil-energy threshold, and calculations are made in the limit of zero threshold energy. It is concluded that the sizes of observable damage spots are not directly predictable from knowledge of this function, unless the cascade is dense: the spot sizes are determined by whatever parameter breaks the power-law energy scaling of the cascade.