[31a-P] Empirical formulas for reflection of light ions. II

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 1985

Empirical formulas for the number- and energy-backscattering coefficients of light ions normally incident on elemental solid targets are given. The formulas are valid for all the light ions of atomic numbers up to two with incident energies from about 10 eV to 100 MeV. Constants in the formulas have been determined by the least-squares fit to available experimental and selected computer-simulation data. The rms deviation of the data from the formulas is 31%.

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2011

The particle reflection coefficient of light keV ions backscattered from heavy solids as a function of the ion incidence angle has been determined by a suitable interpolation formula. The formula has two fitting parameters which are obtained by using results from two limiting analytic approaches: by the single collision model-in case of nearly perpendicular incidence; and by the small-angle multiple scattering theory-in case of glancing angles of incidence. The obtained interpolation formula is a universal function of the scaled transport cross section and the angle of incidence. Comparison of our calculations with Monte Carlo simulation data and the experimental results of other authors gives good agreement for particle reflection coefficient.

2008

The linear Boltzmann transport equation for diffusion and slowing down of low-energy light ions in solids is Laplace transformed in relative path-length and solved by applying the DP0 technique. The ion-target atom interaction potential is assumed to have a form of the inverse-square law and furthermore, the collision integral of the transport equation is replaced by the P_3 approximation in angular variable. The approximative Laplace transformed solution for the reflection function is found and inverted leading to the distribution of backscattered particles in the relative path-length. Analytic expression for the particle reflection coefficient was derived and our result is compared with computer simulation data.

Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2004

The linear Boltzmann transport equation for diffusion and slowing down of low-energy light ions in solids is Laplace transformed in relative path-length and solved by applying the DP0 technique. The ion-target atom interaction potential is assumed to have a form of the inverse-square law and furthermore, the collision integral of the transport equation is replaced by the P 3 approximation in angular variable. The approximative Laplace transformed solution for the reflection function is found and inverted leading to the distribution of backscattered particles in the relative path-length. Analytic expression for the particle reflection coefficient was derived and our result is compared with computer simulation data.

Journal of Applied Physics, 1984

The particle and energy reflection coefficients and the energy distribution of reflected particles for compound targets have been calculated using the single collision approximation. It is shown that for any compound target the reflection coefficients are expressed in terms of a universal function such as was empirically determined for elemental targets, when the Bragg rule is assumed for the stopping cross section. The results calculated numerically for WO3, TiC, and TiB2 are compared with the experimental ones to show reasonable agreement.

Bulletin of University of Osaka Prefecture, Series A, 1993

Electron and photon reflection ratios (in number and energy) for absorbers bombarded by electrons have been computed with the ITS Monte Carlo system version 3, and results are given in the form of tables. Electrons of energies from 0.1 to 100 MeV have been assumed normally incident on an effectively semi-infinite absorber. The absorbers considered are elemental solids of atomic numbers from 4 to 92 (Be, C, Al, Cu, Ag, Au, and U). An empirical equation for the electron number-reflection ratio has been formulated, by least-squares fit to experimental data collected from literature. Values of parameters derived from the Monte Carlo data on photon number- and energy-reflection ratios are graphically presented.

Nuclear Instruments and Methods, 1976

Total reflection coefficients (R), backscattered energy fractions (~,), and backscattered energy spectra are evaluated using a binary collision Monte Carlo technique for a variety of light ions (H, D, T, He) in the energy range 0.25-8 keV, incident on amorphous targets (C, Fe, Nb). The scattering is also evaluated for H on Nb for a range of incident angles and two electronic stopping values. The average scattered energy per reflected particle and the backscattered energy spectra are found to vary in a universal manner as a function of the reflection coefficient between the Rutherford high energy limit and a low energy multiple collision limit. Single crystal effects are also briefly discussed using a diffusional dechanneling model.

495 one employed in these experiments. The number of ions produced by a single a-particle under the special conditions of the experiment is easily found from the curve given in fig. 3. The determination of the ionisation current in the bulb then gives at once the total number of a-particles. Care has to be taken to obtain saturation and to avoid ionisation by collision, which occurs when too large a voltage is applied. I wish to acknowledge the assistance which Mr. E. Marsden has given me in some of these observations. In conclusion, I desire to express my gratitude to Prof. Rutherford for his valuable suggestions and his kind interest in the experiments. When /3-particles fall on a plate, a strong radiation emerges from the same side of the plate as that on which the /3-particles fall. This radiation is regarded by many observers as a secondary radiation, but more recent experi­ ments seem to show that it consists mainly of primary ^-particles, which have 'been scattered inside the material to such an extent that they emerge again at the same side of the plate* For a-particles a similar effect has not previously been observed, and is perhaps not to be expected on account of the relatively small scattering which a-particles suffer in penetrating matter.f In the following experiments, however, conclusive evidence was found of the existence of a diffuse reflection of the a-particles. A. small fraction of the a-particles falling upon a metal plate have their directions changed to such an extent that they emerge again at the side of incidence. To form an idea of the way in which this effect takes place, the following three points were investigated:— (I) The relative amount of reflection from different metals. (II) The relative amount of reflection from a metal of varying thickness. (I ll) The fraction of the incident a-particles which are reflected.

Institute for Data Evaluation and Analysis Technical Reports (IDEA-TR), 2018

The present volume contains five papers, published by Tatsuo Tabata and his coworkers from 1984 to 1985, in the form of the post-print re-edited by the use of LATEX. The studies described were made as a joint work of the former Institute of Plasma Physics, Nagoya University, and the Radiation Center of Osaka Prefecture and are classified as the category of interactions of light ions with solids (continuations of studies in Volume 8). Each paper includes the “Commentary” section written by the present editor at its end. Minor errors, mentioned there, of the published versions are corrected in this volume.

Institute for Data Evaluation and Analysis Technical Reports (IDEA-TR), 2018

The present volume contains two papers, published by Tatsuo Tabata and his coworkers from 1981 to 1983, in the form of the post-print re-edited by the use of LATEX. The studies described were made as a joint work of the former Institute of Plasma Physics, Nagoya University, and the Radiation Center of Osaka Prefecture (RCOP) and are classified as the category of interactions of light ions with solids. Each paper includes the “Commentary” section written by the present editor at its end. Minor errors, mentioned there, of the published versions are corrected in this volume.