Reflection coefficient of low-energy ions as a universal function of the scaled transport cross section

Multiple collision theory of heavy ion ranges in an infinite medium has been used to calculate the reflection coefficient from the penetration profile, by a method first described by Bottiger et al. Interaction with target electrons has been neglected and nuclear collisions have been described by the power cross sections. Calculations are restricted to low reduced ion energies epsilon(0) less than or equal to 0.1 and to target/ion mass ratios mu less than or equal to 10, when electronic stopping is much less than the nuclear stopping. The Gaussian approximation of the pen -tration profile and the reflection coefficient are found in a form of simple analytic formulas. Furthermore, the penetration profile was constructed by using Edgeworth expansion and moments of the distribution up to the fourth order, and the reflection coefficient was determined from the profile. Good agreement between the analytical results and the reflection coefficient obtained from Edgeworth expansion was found, for target atom/ion mass ratios mu greater than or equal to 1.3. It is shown that the reflection coefficient is a universal function of the scaled transport cross section. The scaling is fulfilled for upsilon greater than or equal to 2, when ion reflection is determined by large-angle multiple collisions, and breaks down for upsilon LT 1 i.e. mu LT 1, when scattering angles are small. Results are compared with TRIM computer simulation data. PACS: 79.20. Rf

Scaling properties in single collision model of light ion reflection

Light ion reflection from solids in the keV energy region has been studied within the single collision model. Particle and energy reflection coefficients as functions of the scaled transport cross section have been calculated numerically by utilizing the exact scattering function for the Kr-C potential and analytically with an effective power approximation for the same potential. The obtained analytical formulae approximate very accurately to the numerical results. Comparison of the calculated reflection coefficients with the experimental data and computer simulations for different light ion-heavy target combinations shows that the scaled transport cross section remains a convenient scaling parameter in the single collision domain, as adopted previously in multiple collision theory. (C) 2003 Elsevier B.V. All rights reserved

Reflection coefficients of light ions for the inverse-square interaction potential

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 pathlength. Analytic expressions for the particle and energy reflection coefficients were derived and our results are compared with a large number of computer simulation data. (C) 2001 Elsevier Science B.V. All rights reserved

The albedo problem of low-energy light ions treated analytically in the DP0 flux approximation

The energy dependent albedo problem of low-energy light ions from heavy targets is considered in a multiple-collision model. The ion transport equation is treated with the assumptions that (i) the distribution function is almost isotropic and (ii) the transport cross section depends only on initial ion energy. The transport equation is Laplace transformed in relative path length and solved by applying the DP0 flux approximation in angle, Reflected energy spectra, particle and energy reflection coefficients are analytically derived. A comparison of DP0 results with age theory, computer simulation data and experimental results is made

Analytic approximations of the H-function based on different DPN procedures

Three approximate analytic expressions for the H-function are derived by using ordinary and flux decomposition DPN method. The accuracy of approximations is examined and comparison with similar formulas of the other authors is performed. As an application of the approximate H-functions the energy-dependent particle albedo problem is treated analytically. (C) 1998 Published by Elsevier Science Ltd. All rights reserved

Analytical solutions of the Boltzmann transport equation for light ion reflection

Reflection of light ions from solids have been calculated in the low-energy region where large-angle multiple collisions dominate. Backscattering parameters are obtained as a solution of the Boltzmann equation in the transport approximation. The Laplace transformed equation, which has the form of a one-group transport equation for isotropic scattering, has been solved by using an accurate analytical approximation of Chandrasekhars H-function. Universal curves as well as analytical results are presented for reflected energy spectra integrated over all ejection angles, particle and energy reflection coefficients, and total angular distribution of backscattered ions. Calculations have been done for different angles of incidence. For normal ion incidence and primary energies higher than 100 eV, the agreement between analytical theory and computer simulation data is satisfactory

Influence of anisotropy of Compton scattering on low energy x-ray reflection

The reflection of x-rays from a semi-infinite water target, for energies ranging from 10 to 60 keV, often used in x-ray diagnostics, is investigated by Monte Carlo simulation. The same process was also treated analytically as the classical albedo problem for isotropic scattering without energy loss. Good agreement of results for the angular distribution of reflected photons of the two approaches is obtained for higher photon energies from the energy range considered. Multiple collision scattering dominates at higher energies, leading to isotropization of the photon distribution. Discrepancies between the isotropic scattering model and Monte Carlo results appear at the lower part of the energy range. Monte Carlo results show that at these energies photon reflection is governed mainly by single collisions and that these discrepancies are caused by anisotropy of the distribution of single backscattered photons. It is shown that the inclusion of the anisotropy of single Compton backscattering in the analytical model greatly improves the agreement with Monte Carlo results

The character of reflection and transmission of xrays at energies used in radiological diagnostics

Without greater investments, the improvement of radiation protection and decrease of irradiation of medical workers as well as patients in X-ray diagnostics, may be achieved only by getting first a deeper insight into X-ray transport and reflection in human body like tissues at energies used in X-ray diagnostics. It is shown that at these energies, with high accuracy, the X-ray transport and reflection may be treated as a classical monoenergetic particle transport with isotropic scattering. This situation allows the analytical treatment, what may have practical implications.Conference on Applied Physics in Serbia, May 27-29, 2002, Belgrade, Yugoslavi

Le Grand écho du Nord de la France

18 mars 18961896/03/18 (A78,N78).Appartient à l’ensemble documentaire : NordPdeC