arXiv subjects

Francesc Salvat

Publications and source records attributed to Francesc Salvat.

5 recordsLinked to original sources

arXiv2026

Collisions and Stopping of Fast Charged Particles in Matter

This text is intended to offer a consistent presentation of the theory of collisions and stopping of charged particles in matter, limited to the range of intermediate kinetic energies where atomic aggregation effects are relatively unimportant and processes such as the creation of particle-antiparticle pairs are not likely to occur. The first three Chapters contain introductory material on the classical description of electromagnetic fields in matter, an overview of quantum wave equations for a particle in a central potential, and an account of elementary atomic-structure models. Chapters 4 and 5 are devoted to the classical and quantum theories of elastic collisions of charged particles with atoms. The theory of inelastic collisions and stopping is split into two parts: first, collisions with atoms are considered within the plane-wave Born approximation in Chapter 6, which includes a derivation of the Bethe stopping power formula; second, the theory of inelastic collisions in dense materials is based on the dielectric formalism, which is formulated for the electron gas, and extended to arbitrary materials by means of optical-data models in Chapter 7. Chapter 8 offers a detailed review of the theory of stopping, starting with the classical study by Bohr and ending with derivations of the Bloch and Barkas corrections to the stopping power. Chapter 9 deals with general aspects of transport theory, including derivations of energy-straggling distributions and multiple-scattering distributions, which are the basis for condensed simulation schemes of charged particle transport. Finally, Chapter 10 describes the Fortran programs elastic and sbethe, which implement the main theoretical models presented in the preceding Chapters and are distributed as ancillary information.

physics.atom-ph↗

arXiv2026

Inelastic collisions of fast charged particles with atoms. Relativistic plane-wave Born approximation

A detailed formulation of the relativistic plane-wave Born approximation for inelastic collisions of charged particles with free atoms and positive ions is presented. The wave functions of the target atom or ion are calculated from a central-field independent-electron model with the Dirac-Hartree-Fock-Slater self-consistent potential, and the electromagnetic field is expressed in the Coulomb gauge. The double-differential cross section, depending on the energy loss and the recoil energy, is given as a sum of two terms which are products of purely kinematic factors and the generalized oscillator strengths (GOSs). Transitions induced by the instantaneous Coulomb interaction between the projectile and the active target electron are described by the longitudinal GOS. Transitions caused by the transverse interaction (exchange of virtual photons) are accounted for by a transverse GOS. We derive closed expressions for the longitudinal and transverse GOSs in terms of vector coupling coefficients and radial integrals. A set of Fortran programs have been written to compute the GOSs, the energy-loss differential cross section, and integrals of the latter. A complete numerical database of GOSs has been calculated for all the subshells of the ground-state configuration of neutral atoms of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). A systematic derivation of asymptotic formulas for the total cross section, the stopping cross section and the energy-straggling cross section is presented. The shell correction to the asymptotic formula for the stopping cross section of protons is obtained from the difference between computed numerical values and the predictions of that formula.

physics.atom-ph↗

arXiv2024

Causality and dielectric functions for linear media with spatial dispersion

We extend Kramers-Kronig relations beyond the optical approximation to dielectric functions that depend not only on frequency but on the wave number as well. This implies extending the notion of causality commonly used in the theory of Kramers-Kronig relations to include the fact that signals cannot propagate faster than light in vacuo. The extension is applied to some microscopic models for the dielectric function and is compared with previous generalizations. The results derived here also apply to general theories of isotropic linear response in which the response function depends on both wave number and frequency.

physics.class-ph↗

arXiv2023

Electromagnetic interaction models for Monte Carlo simulation of protons and alpha particles

Electromagnetic interactions of protons and alpha particles are modeled in a form that is suitable for Monte Carlo simulation of the transport of charged particles. The differential cross section (DCS) for elastic collisions with neutral atoms is expressed as the product of the DCS for collisions with the bare nucleus and a correction factor that accounts for the screening of the nuclear charge by the atomic electrons. The screening factor is obtained as the ratio of the DCS for scattering of the projectile by an atom with a point nucleus and the parameterized Dirac-Hartree-Fock-Slater (DHFS) electron density, calculated from the eikonal approximation, and the Rutherford DCS for collisions with the bare point nucleus. Inelastic collisions, which cause electronic excitations of the material, are described by means of the plane-wave Born approximation, with an empirical simple model of the generalized oscillator strength (GOS) that combines several extended oscillators with resonance energies and strengths determined from the atomic configurations and from the empirical mean excitation energy of the material. The contributions from inner subshells are renormalized to agree with realistic ionization cross sections calculated numerically from the DHFS self-consistent model of atoms by means of the plane-wave Born approximation. The resulting DCS allows analytical random sampling of individual hard inelastic interactions.

nucl-th↗

arXiv2020

Nuclear effects in proton transport and dose calculations

Interactions of protons with nuclei are modeled in a form that is suitable for Monte Carlo simulation of proton transport. The differential cross section (DCS) for elastic collisions of protons with neutral atoms is expressed as the product of the Rutherford DCS, which describes scattering by a bare point nucleus, and two correction factors that account for the screening of the nuclear charge by the atomic electrons and for the effect of the structure of the nucleus. The screening correction is obtained by considering the scattering of the projectile by an atom with a point nucleus and the atomic electron cloud described by a parameterization of the Dirac-Hartree-Fock-Slater self-consistent electron density. The DCS for scattering by this point nucleus atom is calculated by means of the eikonal approximation. The nuclear correction to the DCS for elastic collisions is calculated by conventional partial-wave analysis with a global optical-model potential that describes the interaction with the bare nucleus. Inelastic interactions of the projectile with target nuclei are described by using information from data files in ENDF-6 format, which provide cross sections, multiplicities, and angle-energy distributions of all reaction products: light ejectiles (neutrons, protons, . . . ), gammas, as well as recoiling heavy residuals. These interaction data have been used in the Monte Carlo transport code PENH, an extension of the electron-gamma code PENELOPE, which originally accounted for electromagnetic interactions only. The combined code system PENH/PENELOPE performs simulations of coupled electron-photon-proton transport. A few examples of simulation results are presented to reveal the influence of nuclear interactions on proton transport processes and on the calculation of dose distributions from proton beams.

nucl-th↗