F. Salvat

PENELOPE: An algorithm for Monte Carlo simulation of the penetration and energy loss of electrons and positrons in matter

Abstract A mixed algorithm for Monte Carlo simulation of relativistic electron and positron transport in matter is described. Cross sections for the different interaction mechanisms are approximated by expressions that permit the generation of random tracks by using purely analytical methods. Hard elastic collisions, with scattering angle greater than a preselected cutoff value, and hard inelastic collisions and radiative events, with energy loss larger than given cutoff values, are simulated in detail. Soft interactions, with scattering angle or energy loss less than the corresponding cutoffs, are simulated by means of multiple scattering approaches. This algorithm handles lateral displacements correctly and completely avoids difficulties related with interface crossing. The simulation is shown to be stable under variations of the adopted cutoffs; these can be made quite large, thus speeding up the simulation considerably, without altering the results. The reliability of the algorithm is demonstrated through a comparison of simulation results with experimental data. Good agreement is found for electrons and positrons with kinetic energies down to a few keV.

An algorithm for Monte Carlo simulation of coupled electron-photon transport

Abstract An algorithm for Monte Carlo simulation of coupled electron-photon transport is described. Electron and positron tracks are generated by means of PENELOPE, a mixed procedure developed by Baro et al. [Nucl. Instr. and Meth. B 100 (1995) 31]. The simulation of photon transport follows the conventional, detailed method. Photons are assumed to interact via coherent and incoherent scattering, photoelectric absorption and electron-positron pair production. Photon interactions are simulated through analytical differential cross sections, derived from simple physical models and renormalized to reproduce accurate attenuation coefficients available from the literature. The combined algorithm has been implemented in a FORTRAN 77 computer code that generates electron-photon showers in arbitrary materials for the energy range from ∼1 GeV down to 1 keV or the binding energy of the L-shell of the heaviest element in the medium, whichever is the largest. The code is capable of following secondary particles that are generated within this energy range. The reliability of the algorithm and computer code is demonstrated by comparing simulation results with experimental data and with results from other Monte Carlo codes.

Experimental benchmarks of the Monte Carlo code penelope

Abstract The physical algorithms implemented in the latest release of the general-purpose Monte Carlo code penelope for the simulation of coupled electron–photon transport are briefly described. We discuss the mixed (class II) scheme used to transport intermediate- and high-energy electrons and positrons and, in particular, the approximations adopted to account for the energy dependence of the interaction cross-sections. The reliability of the simulation code, i.e. of the adopted interaction models and tracking algorithms, is analyzed by means of a comprehensive comparison of simulation results with experimental data available from the literature. The present analysis demonstrates that penelope yields a consistent description of electron transport processes in the energy range from a few keV up to about 1 GeV.

Monte Carlo simulation of 0.1–100 keV electron and positron transport in solids using optical data and partial wave methods

Abstract A new Monte Carlo code for the detailed simulation of the transport of low-energy electrons and positrons in solids is presented, including a critical discussion of concepts and approximations in the scattering model. Inelastic scattering is calculated using a Bethe surface model based on optical and photoelectric data for the solid, making possible a good accuracy at low energies, and a high resolution (∼1 eV) in simulated energy loss spectra. Exchange corrections for electrons and relativistic corrections for energies up to ∼100 keV are included. Elastic scattering is calculated by means of a differential cross section obtained by relativistic partial wave analysis for an exchange corrected muffin-tin Dirac-Hartree-Slater atomic potential. In the simulation, no adjustments of parameters to empirical scattering data are made. For comparison, measurements have been made of the characteristic low energy loss spectrum of 100 keV electrons through a thin silicon film. Simulated results for electrons and positrons are also compared with other available experimental data, in particular at low (a few keV) energies. In general, very good agreement is obtained.

Monte Carlo simulation of x-ray spectra generated by kilo-electron-volt electrons

We present a general algorithm for the simulation of x-ray spectra emitted from targets of arbitrary composition bombarded with kilovolt electron beams. Electron and photon transport is simulated by means of the general-purpose Monte Carlo code PENELOPE, using the standard, detailed simulation scheme. Bremsstrahlung emission is described by using a recently proposed algorithm, in which the energy of emitted photons is sampled from numerical cross-section tables, while the angular distribution of the photons is represented by an analytical expression with parameters determined by fitting benchmark shape functions obtained from partial-wave calculations. Ionization of K and L shells by electron impact is accounted for by means of ionization cross sections calculated from the distorted-wave Born approximation. The relaxation of the excited atoms following the ionization of an inner shell, which proceeds through emission of characteristic x rays and Auger electrons, is simulated until all vacancies have migra...

Monte Carlo simulation of bremsstrahlung emission by electrons

An algorithm for the simulation of bremsstrahlung emission by fast electrons using numerical cross sections is described. It is based on natural factorization of the double-differential cross section and on the fact that the intrinsic angular distribution of photons with a given energy can be very closely approximated by a Lorentz-boosted dipole distribution. The parameters of this angular distribution vary smoothly with the atomic number of the target atom and with the energies of the projectile’s electron and the photon emitted. Results from simulations of thick-target bremsstrahlung are compared with experimental data.

Cross sections for K-shell ionisation by electron impact

A semi-phenomenological method to compute the cross section for bound shell ionisation of atoms by impact of relativistic electrons is proposed. This method involves a simple schematisation of the Bethe surface, which is obtained from the experimental optical oscillator strength distribution. The authors approach may be used to describe the ionisation from any bound shell. They consider in detail the case of K-shell ionisation and derive an analytical formula for the differential cross section on the basis of a hydrogenic optical oscillator strength density. Close collisions are described by the Moller differential cross section, thus incorporating exchange effects. Empirical corrections to the Born approximation for energies near the ionisation threshold are introduced. The relationship of their approximation and the Weizsacker-Williams method of virtual quanta is also discussed.

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

A physical model for the simulation of x-ray emission spectra from samples irradiated with kilovolt electron beams is proposed. Inner shell ionization by electron impact is described by means of total cross sections evaluated from an optical-data model. A double differential cross section is proposed for bremsstrahlung emission, which reproduces the radiative stopping powers derived from the partial wave calculations of Kissel, Quarles and Pratt [At. Data Nucl. Data Tables 28, 381 (1983)]. These ionization and radiative cross sections have been introduced into a general-purpose Monte Carlo code, which performs simulation of coupled electron and photon transport for arbitrary materials. To improve the efficiency of the simulation, interaction forcing, a variance reduction technique, has been applied for both ionizing collisions and radiative events. The reliability of simulated x-ray spectra is analyzed by comparing simulation results with electron probe measurements.

Measurements of K-shell ionization cross sections of Cr, Ni and Cu by impact of 6.5-40 keV electrons

Results from measurements of K-shell ionization cross sections of the elements Cr, Ni and Cu by electron impact with energies in the range 6.5-40 keV are presented. Cross sections were obtained by measuring characteristic x-rays emitted from (1-6 nm thick) films of the studied elements deposited on self-supporting carbon backing films. The procedure yields relative cross sections with uncertainties of the order of 2%. Transformation to absolute units increases the uncertainties to about 10%. Our results are compared with those from other groups and with two calculations based on the first Born approximation, which include corrections for exchange, Coulomb and relativistic effects. A simple empirical formula that accurately describes the energy dependence of the measured cross sections is provided.

Monte Carlo simulation of kilovolt electron transport in solids

A Monte Carlo procedure to simulate the penetration and energy loss of low‐energy electron beams through solids is presented. Elastic collisions are described by using the method of partial waves for the screened Coulomb field of the nucleus. The atomic charge density is approximated by an analytical expression with parameters determined from the Dirac–Hartree–Fock–Slater self‐consistent density obtained under Wigner–Seitz boundary conditions in order to account for solid‐state effects; exchange effects are also accounted for by an energy‐dependent local correction. Elastic differential cross sections are then easily computed by combining the WKB and Born approximations to evaluate the phase shifts. Inelastic collisions are treated on the basis of a generalized oscillator strength model which gives inelastic mean free paths and stopping powers in good agreement with experimental data. This scattering model is accurate in the energy range from a few hundred eV up to about 50 keV. The reliability of the sim...