J. D. Martinez

TRANSPORT MEAN FREE PATH TABULATED FOR THE MULTIPLE ELASTIC SCATTERING OF ELECTRONS AND POSITRONS AT ENERGIES 20 MEV

The transport mean free path, or transport cross section, is tabulated for the elastic scattering of electrons and positrons in solid matter by means of a correction factor tc applied to the result of a simple screened Rutherford cross section. The correction factor table is based on differential cross‐section calculations using a combination of partial‐wave analysis (PWA), the Wentzel–Kramers–Brillouin approximation, and the Born approximation, and covers kinetic energies from 100 eV to 20 MeV. Results at low energies are compared with PWA calculations of higher accuracy. Nuclear size effects are discussed but not explicitly included. Applications are discussed.

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...

A simple model for electron scattering: inelastic collisions

A simple scattering model-providing analytical expressions of electron inverse mean free path, stopping power and straggling parameter-is proposed. Such a model can be used in Monte Carlo simulations of electron transport problems. Cross-sections are derived from a schematic Bethe surface based on the single-mode approximation for the free electron gas. Fairly good agreement with experiment results and with other theoretical calculations is found for electron energies in the range between 50 eV and 50 keV for free-electron-like materials. An easy empirical correction to the conduction band cross-section allows one to use the model for transition and noble metals.

Weight functions for integral conversion electron mössbauer spectroscopy (ICEMS)

Abstract Weight functions for ICEMS, computed from Monte Carlo simulation of electron transport, are tested for scaling properties. It is shown that energy scaling holds with high accuracy for a wide range of materials and electron energies. Mass scaling from iron to other materials is shown to be adequate except for low atomic number materials.

Elastic scattering of electrons by atoms: a semiphenomenological approach

Elastic scattering of non-relativistic electrons by atoms is described using a semiphenomenological effective potential which is based on the self-consistent Dirac-Hartree-Fock-Slater field and accounts for exchange and polarisation effects in a simple way. The reliability of an approximate method, yielding accurate cross sections with little numerical work, is investigated for energies down to about 100 eV. Theoretical results are compared with available experimental data.

Simple method for the simulation of multiple elastic scattering of electrons

A screened Rutherford cross section is modified by means of a correction factor to obtain the proper transport cross section computed by partial‐wave analysis. The correction factor is tabulated for electron energies in the range 0–100 keV and for elements in the range from Z=4 to 82. The modified screened Rutherford cross section is shown to be useful as an approximation for the simulation of plural and multiple scattering. Its performance and limitations are exemplified for electrons scattered in Al and Au.

Effect of the Wigner-Seitz boundary conditions on internal conversion coefficients

Solid state effects are taken into account in an internal conversion coefficients computation by using Wigner-Seitz boundary conditions. Both the bound and free electron wave functions are calculated from an atomic Dirac-Hartree-Fock-Slater self consistent potential. These internal conversion coefficients are compared with those obtained from the usual free atom boundary conditions.

A simplified method for the detailed Monte Carlo simulation of electron transport

A detailed simulation of electron transport in condensed materials is considered from an unconventional point of view. The basic ingredient of the approach presented is the well known fact that multiple scattering distributions are mainly sensitive to a few average quantities, namely the mean free paths and the first and second moments of the elastic and inelastic differential cross sections. These characteristic functions are assumed to be known and are introduced in the simulation code as input data characterizing the scattering medium. Angular deflections and energy losses are sampled from artificial probability distributions which reproduce the input values of the characteristic functions and allow the random generation of the involved variables in an easy way. The reliability of this scheme is demonstrated by comparing the simulation results, for transmission and backscattering of keV electron beams through aluminium and gold foils, with those from a detailed Monte Carlo code which uses realistic differential cross sections.

Theoretical estimates of mean excitation potentials of solids

Abstract Electron stopping powers for single element solid materials are computed by using the local density approximation. The scattering properties of the homogeneous electron gas are described by the Lindhard dielectric function and by a suitable analytical approximation allowing the introduction of exchange and relativistic effects. Estimated values of the mean excitation potential are obtained through numerical fitting of the Bethe formula to the computed stopping power.

A spin-polarized internal conversion coefficients computation for iron

The effect of electron spin polarization in the Fe atom has been introduced in an internal conversion (IC) computation. Two different models for the IC process have been used, but the results show no dependence on the model. The effect of spin polarization is larger than other corrections normally made in IC calculations. The ratio of the partial IC coefficient to the electron density at the nucleus has been studied for all shells in the Fe atom and all possible final states. This ratio has been found to be the same for electrons with equal initial angular momentum.