R. Mayol

Elastic scattering of electrons and positrons by atoms. Schrödinger and Dirac partial wave analysis

Abstract Two FORTRAN 77 codes are described which provide a complete description of elastic scattering of electrons and positrons by atoms using the static field approximation with non-relativistic (Schrodinger) and relativistic (Dirac) partial wave analysis. The delivered information includes phase shifts, differential cross-sections, scattering amplitudes and percentage points of the single scattering angular distribution. The scattering field may be internally generated by the codes (which incorporate an accurate analytical approximation to the Dirac-Hartree-Fock-Slater field of free atoms) or read from the input file. Solid state effects for scattering in solids are described by means of a simple muffin-tin model. For electron scattering, exchange corrections are also taken into account. Phase shifts are obtained by using the RADWEQ subroutine package [Comput. Phys. Commun. 62 (1991) 65] to solve the radial equations. The relativistic code provides reliable cross-section data for kinetic energies between ≈ 1 keV and ≈ 1 MeV.

On the theory and simulation of multiple elastic scattering of electrons

Abstract Multiple elastic scattering of electrons in matter is analyzed on the basis of accurate single scattering differential cross sections obtained from partial wave calculations. We give a brief derivation of Molieres multiple scattering theory that clarifies its physical content and points out its limitations. In particular, it is shown that transport mean free paths calculated from the Moliere single scattering cross section differ significantly from the values obtained from partial wave calculations. We present a mixed simulation algorithm that overcomes most of the limitations of the currently available condensed Monte Carlo codes. This algorithm takes advantage of the fact that most of the collisions experienced by a high-energy electron along a given path length are soft, i.e. the scattering angle is less than a selected small value χs. The global effect of these soft collisions is described by using a multiple scattering approximation. Hard collisions, with scattering angle larger than χs, occur in a moderately small number and are described as in detailed simulations. This mixed algorithm can be applied to any single scattering differential cross section, it leads to the correct spatial distributions and it completely avoids problems related to boundary crossing. Moreover, when the single scattering law underlying Molieres theory is adopted, the algorithm can be formulated in a completely analytical way.

Inelastic scattering of electrons in solids from a generalized oscillator strength model using optical and photoelectric data

Inelastic scattering of electrons in solids is computed from a generalized oscillator strength model based on optical and photoelectric data. The optical oscillator strength is extended into the non-zero momentum transfer region by using free-electron gas dispersion for the weakly bound electrons. The applicability of this method to non-conduction valence electrons and to inner shells is discussed. A different extension method, which reproduces ionization thresholds, is used for inner-shell ionization. The calculations are simplified by using a two-modes model for the Lindhard theory of the free-electron gas. Exchange effects are accounted for by means of a modified Ochkur approximation. Inelastic mean free paths and stopping powers obtained from this optical-data model for four materials (Al, Si, Cu and Au) and for electrons with energies from 10 eV to 10 keV are presented.

Freezing of 4He and its liquid-solid interface from density functional theory

We show that, at high densities, fully variational solutions of solid-like type can be obtained from a density functional formalism originally designed for liquid 4He. Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased DF methods to study highly non-homogeneous systems, like 4He interacting with strongly attractive impurities/substrates, or the nucleation of the solid phase in the metastable liquid.

Pinning of Quantized Vortices in Helium Drops by Dopant Atoms and Molecules

Using a density functional method, we investigate the properties of liquid 4He droplets doped with atoms (Ne and Xe) and molecules ( SF6 and hydrogen cyanide). We consider the case of droplets having a quantized vortex pinned to the dopant. A liquid-drop formula is proposed that accurately describes the total energy of the complex and allows one to extrapolate the density functional results to large N. For a given impurity, we find that the formation of a dopant+vortex+(4)He(N) complex is energetically favored below a critical size N(cr). Our results support the possibility to observe quantized vortices in helium droplets by means of spectroscopic techniques.

STRUCTURE OF LARGE 3HE-4HE MIXED DROPS AROUND A DOPANT MOLECULE

We have investigated how helium atoms are distributed within a mixed

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

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The Structure and Energetics of 3He and 4He Nanodroplets Doped with Alkaline Earth Atoms

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A simple model for electron scattering: inelastic collisions

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Absorption spectrum of Ca atoms attached to 4He nanodroplets

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