Abstract
(Englisch)
|
Electron and positron atomic and electron H2O cross sections and secondary spectra were calculated in the energy range form 1 eV to 100 GeV. Considered were the elastic scattering, ionization, excitation,
Bremsstrahlung, and in case of positrons annihilation into one and two photons.
Special care was taken to obtain the elastic scattering cross sections. The variationally optimised effective atomic central potential for all Z from 1 to 100 was calculated solving the relativistic Dirac equations for bound electron states. Whereas the electrostatic or Hartree part of the potential is obtained in a straightforward way from the electron density, the 'variationally optimum' exchange potential for bound electrons is calculated satisfying a Volterra type integral equation of the first kind. The problem is solved self-consistently by starting with an initial approximate potential, solving for the single-particle orbitals and energies, constructing the kernel and inhomogeneous terms in the integral equation, and solving the integral equation numerically. The procedure is then iterated until a self-consistency requirement is met.
The double differential elastic scattering cross sections were calculated applying the relativistic Dirac partial wave analysis. Here the Hartree potential, exchange potential (dependent on energy of incident electron) and polarisation potential were used for incident electron. For incident positrons only Hartree and polarisation potentials were applied. .The solid state effects for scattering in solids are described by means of a simple muffin-tin model, i.e. the potentials of neighbouring atoms are superposed in such a way that the derivation of superposed potential is zero midway between atoms. The theoretical results were compared with experimental values for electrons scattered from hydrogen, helium, nitrogen, oxygen, argon, krypton, xenon and mercury, and for positrons scattered from helium, neon and argon. Very good agreement was obtained for both the integrated and differential cross sections.
Also compared with the experimental values were the electron ionisation cross sections for hydrogen, carbon, nitrogen, oxygen, aluminum, nickel and gold. Again very good agreement were obtained. For the case of electron-water molecule collisions, the theory of the R-matrix was used. With this method, the K-matrices were obtained, from which the T-matrices were calculated, taking the eigenfunctions of the
harmonic oscilator as weight. For the case of water the three vibrational modes were analysed:
symmetric stretching, asymmetric stretching and bending. The results for the bending mode agree well with the experimental data. For the case of the stretching modes, the cross sections must be added, since for the moment, it is not possible to measure the stretching modes separately.
This theory cal also be applied to the H2S molecule, since the vibrational modes are the same as for water.
|
