On Solutions and Higher Moments for the Linear Boltzmann Equation with Infinite-Range Forces

This paper considers an integral form of the linear, space-inhomogeneousBoltzmann equation with infinite-range forces in the collisionterm, and with periodic boundary conditions. The existence ofa measure solution is proved in the case of hard-potential forcesincluding kth power forces with k 5. The solution conservesmass and has bounded energy. Also, higher moments of the solutionremain globally bounded in time, if they exist initially. Inthe course of the proof, some collision estimates for the velocitiesare obtained.     

Existence Theorems for the Linear, Space-inhomogeneous Transport Equation

This paper studies existence problems in L¹ for the linear,space-inhomogeneous Boltzmann equation with periodic or (perfectly)absorbing boundary conditions under realistic assumptions onthe cross-sections. By an iteration technique, solutions arefirst constructed to an integral equation variant of the transportequation in the case of bounded impact parameters and an L¹type of cross-sections. They are then used to study the existenceof solutions of a measure form of the transport equation inthe case of unbounded impact parameters. These solutions conservemass. Estimates of their higher moments are also given. In particularthe results hold for inverse kth-power forces with 3 < k 5.     

Cluster modelling of O(1s) core excitons at the (100) surface of alkaline-earth oxides

Calculations have been performed on the O(1s) X-ray absorption spectra of the O^2- ion in the series of alkaline-earth oxides MgO, CaO, SrO. The static exchange approach has been used to calculate the near-edge X-ray absorption fine structure (NEXAFS) spectra for a range of cluster models (up to 50 atoms), representing both the (100) surface and the bulk of the different lattices. The clusters have been embedded in a proper representation of both the surrounding crystal ions and the Madelung potential generated by the infinite crystal. In the surface clusters discrete levels lying around 1.5 eV below the calculated ionization potential were found and characterized. This surface state has been studied further by performing complete active space self-consistent field (CASSCF) calculations in which the polarization of the crystal ions has been taken into account by means of a core polarization potential (CPP) method as well as the Mott-Littleton approach. After inclusion of this potential, the calculated ionization potentials show good agreement with XPS measurements.