Energy-band structure of SiC polytypes by interface matching of electronic wave functions

We interpret SiC polytypes as natural superlattices, consisting of mutually twisted cubic layers. A method is presented to calculate the electron band structure of any polytype, based on an empirical pseudopotential description of cubic SiC. Bloch and evanescent waves belonging to cubic layers are matched at interfaces in order to make up the wave functions of the respective polytypes. Band gaps of hexagonal and rhombohedral modifications are in excellent agreement with experimental data such that the nearly linear relationship between the indirect gap and the hexagonal nature is reproduced. A simple explanation of this relationship is given in terms of a Kronig-Penney-like mode

Energy-band structure of SiC polytypes by interface matching of electronic wave functions

We interpret SiC polytypes as natural superlattices, consisting of mutually twisted cubic layers. A method is presented to calculate the electron band structure of any polytype, based on an empirical pseudopotential description of cubic SiC. Bloch and evanescent waves belonging to cubic layers are matched at interfaces in order to make up the wave functions of the respective polytypes. Band gaps of hexagonal and rhombohedral modifications are in excellent agreement with experimental data such that the nearly linear relationship between the indirect gap and the hexagonal nature is reproduced. A simple explanation of this relationship is given in terms of a Kronig-Penney-like mode

Ground-state properties of polytypes of silicon carbide

The ground-state properties of cubic silicon carbide are calculated as a stepping stone towards a description of the polytypes of silicon carbide. The pseudopotential-density-functional method is used to calculate the self-consistent valence charge density as well as the equilibrium lattice constant and bulk modulus. Comparison with experimental data and earlier less rigorous calculations shows good agreement. A strategy is indicated to obtain a description of all polytypes.FWN – Publicaties zonder aanstelling Universiteit Leide

Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of ${A}$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the AGS form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a new formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the $(A+2)$-body operators onto target states, matrix three-body integral equations are derived which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering $T$-matrix which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb T-matrix are regularized to make the obtained equations suitable for calculations. For $NN$ and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.Comment: 34 pages, 13 figure

N-d scattering above the deuteron breakup threshold

The complex Kohn variational principle and the (correlated) Hyperspherical Harmonics technique are applied to study the N--d scattering above the deuteron breakup threshold. The configuration with three outgoing nucleons is explicitly taken into account by solving a set of differential equations with outgoing boundary conditions. A convenient procedure is used to obtain the correct boundary conditions at values of the hyperradius $\approx 100$ fm. The inclusion of the Coulomb potential is straightforward and does not give additional difficulties. Numerical results have been obtained for a simple s-wave central potential. They are in nice agreement with the benchmarks produced by different groups using the Faddeev technique. Comparisons are also done with experimental elastic N--d cross section at several energies.Comment: LaTeX, 13 pages, 3 figure

Scattering theory for arbitrary potentials

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.Comment: To be published in Phys Rev