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Magnetic-field effects on the ##IMG## [http://ej.iop.org/images/0953-4075/31/6/007/img3.gif] Feshbach resonances below the H ( N = 2) threshold and the ##IMG## [http://ej.iop.org/images/0953-4075/31/6/007/img3.gif] shape resonance of ##IMG## [http://ej.iop.org/images/0953-4075/31/6/007/img5.gif] lying above the H ( N = 3) threshold are investigated theoretically using a method of complex-coordinate rotation. Products of Slater-type orbitals (STOs) are used to represent the two-electron wavefunctions, with ##IMG## [http://ej.iop.org/images/0953-4075/31/6/007/img6.gif] being employed for individual electrons. Block matrices with up to ##IMG## [http://ej.iop.org/images/0953-4075/31/6/007/img7.gif] (K-states) are used. Convergence behaviour for the resonance parameters (resonance energy and width) is examined by using different values of ##IMG## [http://ej.iop.org/images/0953-4075/31/6/007/img8.gif] . When the external magnetic field is turned on, we examine the field effects on the resonance energies and the autoionization widths. A physical interpretation of our results is given.

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A model interaction is introduced for quantum many-body simulations of Coulomb systems using periodic I boundary conditions. The interaction gives much smaller finite size effects than the standard Ewald interaction and is also much faster to compute. Variational quantum Monte Carlo simulations of diamond-structure silicon with up to 1000 electrons demonstrate the effectiveness of our method.

The structural bases on the metal/semiconductor interfaces, such as gold trimers on the Au/Si (111)(root 3 x root 3)R30 degrees surface and antimony trimers on the Sb/Si(111)(root 3 x root 3)R30 degrees surface, can be imaged directly with a simple inversion of low-energy (<600 eV) Kikuchi-electron patterns (Kikuchi-electron holography-KEH). The relative positions of the building blocks (trimers) on the adsorbates to the substrate atoms are also determined. This short-range-order KEH tool, which provides the 3D Patterson function, can be viewed as a twin of grazing-incidence X-ray diffraction. Using direct structural information obtained by KEH, one can greatly reduce the tested models in a complete trial-and-error structural-determination process.

This paper gives a brief overview of the capability of modern electron-structure calculations, the widely used density-functional theory, and the challenge to search for the exact nonlocal exchange-correlation functional. The study of the thermal properties of silicon is used as an example to illustrate the accuracy accomplished by the state-of-the-art first-principles calculations. A recent attempt to extract quantities of central importance in density function theory via computational many-body techniques is also discussed.

Realistic many-body wave functions for diamond-structure silicon are constructed for different values of the Coulomb coupling constant. The coupling-constant-integrated pair correlation function, the exchange-correlation hole, and the exchange-correlation energy density are calculated and compared with those obtained from the local density and average density approximations. We draw conclusions about the reasons for the success of the local density approximation and suggest a method for testing the effectiveness of exchange-correlation functionals.