Tight-bonding calculation of acceptor energies in germanium and silicon

The differences of hole ionization energies among the group-III elements acting as acceptors in silicon indicate the necessity of considering the specific contribution of the acceptor atom. Energies of two electron bonds are calculated using Morse curves to approximate interatomic potentials. The additional binding energy increases sharply from gallium to indium in accord with experiment. Arguments are presented to show why varying the acceptor element is less important in germanium.     

A variational calculation of nuclear binding energies

We show that the interaction energy of a nuclear system interacting with a central Yukawa plus a velocity-dependent δ-function two-body interaction can be reasonably approximated as a function of the local densities. The resulting expressions bear general resemblance with the Weiszsacker semi-empirical mass law. A simple variational calculation is carried out with these expressions for the ⁴He, ¹⁶O, ⁴⁰Ca and ⁵⁶Ni nuclei and nuclear matter. The calculated binding energies and radii are in excellent agreement with the experimental data.     

Precise calculation of coulomb binding energies of mesomolecules

The best variational energies obtained to date for the ground states of all -mesomolecules are presented. The results are of rather high accuracy and can serve as a theoretical basis for the experimental study of three-body systems. The energies of thee ^– e ⁺ e ^–,H^– and 1¹ S, 2³ S, 2³ P, 2³ P states ofHe are calculated using the same method.     

Theoretical calculation of excitonic binding energies and optical absorption spectra for Armchair graphene nanoribbons

In this paper the excitons of armchair graphene nanoribbons with layers of different width and thickness have been investigated. In this investigation, the band structure and energy gap of armchair graphene nanoribbons have been calculated using a tight-binding model including edge deformation effects (all edge atoms have been passivated with hydrogen atoms). Also, by calculating the conductance in armchair graphene nanoribbons (A-GNRs) optical absorption of armchair graphene nanoribbon in the single-electron approximation has been obtained. Finally, the binding energy of excitons in armchair graphene nanoribbons has been calculated using the Wannier model, Hartree-Fock approximation and the Bethe-Salpeter equation.     

Direct calculation of ionization energies

The advantages of the propagator formalism, as a direct method of calculating ionization energies, are stressed. The propagator equations are derived for closed-shell systems using an operator method instead of the usual diagrammatic derivations. The equations enable the development of an interpretation of the ionization energies in terms of conceptually simple quantities, such as pair correlation energies and associated relaxation effects, and retain the idea of orbital ionization. Infinite summations appearing in the self-energy terms are replaced by finite expressions involving functions satisfying uncoupled inhomogeneous differential equations. Certain high-order propagator equations are derived, and a connection with the Bethe-Goldstone formulation of pair correlation is made. Several computational procedures are advocated as forming the basis for balanced calculations of atomic and molecular ionization energies.     

Wave functions and energies of shallow acceptor states in germanium

Approximate wave functions and energies of shallow acceptor states in germanium have been obtained by solving the effective mass equations in the limit of very strong spin-orbit coupling. The variational approach used by Schechter was followed, but with more general trial functions that allow a more complete calculation of the energy spectrum of the acceptor. The new trial functions are constructed from terms with the angular dependence derived by Schechter, each multiplied by an arbitrary radial function. The variational procedure leads to systems of differential equations for the radial functions and energies of the states.Degenerate wave functions for a given acceptor level transform as a basis for a Γ₆, Γ₇ or Γ₈ irreducible representation of the double tetrahedral group. Energies and wave functions were obtained for the ground state, which has Γ₈ symmetry and envelope functions with even parity, and for the first excited state having the same symmetry and parity. Energies and wave functions were also obtained for excited states with Γ₆, Γ₇ and Γ₈ symmetries and envelopes with odd parity. States with Γ₆ or Γ₇ symmetry and envelope functions with even parity were not considered. The resulting energies show fair agreement with the experimental energies. As the new trial functions are quite flexible, it appears that the remaining discrepancy may be due to the inadequacy of the effective mass approximation.     

Electron binding energies in thorium

Sixteen atomic level energies in theL, M, N, andO shells of thorium have been measured by the electron spectroscopic method. The precision achieved in the measurements is better than one electron volt. The Fermi level is observed as an edge in the photo electron spectrum. A complete set of electron binding energies, based on electron spectroscopic data, is given.     

ZnO薄膜的激子能量和束缚能的计算

采用有效质量近似，将耦合在一起的6×6价带本征方程分开来考虑, 取激子试探波函数为z方向和x-y平面分离的形式，用变分法计算了ZnO薄膜重空穴带激子基态能、第一激发态能、束缚能和激子的半径随薄膜厚度的变化关系，并讨论了电子波函数的量子隧穿效应对厚度d<2.0 nm薄膜的能量修正. 关键词： 激子 ZnO薄膜 纤锌矿     

Variational calculation of metal surface energies

A one-parameter model potential variational calculation of jellium—metal surface energies in the local density approximation is performed, the results very closely approximating those of the self-consistent calculations of Lang and Kohn. The use of this model potential for the determination of superior upper bounds for the surface energy and the study of various density gradient expansions is indicated.     

Bivariational calculation of complex resonance energies

The least-squares bivariational method is discussed and proposed to calculate complex resonance energies and asymptotically diverging wave functions.     

Piezospectroscopy of the triple acceptor neutral copper in germanium

Experimental and theoretical results are presented for the behaviour of the optical absorption lines of neutral copper, a triple acceptor, in germanium under applied uniaxial compression. The ground state for the three equivalent holes is found to be the four-fold degenerate Λ₈ state of $\text{T}{}_{\mathrm{d}}$. The interpretation of the results requires that, for F6〈111〉, there be no splitting of either the ground state or the excited state of the D-line. However, this interpretation produces a violation of the predicted selection rules for the G components with F6〈100〉.