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ELECTRONIC STRUCTURE OF JAHN-TELLER DISTORTED PHOSPOROUS-VACANCY COMPLEX IN SILICON

Under the extended defect potential approximation, the electronic wave function which is a function of the PV defect energy has been derived using a tight binding Koster-Slater Green function technique. Taking the experimental value of the defect energy level as input parameter, the obtained wave function describes quantitatively the data of the electron paramagnetic resonance and electron-nuclear double resonance. Especially, the hyperfine interaction constants of the four nearest neighbor atoms around the vacancy given by the theory, are in good agreement with the experiment.

Analysis of bound states of charged fermion and Abelian dyon.

One method of detecting dyons astronomically is to find the electromagnetic spectrum of their bound systems. In this paper we obtain wave functions and the energy spectrum of the bound states for a fermion and an Abelian dyon with electric charge {ital Z}{sub {ital d}}{lt}Z{sub d}{sup c}, a critical value of order {alpha}{sup {minus}1}, magnetic charge {ital q}, and for total angular momentum {ital j}{ge}{vert bar}{ital q}{vert bar}+{1/2}. Selection rules of this system in an external electromagnetic field are also given.

Comments on the quantum hall conductivity in cylinder geometry with finite width

The Hall conductivity in a cylinder geometry with a finite width L x and a periodicity L y in the x- and y-directions, respectively, is investigated in the quantum Hall regime following the recent approach of Hajdu, Janßen and Viehweger. Using the numerically obtained wave function in this geometry, we discuss the Hall conductivity, particularly the effect of the localized states whose localization length is larger than or comparable to L y . It is shown that the contribution of such virtually extended states to the Hall conductivity vanishes as far as the corresponding energy spectrum does not cross the Fermi level.

Uniform semiclassical approximation to supersymmetric quantum mechanics.

Recently, A. Comtet, A. D. Bandrauk, and D. K. Campbell [Phys. Lett. 150, 159 (1985)] introduced a modified semiclassical quantization rule motivated by the structure of supersymmetric quantum mechanics. In this paper, following their modified semiclassical framework, we provide a method to obtain wave functions in a uniform approximation. We demonstrate our method by constructing wave functions for the Morse, Rosen-Morse, and anharmonic oscillator potentials. Accurate fits to the wave functions are found for all three potentials.

Signature-inversion in particle-triaxial rotor system

Abstract We study the dependence of energy spectra of odd- A nuclei on the signature in the framework of a quasiparticle-triaxial rotor model with various combinations of parameter values, expecting that the observed signature inversion in some odd- A nuclei may be explained as a consequence of a rotation around the shortest axis. If the irrotational flow (IRE) model is used for the moments of inertia, the obtained wave functions bear some similarity to rotation around the shortest axis only at low spins and the signature dependence is only slightly inverted. If the sign of γ of the IRF moments of inertia is reversed (γ-rev. IRE), one sees some characteristic features of rotation around the shortest axis in the resulting wave functions except at low spins and the signature dependence gets inverted depending on the condition. However, this occurs only for rather large values of γ.

Calculation of warm electron transport in AlGaAs/GaAs single heterostructures using a Monte Carlo method

A simulation of electronic transport in AlGaAs/GaAs single-well structures including multisubband conduction has been performed based upon an ensemble Monte Carlo method. During the transient calculation, the electronic states of the quantum well are calculated in a fully self-consistent manner by including the influence of the changes in the energy distribution on the quantum well potential. The numerically obtained wave functions and energy levels are also used to update the major scattering matrix elements. The increase in electron energy with time and the corresponding changes of matrix elements and self-consistent field (through dependence of screening on the electron energy distribution) lead to a decrease in both velocity overshoot effects and steady-state drift velocity in low electrical fields at a low lattice temperature.

Potential separable expansion method and its relation to the Siegert method and the complex rotation technique.

It is demonstrated with the example of an atomic-physical model potential that the performance of the approximation method for determining resonances, based on a separable expansion of the potential (PSE method), is comparable with that of the Siegert method and of the complex rotation technique. In fact, it is shown that when converged, the PSE method with a real harmonic-oscillator wave-function basis is equivalent to the complex variational method with a trial function set containing a Siegert function; if the potential is dilation analytic the PSE method with a complex oscillator wave-function basis amounts to solving the complex rotated Schr\"odinger equation with the real PSE method and rotating back the obtained wave function. The results are tested against those yielded by direct numerical integration and against the complex virial theorem.

Monte Carlo study of electronic transport in Al1-xGaxAs/GaAs single-well heterostructures.

A study of electronic transport in ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ga}}_{\mathrm{x}}$As/GaAs single-well structures including multisubband conduction at 77 and 300 K has been performed. The electronic states of the quantum well are calculated self-consistently taking the five lowest subbands into account. The numerically obtained wave functions and energy levels are used to obtain the major two-dimensional scattering rates in each subband. Polar optical- and acoustic-phonon (via deformation-potential) scattering are considered including intersubband transitions. For ionized impurity scattering, the screening effects due to the five lowest subbands are taken into account to obtain the Fourier-transformed Coulomb potential. The steady-state and transient behavior of the electrons in the well are studied through a Monte Carlo particle simulation. It is shown that high transient velocities [(3--8)\ifmmode\times\else\texttimes\fi{}${10}^{7}$ cm/sec] can be expected at low and intermediate fields.

Approximate solutions to the one-particle Dirac equation: numerical results

The zero-, first-, and second-order differential equations in a previously defined hierarchy of equations giving approximate solutions to the one-particle Dirac equation and the corresponding eigenvalue contributions are each written as power series in α, the fine structure constant, for an arbitrary, spherically symmetric potential. These equations are solved numerically for the hydrogen-atom potential to obtain wave functions to order α2 and eigenvalues to order α4 for all states with n = 1–4, inclusive. The numerical solutions are then used to evaluate a number of matrix elements to order α2. A comparison with the exact expressions shows that the numerical values for the coefficients of the different powers of α have at least six significant figures in the eigenfunctions and eigenvalues and five in the matrix elements. Thus, the procedure is validated and can be applied with confidence to other atomic systems.

Combined hyperspherical and close-coupling description of two-electron wave functions: Application toe−−Helastic-scattering phase shifts

A new procedure for matching hyperspherical coordinate (HS) wave functions onto close-coupling (CC) wave functions for two-electron systems at a hyperradius $R={R}_{0}$ is shown to give agreement with accurate $^{1}S$ phase shifts for $e+\mathrm{H}$ up to the ${2s}^{2}$ resonance. The procedure uses far fewer basis functions than are required in either a HS or a CC calculation alone. The strengths of each method are thus effectively combined to obtain wave functions describing highly correlated two-electron motion near the nucleus ($R<{R}_{0}$) and largely independent electron motion away from the nucleus ($R>{R}_{0}$).

Neutron core-excited high-spin states in N = 50 nuclei

High-spin states in the N = 50 nuclei are studied in terms of the shell model, assuming π( p 1 2 , g 9 2 ) n + π p 1 2 , g 9 2 n × ν( p 1 2 , g 9 2 ) −1 d 5 2 + π( p 1 2 , g 9 2 ) n−1 d 5 2 ) configurations on the 88Sr core. The observed high-spin states in 94Ru are satisfactorily reproduced by one-neutron excitation. It is also suggested that one of the two high-spin structures lying above 4 MeV in 91Nb corresponds to neutron excited states. The obtained wave functions of the yrast high-spin states in N = 50 isotones are composed mainly of stretched or almost stretched coupling of a d 5 2 neutron to the yrast states of N = 49 isotones.

Obtaining self–consistent wave functions which satisfy the virial theorem

AbstractThe virial theorem has played an important role in applying quantum mechanics to chemical problems. It has served as one criterion of a satisfactory wave function and its consequences on chemical bonding, molecular structure, and substituent effects have been analyzed extensively. A common method of gaining compliance with the virial theorem is to introduce a “scale” factor which adjusts all distances by a factor η. Optimizing the scale factor through the variational principle produces a wave function satisfying the virial theorem. In the present paper it is shown that when this “scaling” procedure is applied to self‐consistent wave functions, the virial theorem can be satisfied, but self‐consistency is lost. Scaling generally has a small effect on the total energy, but the effects on the energy components (T, Vne, Vee, Vnn) can be two to three orders of magnitude larger and in the range of tens to hundreds of kcal. Consequently, for applications where the energy components are useful, it is highly desirable to obtain wave functions which satisfy the virial theorem and are self‐consistent. In the present paper, a simple, inexpensive extrapolation technique is reported which requires one integral evaluation and two SCF cycles to achieve convergence. Applications to atoms and small molecules are reported.

One-dimensional hydrogen molecule revisited

The energy of the one-dimensional hydrogen molecule with δ-function interactions between the particles is obtained using exact hydrogen molecule ion wave functions, a symmetrized product of hydrogen atomic wave functions and a linear combination of hydrogen atomic orbital wave functions. A variational calculation is carried out for each of the three cases to obtain wave functions that yield lower total molecular electronic energies.

Wave functions in momentum space. I. Iterative computation for the helium atom in Hartree–Fock approximation

The possibilities of obtaining wave functions for atoms and molecules by iteration of equations in momentum space have been examined. Using a first-iterate orbital some approximations to the Hartree–Fock ground state energy have been calculated. The accuracy of these results is strongly dependent on a variation of the parameters that characterize the orbital. The second-iterate orbital contains logarithmic and arctangent functions and there appear unfamiliar special functions in the third- and higher-iterate orbitals.

Theoretical description of fluidity in biological membranes: Rotational motion in lipid hydrocarbon chains

AbstractA mathematical model to relate order and rotational motion in lipid hydrocarbon chains in biological membranes is proposed. Schrödinger equations with suitable potential functions for CC rotations in lipid hydrocarbons chains have been solved to obtain wave functions characterizing these motions. For a free chain a threefold potential function has been assumed. The effect of collisions between neighboring chains in a membrane is considered by including another term (δ function) in the potential function.

Calculation of the g‐shift and superhyperfine structure tensor of Mn2+ ion in AIIBVI tetrahedral semiconductors

AbstractMultiple scattering method is used to obtain wave functions and energy levels of the 17‐atom cluster MnB4A12. The influence of all other atoms of the crystal is assumed to produce an additional constant potential only. At the Mn site, the correction to the potential is introduced to give most probable values of the cubic field splitting parameter Δ. For these values of Δ, the g‐shift and superhyperfine structure tensor are calculated and compared with experimental data.

Vertex functions and form factors for conformal spin-1/2 systems

Conformal on-shell wave functions are derived for spin-1/2 particle decaying virtually in spin 0 and spin 1/2. The relation to the off-shell vertex function is worked out and it is shown that shadow singularities are shifted tod′=5/2,d′ being the dimension of the particle field. The obtained wave functions are used to compute the conformal contribution to the form factors. Ford′ 5/2 the appearance of infra-red divergences enhances this contribution above the dimensional bound and the enhancement is computed in terms of the dimensions of the various fields.

ChemInform Abstract: A THEORETICAL STUDY OF THE ELECTROMAGNETIC PROPERTIES OF FERROCENE AND THE FERROCENIUM ION

An iterative extended Huckel molecular orbital calculation was used to obtain wave functions for the ground state of ferrocene and several low lying states of the ferrocenium ion. Photoemission spectra in terms of relative ionization potentials and the electric field gradient at the iron nucleus were calculated for ferrocene andg values and the electric field gradient were calculated for the ferrocenium ion. These values are in good agreement with experiment. The nature of the molecular orbitals was compared with results of previous semi-empirical andab initio calculations.

A theoretical study of the electromagnetic properties of ferrocene and the ferrocenium ion

An iterative extended Huckel molecular orbital calculation was used to obtain wave functions for the ground state of ferrocene and several low lying states of the ferrocenium ion. Photoemission spectra in terms of relative ionization potentials and the electric field gradient at the iron nucleus were calculated for ferrocene andg values and the electric field gradient were calculated for the ferrocenium ion. These values are in good agreement with experiment. The nature of the molecular orbitals was compared with results of previous semi-empirical andab initio calculations.

Interpretation of Shake-up Satellites in the X-Ray Photoelectron Spectra of Small Hydride Molecules by One-Center-Expansion ab initio Calculation with Equivalent-Core Approximation

Abstract One-center-expansion ab initio calculations with STO basis set were carried out on H2O, NH3, CH4 and BH3, to estimate the energies and probabilities of shake-up processes accompanying the photoionization of a core level. A method based on equivalent-core approximation and that based on configuration interaction procedure were applied to obtain wave functions of core-hole ions. It is shown that the calculations by the former method yield very satisfactory results, not only for the core ionization potential, but also for the energies and intensities of shake-up satellites.