Shape change in Hf,W and Os-isotopes: A non-relativistic Hartree-Fock versus relativistic Hartree approximation

We have investigated the ground-state structures of even-even Hf, W and Os isotopes within the framework of a deformed non-relativistic Hartree-Fock and a relativistic mean field formalism. A majority of the nuclei are predicted to be prolate in shape in the relativistic calculations. On the other hand, contrary to the relativistic results, we predict a shape change in a cyclic order in the non-relativistic calculations. However, in both the cases, the magnitude of the quadrupole deformation parameter agrees well with the experimental data. We also evaluated the hexadecapole deformation parameter for Hf, W and Os isotopes and irrespective of the shape change in quadrupole moments, we find a cyclic change in hexadecapole shape from positive to negative and vice versa in both the relativistic and non-relativistic formalisms.     

Comparison studies of infrared photodetectors with a quantum-dot and a quantum-wire base

This paper mainly presents a theoretical analysis for the characteristics of quantum dot infrared photodetectors (QDIPs) and quantum wire infrared photodetectors (QRIPs). The paper introduces a unique mathematical model of solving Poisson’s equations with the usage of Lambert W functions for infrared detectors’ structures based on quantum effects. Even though QRIPs and QDIPs have been the subject of extensive researches and development during the past decade, it is still essential to implement theoretical models allowing to estimate the ultimate performance of those detectors such as photocurrent and its figure-of-merit detectivity vs. various parameter conditions such as applied voltage, number of quantum wire layers, quantum dot layers, lateral characteristic size, doping density, operation temperature, and structural parameters of the quantum dots (QDs), and quantum wires (QRs). A comparison is made between the computed results of the implemented models and fine agreements are observed. It is concluded from the obtained results that the total detectivity of QDIPs can be significantly lower than that in the QRIPs and main features of the QRIPs such as large gap between the induced photocurrent and dark current of QRIP which allows for overcoming the problems in the QDIPs. This confirms what is evaluated before in the literature. It is evident that by increasing the QD/QR absorption volume in QDIPs/QRIPs as well as by separating the dark current and photocurrents, the specific detectivity can be improved and consequently the devices can operate at higher temperatures. It is an interesting result and it may be benefit to the development of QDIP and QRIP for infrared sensing applications.     

Hartree-Fock interaction between a helium atom and lithium metal: A test for the effective medium theory

The interaction of a helium atom with 6 and 10 atom clusters of lithium has been calculated using the unrestricted Hartree-Fock method, Hartree-Fock method with correlation corrections, and the effective medium theory. Inside the cluster the helium embedding energy is found to be proportional to the electron density of the cluster. The proportionality constant obtained by the Hartree-Fock method is in fair agreement with that calculated in the homogeneous electron gas using the local density approximation. Outside the cluster, in the region compatible with the helium diffraction experiments, the self-consistent calculations give much larger repulsion than the effective medium theory.     

Voltage-controlled storage and retrieval of an infrared-light pulse in a quantum-dot molecule

Dynamic storage and retrieval of a weak infrared (IR)-light pulse are investigated theoretically with feasible parameters in an asymmetric double quantum dot system, a quantum dot molecule (QDM). It is shown that, with a voltage-controlled tunneling, we are able to store and retrieve the IR signal pulse in this three-subband QDM medium by slowly switching off and on the tunneling. The scheme proposed may open up the electrical controllability of quantum optical information storage and retrieval, which is expected to be useful in quantum information science in an asymmetric double quantum dot controlled by voltage.     

Transient response of a spherical shell in an acoustic medium—Comparison of exact and approximate solutions

The transient response of a spherical shell in an acoustic medium is studied. The exact solution is obtained by expressing the classical spherical wave equation in terms of a residual potential. Approximate solutions are obtained from the use of eight functions; namely, doubly asymptotic approximations, δ-sequence functions, and spherical wave approximations. The advantages and disadvantages of these approximate solutions are pointed out. The third member of the class of the modal doubly asymptotic approximations for a spherical surface and an improved spherical wave approximation are introduced.     

Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle

A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamilton's principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinates and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics.     

Geometric phase, Hannay's angle, and an exact action variable

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.     

Comparison of exact and mean beam length results for a radiating hydrogen plasma

The purpose of this work is to investigate the accuracy of the mean beam length technique in high-temperature radiative heat transfer, combined with other modes of heat transfer. In order to study the validity of the mean beam length method, Nusselt numbers are presented for fully developed channel flow of a radiating nonisothermal hydrogen plasma. Black isothermal boundaries are considered. Numerical results obtained from the exact integrodifferential equation have been obtained previously for this problem. Linearized radiation and local thermodynamic equilibrium are assumed.The results show that the Nusselt numbers obtained by using the geometric mean beam length are in close agreement with results obtained by using the mean beam length. Therefore the complicated calculations needed to obtain the mean beam length are unnecessary.A comparison of the results obtained in the present work with previously reported work shows that the mean beam length technique is a better approximation to the exact solution than the optically-thick, or nongray differential approximation solutions.     

Comparison of fifth and third harmonic conversion in helium

Fifth and third harmonic conversion in helium are compared experimentally and theoretically. Conversion to the fifth harmonic is observed to exceed conversion to the third by about an order of magnitude, in good agreement with theoretical expectations. A comparison of the saturation behavior of each harmonic at high pump powers is made and implications concerning the physical processes responsible for the observed saturation of the fifth harmonic are described.     

Relation between total energy,electronic potential at the nucleus and chemical potential. Application to the helium isoelectronic series in Hartree-Fock theory

A formal relation between the total energy, the electronic potential at the nucleus and the chemical potential is derived within the context of density functional theory of atomic ions, using the homogeneity properties of the energy functional. An explicit application is then performed for two-electron ions in the context of the Hartree-Fock approximation.     

Kondo effect in a double quantum-dot molecule under the effect of an electric and magnetic field

Electron tunneling through a double quantum-dot molecule, in the Kondo regime, under the effect of a magnetic field and an applied voltage, is studied. This system possesses a complex response to the applied fields characterized by a tristable solution for the conductance. The different nature of the solutions are studied in and out thermodynamical equilibrium. It is shown that the interdot coupling and the fields can be used to control the region of multistability. The mean-field slave-boson formalism is used to obtain the solution for the problem.     

An exact analytic treatment of an ordered binary alloy in a Bethe lattice including first and second nearest neighbour interactions

Exact analytic formulae are obtained for the electronic structure of an ordered binary alloy in a Bethe lattice described by a tight-binding hamiltonian that includes nearest neighbour and second nearest neighbour interactions. Some interesting results are obtained and discussed in the text.     

Bound states of an electron and a macroscopic cluster at a liquid helium surface

In a strong electric field, there are bound states of an electron at the surface of liquid helium, interacting with a large cluster of atoms in the bulk of liquid. This phenomenon is related to long-range interaction between the electron and the dipole moment of the cluster. The electron, holding the cluster under the liquid surface, is localized at this surface. One electron is capable of binding a cluster of up to 10⁶ atoms. The value of the binding energy may reach up to several kelvins.     

Calculation of the cross section of helium ionization by an electron impact with the formation of a helium ion in an excited state

The total cross sections of He and He⁺ ionization by an electron impact are calculated in the first Born approximation. Calculations of the matrix elements are carried out by the Fock-Dirac multiconfiguration relativistic method using an intermediate type of coupling with orthogonal functions of the initial and final states. A single-electron wave function of the continuous spectrum for an Auger electron is obtained using the Fock-Dirac single-configuration method. The results of the calculations performed with orthogonal and nonorthogonal wave functions of the initial and final states are compared. The ionization cross sections are calculated for cases in which a knock-on electron of the continuous spectrum is described by both the orthogonal and nonorthogonal wave functions with respect to the wave functions of the core electrons.     

Comparison of the structure of Jastrow and exact many fermion theories

The structure of Jastrow and exact many body theory (in expS-form) are compared. The results are: 1. The correct linked clusters can be computed in terms of Jastrow correlation functions; 2. especially the Bethe-Goldstone (or defect) wave functions are defined uniquely and differ from those used in former comparisons; 3. one should use the (Jastrow) model energy instead of the expectation value thereby avoiding violation of the Pauli principle and some problems with higher order terms.     

Comparison of the structure of Jastrow and exact many fermion theories

The structure of Jastrow and exact many body theory (in expS-form) are compared. The results are: 1. The correct linked clusters can be computed in terms of Jastrow correlation functions; 2. especially the Bethe-Goldstone (or defect) wave functions are defined uniquely and differ from those used in former comparisons; 3. one should use the (Jastrow) “model energy” instead of the expectation value thereby avoiding violation of the Pauli principle and some problems with higher order terms.