Intermediate Coupling Method Research Articles

Radiative Constants in the W VII Ion Spectrum

The probabilities of the 4 f 135p66p + 4 f 145p56p – 4 f 136s, 4 f 137s radiative transitions and the lifetimes of the 4 f 137s levels in the spectrum of the erbium-like W VII ion are calculated in the electric dipole approximation by the semiempirical intermediate coupling method using experimental energy levels known from the literature. The radial integrals necessary for calculating the absolute transition probabilities are obtained in the form of length with the Hartree–Fock functions.

The influence of built-in electric field on binding energy of bound polaron and polaron effects in wurtzite ZnO/MgxZn1−xO quantum well

The influence of the built-in electric field on the binding energy of a bound polaron and the polaron effect in a wurtzite ZnO/MgxZn1−xO quantum well are studied using the improved Lee-Low-Pines intermediate coupling method. The ground-state binding energy, the contributions from different branches of optical phonons to the energy and the binding energy are presented as the functions of well width, impurity position and composition. In the numerical calculations, the anisotropic properties of the frequencies of the different branches of optical phonons, electron effective mass, dielectric constant, the electron-optical phonon interaction and the impurity center-optical phonon interaction are considered. The results show that the built-in electric field has obvious influence on the energy, the binding energy and the polaron effect, and it affects the contributions of different phonon modes to the energy and the binding energy with different degrees. The built-in electric field significantly increases the total phonon contribution to the energy, but it reduces the total phonon contribution to the binding energy. The binding energy of the bound polaron with the built-in electric field is less than that without the built-in electric field, and it declines rapidly with increasing well width. Because of the built-in electric field effects, the contributions from different branches of phonons to the energy and the binding energy and the functions of binding energy with well width and impurity center position are different from the cases without the built-in electric field. The built-in electric field in the wurtzite ZnO/MgxZn1−xO quantum wells has a great impact on the binding energy and polaron effect, and the polaron effect in the wurtzite ZnO/MgxZn1−xO quantum wells is significantly greater than that in the zinc blende GaAs/AlxGa1−xAs QWs, hence, it is necessary to discuss the built-in electric field and polaron effect when considering the problem of electronic state in such systems.

The effects of optical phonon on the binding energy of bound polaron in a wurtzite ZnO/MgxZn1−xO quantum well

An improved Lee-Low-Pines intermediate coupling method is used to study the energies and binding energies of bound polarons in a wurtzite ZnO/MgxZn1−xO quantum well. The contributions from different branches of long-wave optical phonons, i.e., confined optical phonons, interface optical phonons, and half-space optical phonons are considered. In addition to electron-phonon interaction, the impurity-phonon interaction, and the anisotropy of material parameters, such as phonon frequency, electron effective mass, and dielectric constant, are also included in our computation. Ground-state energies, binding energies and detailed phonon contributions from various phonons as functions of well width, impurity position and composition are presented. Our result suggests that total phonon contribution to ground state and binding energies in the studied wurtzite ZnO/Mg0.3Zn0.7O quantum wells varies between 28–23 meV and 62–45 meV, respectively, which are much larger than the corresponding values (about 3.2–1.8 meV and 1.6–0.3 meV) in GaAs/Al0.3Ga0.7As quantum wells. For a narrower quantum well, the phonon contribution mainly comes from interface and half-space phonons, for a wider quantum well, most of phonon contribution originates from confined phonons. The contribution from all the phonon modes to binding energies increases slowly either when impurity moves far away from the well center in the z direction or with the increase in magnesium composition (x). It is found that different phonons have different influences on the binding energies of bound polarons. Furthermore, the phonon contributions to binding energies as functions of well width, impurity position, and composition are very different from one another. In general, the electron-optical phonon interaction and the impurity center-optical phonon interaction play an important role in electronic states of ZnO-based quantum wells and cannot be neglected.

Size dependence of ground-state energy of the excitons in spherical Y2O3

The exciton energies of rare earth oxides (Ln2O3) have rarely been calculated by the theory. Experimentally, the blue-shift of exciton energy in nanocrystals deviates from the traditional size confinement effect. Herein, the dependence of the ground-state energy of an exciton in Y2O3 spheres on particle radius was calculated by using a variational method. In the model, an exciton confined in a sphere surrounded by a dielectric continuum shell was considered. The ground-state energy of exciton comprises kinetic energy, coulomb energy, polarization energy and exciton–phonon interaction energy. The kinetic and coulomb energy were considered by the effective mass and the dielectric continuum and the exciton–phonon interaction energy was given by the intermediate coupling method. The numerical results demonstrate that the present model is roughly consistent with the experimental results. The confinement effect of the kinetic energy is dominant of the blue-shift of the exciton energy in the region of R<5nm, while confinement effect of the coulomb energy is dominant of the blue-shift of the exciton energy in the region of R>5nm. The polarization energy contributes largely to the exciton energy as the particle size is smaller than ~10 nm, while the exciton–phonon interaction energy takes only a little contribution in all the range.

An Effective Interaction Approach to Anisotropic Superconductors Beyond the Weak Coupling Theory—An Origin of the d-wave Symmetry in High-T c Cuprate

We propose an effective interaction approach to superconducting systems which is adapted to periodic systems and intermediate net coupling between charge carriers by phonon mediated and Coulomb repulsive interactions. A coupling function of effective interaction is given for homogeneous field beyond the weak coupling approximation by using a generalized intermediate coupling method. Adequate kernel for the periodic systems is also reduced to that coupling function in homogeneous field and the Fourier coefficients relevant to the Bloch function. Within the present approach we discuss the symmetry of the superconducting gap in cuprate under the assumption that a nonbonding band filled by 2p_σ electrons exists in an undoped system and that doped holes occupy orbitals in this band. Those orbitals are represented by linear combinations of p x and p y functions. It is argued, in the tetragonal limit, that the symmetry of the gap function is d-wave-like on account of the products of orbital functions in combination of singlet spin-pair in the kernel.

BOUND POLARON IN A POLAR SEMICONDUCTOR HETEROJUNCTION IN STATIC ELECTRIC FIELD

The binding energy of the ground state of a bound polaron near the interface of a polar-polar semiconductor heterojunction is investigated by using the Lee–Low–Pines intermediate coupling method. The influence of a triangular potential approximation of the interface, the electron-phonon and impurity-phonon interactions as well as the half-space bulk longitudinal and interface-optical phonon modes are all taken into account. We have performed numerical calculations on the GaAs / Al x Ga 1-x As (0.2 ≤ x ≤ 0.4) heterojunction system and studied the relations between the ground state binding energy of the polaron and the impurity position, electric field strength and electron area density, respectively. It is found that with the increase in the distance between the impurity and the interface, the binding energy and the contribution of phonons reach the maximum. It is also found that the binding energy of the bound polaron increases slowly with the increase in an electric field while the total polaronic correction decreases the binding energy. When the electron area density is increased, the contribution of the interface-optical (IO) modes is greater than that of the bulk longitudinal optical (LO) mode.

Spin–orbit CI study on multiplet terms of trivalent lanthanide cations

In this paper we calculate the low energy spin–orbit multiplet terms of trivalent lanthanide cations Ce 3+ to Yb 3+, except for Gd 3+, with three different RECPs, including the spin–orbit effect explicitly, to assess their reliability. Although there is fairly good agreement with experiment for the ground LS multiplet splittings, implying the accuracy of the spin–orbit Hamiltonian, the agreement is less for the higher LS terms. The source of the error was found to be the significant semi-core correlations in the 4d, 5s, and 5p shells, which have very strong effects on the spin-free excitation energies. The degree of the intermediate coupling is also studied and related to the deviation from the Landé interval rule. The differences between the intermediate coupling method and the fully variational spin–orbit CI method are numerically analyzed.

Bipolarons in the intermediate coupling method

The properties of polarons and bipolarons are studied by the intermediate coupling method, which takes electron-lattice coupling into account. A Coulomb correlation in the electron motion is included. When the Frohlich coupling constant is reduced, at α*=5.7 a bipolaron decays suddenly from a self-trapped state into two delocalized polarons. A phase diagram is constructed for the region where the stable bipolaron exists. These results are compared with those obtained by integration along trajectories.

Influence of interface phonons on a polaron near a polar semiconductive heterointerface

With the Lee-Low-Pines intermediate coupling method, a polaron very near a polar semiconductive heterointerface is discussed by considering the influence of both branches of the interface optical phonon modes. The ground state energy and the normalized effective mass of the polaron are calculated. It is shown that one of the two branches of the phonon modes is the more important, but the contribution of the other branch to the polaron is not negligible.

Fermi-Edge Singularity in One-Dimensional Metals: Effects of Hole Recoil and Electronic Correlation

The Fermi-edge singularity in optical spectra is studied theoretically for one-dimensional (1D) metals. Using the intermediate-coupling method, the critical exponent is obtained analytically for an arbitrary mass of an optical hole. The electronic correlation is also taken exactly into account by the Tomonaga-Luttinger's bosonization technique. The exponent is found to be independent of the hole dynamics in 1D, which is in striking contrast to the 2D and 3D cases. Weak repulsive interaction among the conduction electrons sharpens the power-law peak in the edge spectrum.

Electronic structure and energy levels of the phosphor ZnS:Tm 3+ using nonrelativistic and relativistic cluster models

Energy levels, density of states (DOS), and electronic densities for ZnS: Tm 3+ were calculated self-consistently, using both nonrelativistic Hartree-Fock-Slater (HFS) and relativistic Dirac-Slater (DS) one-electron local- density spin restricted or polarized cluster models. The L-S coupling parameter ζ(4f) and electrostatic integrals F(k) were calculated. Luminescence transitions obtained using the intermediate coupling method are compared with experiment.

Energy Levels of Polarons in a Magnetic Field

A variational method closely related to the intermediate coupling method of Lee, Low, and Pines is used to calculate the ground-state energy and low-lying excited states of the Fr\ohlich Hamiltonian with a uniform time-independent magnetic field. The energy is calculated in a power series in $\frac{{\ensuremath{\omega}}_{c}}{\ensuremath{\omega}}$ to order ${(\frac{{\ensuremath{\omega}}_{c}}{\ensuremath{\omega}})}^{2}$, where ${\ensuremath{\omega}}_{c}$ is the cyclotron resonance frequency of the electron in the absence of electron-phonon interaction and $\ensuremath{\omega}$ is the frequency of the longitudinal optical phonons. It is shown that in the presence of electron-phonon interaction the energy of the $n\mathrm{th}$ magnetic level is no longer proportional to $n$ and that the effective mass for motion along the direction of the magnetic field is a function of $n$. The calculated variational energies approach the weak field result expected from the calculation of Lee, Low, and Pines (LLP) when $\frac{{\ensuremath{\omega}}_{c}}{\ensuremath{\omega}}\ensuremath{\rightarrow}0$, and in the weak coupling limit the ground-state energy becomes exact to order ${(\frac{{\ensuremath{\omega}}_{c}}{\ensuremath{\omega}})}^{2}$.

Nucleon-antinucleon forces in the intermediate coupling theory

A semi-phenomenological approach to meson theory is used in order to calculate the nucleon-antinucleon complex interaction responsible for the scattering and annihilation of antinucleons in hydrogen. It is assumed that the main part of the imaginary potential is due to processes involving virtual annihilation into an arbitrary number of mesons, all of them but one being emitted or absorbed in a p-state. An effective Hamiltonian is derived for such processes, from which a static interaction can be calculated, the nucleon and antinucleon being treated as fixed sources. The intermediate coupling theory of Tomonaga is extended to the two-body problem and applied first to the calculation of ordinary nuclear forces and of the real part of the nucleon-antinucleon interaction. The annihilation Hamiltonian is then treated approximately by the intermediate coupling method. The imaginary part of the potential is found to have a range of the order of 2 to 3.10-3 cm, beyond which it becomes a weakly oscillating function of the nucleon-antinucleon distance. The physical meaning of this result is discussed, as well as the effects which would tend to sharpen the definition of the emitted pions multiplicity. In particular, a method is proposed to investigate, in the framework of the intermediate coupling theory, the influence of the excited states of the nucleon-antinucleon system.

The range of validity of strong and weak coupling approaches in field theory

The solutions of scalar meson theory with infinitely heavy nucleons are well known in the limits of weak and strong coupling, and also there is the intermediate coupling method of Tomonaga which bridges the gap between them. However, the latter requires special trial functions and a cut-off procedure, so it is interesting to try to construct a method which develops a general solution analytically, particularly in order to answer the following question: When infinite quantities are absorbed by renormalization does the weakness or strongness of the coupling depend upon the renormalized quantities only? In this paper the problem of one nucleon is tackled in the functional integration formalism. It has been shown that this method encompasses both strong and weak limits, and here an attempt will be made to develop a general solution using the method of stationary phase.

The Properties of the Meson Theoretical Potentials in Li6

To study the properties of the symmetrical pseudoscalar meson theoretical potentials in nuclei, we apply them to Li6 that is expected ro disclose the properties of two-body forces in nuclei as directly as possible and investigate how favourable these potentials are to the static properties of Li6• The potentials between two nucleons are divided into two regions at 0.6 times the meson Compton wave length. The outside potentials are derived from the symmetrical pseudoscalar meson theory, while the inside potentials are determined from nucleon-nucleon scattering experiments phenomenologically. The excitation energies of the levels and the nuclear moments are calculated according to the intermediate coupling method. The meson theoretical potentials are very favourable to Li6 without any modification, though the contribution from the potentials of the inside region is large. The order and spacing of the levels and spins are reproduced correctly up to the 3rd excited state. The corresponding spin-orbit coupling strength is large, namely, -8--12 Mev, and can also explain the nuclear moments in the same region, so it is rather close to the jj-coupling limit than the LS-coupling limit. The tensor force does not affect the results essentially.

Intermediate Coupling Method for Meson-Nucleon Scattering

It is shown that for the meson-nucleon scattering processes an intermediate-coupling method can be applied which joins smoothly the results obtained from the weak- and strong-coupling limits. The method is illustrated by a detailed study of the charged scalar meson field with fixed nucleon.

Pair Creation in Intermediate Coupling Theory

The approximations of the intermediate coupling method are applied to a model of the self-field of a single nucleon (interacting with a pseudoscalar meson field) in which only processes involving pair creation and annihilation are allowed. In order to do this a method of subtracting the vacuum before these approximations are made, is suggested. The magnetic moment of the self-field on this model is investigated, and a comparison is made with the antithetic model of the self-field in which only processes not involving pair creation or annihilation are allowed.