Accuracy and convergence of a variational theory of nuclear matter for ν6 models

A number of higher-order terms in a previously proposed variational theory of nuclear matter are examined to establish the accuracy and convergence of the method. Numerical results for four semirealistic ν₆ model interactions, which include central, spin, isospin and tensor components, are reported. Although individual higher-order terms are substantial (> 1 MeV) they are much smaller than the corresponding lower-order terms, indicating good convergence of the theory. The higher-order terms also tend to cancel out, and three of the four ν₆ models show little net change in their E(k_F) curves, compared to previous work. The method is believed to have an error ?1 MeV for k_F ≦ 1.6 fm^?1.     

Approximative Berechnung von diamagnetischen Suszeptibilitäten

The Hartree-Fock perturbation method formulated in a previous paper [7] for approximate calculations of the magnetic susceptibilities of polyatomic molecules using CNDO/2 or INDO wavefunctions is reviewed. The method uses gauge-invariant atomic orbitals together with a set of approximations proposed in People's MO theory of diamagnetism. An expression is obtained for the susceptibility of a molecule involving three different parts which are referred to as intra-atomic, interatomic and cross contributions, respectively. All these contributions are used to calculate the susceptibilities of a series of hydrocarbons (CH₄, C₂H₆, C₂H₄, C₂H₂, cyclopropane). The mean values are in good agreement with experiment (except C₂H₂). Surprisingly, the interatomic and cross terms make considerable contributions to the total susceptibility. It seems justified to include the cross terms in the other terms and to define new terms which can be referred to as local or non-local contributions to the susceptibility. The local part can be divided up into a sum of atomic contributions which are comparable with the empirical Pascal constants. The numerical results reproduce very well the empirical atomic contributions and the constitutive correction for the carbon-carbon double bond. The calculations cover also the principal components of the atomic contributions. The non-local contribution may be considered as a generalization of the formula of Hall and Hardisson to all valence electrons.     

An algebraic description of anharmonic diatom–diatom inelastic collisions in the semiclassical approximation

An algebraic model to describe inelastic collisions between two anharmonic diatomic molecules in the semiclassical approximation is presented. The interactions for the diatomic systems are modelled in terms of Morse potentials, while an exponential repulsive potential is taken for the interactions between the nearest atoms of the diatomic systems. This problem is treated in the interaction potential framework, where an approximation in terms of the generators of three SU(2) groups is proposed, two corresponding to the Morse oscillators and the other to the interaction. The transition probabilities are given in terms of a sum of the products of three Wigner's d(β) functions corresponding to the three SU(2) groups. As an example the systems N₂?+?N₂ and H₂?+?H₂ are described and compared with exact quantum mechanical calculations.     

Nuclear relaxation in a one-dimensional triplet-exciton system

The proton spin-lattice relaxation time has been measured in (?₃AsCH₃)⁺ (TCNQ)^-₂ at 145 K as a function of the frequency. The results are interpreted in terms of interrupted one-dimensional random walk of the excitons along the TCNQ chains. The interruption is discussed in terms of the exciton-exciton collisions.     

The study of electronic conduction in amorphous thin films of Al-In<Subscript>2</Subscript>O<Subscript>3</Subscript>-Al structure deposited by thermal evaporation

A discussion of electronic conduction in amorphous thin films of Al-In₂O₃-Al structure is presented. Particular attention is given to the question of film thickness, substrate temperature during deposition and post-deposition annealing, since these conditions are known to have a profound effect on the structure and electrical properties of the films. The effects of temperature on the V-I characteristics and effects of frequency on conductivity and capacitance of the Al-In₂O₃-Al structure are also reported. Activation energies for conduction processes are estimated and the results are discussed in terms of the hopping model. The conduction at higher temperature is seemingly a contact-limited, i.e. Schottky type process, so a transition from hopping to free-band conduction takes place. The capacitance decreases with the rise of frequency and the lowering of temperature. The values of dielectric constants are estimated and the results are discussed in terms of Schottky type of conduction. The increase in conductivity with the increase in temperature during measurements of electrical properties, film thickness, substrate temperature and post deposition annealing is reported and results are discussed in terms of current theory.     

Cartesian Dynamics of Simple Molecules X Linear Quadratomics (C∞v Symmetry)

The vibrations of linear ABC₂ type molecules with C_∞V point group are analysed in terms of Cartesian co-ordinates. Algebraic expressions for the three stretching and two bending normal mode frequencies are derived in terms of longitudinal and transverse force constants, atomic masses and bond lengths. Values of non-valence interaction parameters are transferred from A₂B₂ (D_∞h) molecules, and values of the principal force constants are adjusted to reproduce the observed frequencies for a number of asymmetric halogen derivatives of acetylene. Normal mode frequencies of various isotopic species are also calculated. The nature of the computed eigenvectors for these molecules is briefly discussed. It is found that the carbon-carbon and carbon-hydrogen valence interactions remain approximately constant for these molecules, whereas the carbon-halogen bonds show a weakening trend with increasing halogen mass.     

Second-order corrections to correlations in muon capture

Muon capture by a nucleus with an arbitrary spin is considered. Second-order terms in 1/M in the effective weak-interaction Hamiltonian are taken into account. New terms in the Hamiltonian associated with the nucleon-nucleus potential are found. A general expression for the angular distribution of neutrinos (recoil nuclei) is derived for polarized muons and oriented target nuclei. Second-order contributions to the amplitudes M _u (k) are obtained. This allows one to calculate second-order corrections to any integral and correlation characteristics in muon capture that are expressed in terms of M _u (k).     

On the origin of supergravity boundary terms in the AdS /CFT correspondence

The standard formulation of the AdS/CFT correspondence is incomplete since it requires adding to a supergravity action some a priori unknown boundary terms. We suggest a modification of the correspondence principle based on the Hamiltonian formulation of the supergravity action, which does not require any boundary terms. Then all the boundary terms of the standard formulation naturally appear by passing from the Hamiltonian version to the Lagrangian one. As examples the graviton part of the supergravity action on the product of AdS_d+1 with a compact Einstein manifold ϵ and fermions on AdS_d+1, are considered. We also discuss conformal transformations of gravity fields on the boundary of AdS and show that they are induced by the isometrics of AdS.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

Abstract

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Relativistic kinetic theory of quantum systems: V. Transport equations for the massive components of an eeveve-mixture

Covariant transport equations are derived for the Wigner function matrices describing the massive components of a non-degenerate e$\text{e}$v_e$\text{v}$_e-mixture. The collision terms pertaining to the various collision processes involve spin-dependent transition amplitudes which are specified in terms of an effective Hamiltonian density obtained from the Weinberg-Salam theory.     

Nonstandard GLh(n) quantum groups and contraction of covariant q-bosonic algebras

GL_h(n) × GL_h(m)-covariant h-bosonic algebras are built by contracting the GL_q(n) × GL_q(m)-covariant q-bosonic algebras considered by the present author some years ago. Their defining relations are written in terms of the corresponding R _h-matrices. Whenever n = 2, and m = 1 or 2, it is proved by using U_h(sl(2)) Clebsch-Gordan coefficients that they can also be expressed in terms of coupled commutators in a way entirely similar to the classical case. Some U_h(sl(2)) rank-(1/2) irreducible tensor operators, recently constructed by Aizawa in terms of standard bosonic operators, are shown to provide a realization of the h-bosonic algebra corresponding to n = 2 and m = 1.     

Vibration and the Kerr effect

The theory of the Kerr effect (electric birefringence) is developed with explicit inclusion of molecular vibration. When the theory is applied to CHCl₃ and CHF₃, it is found that terms with a vibrational origin are an important component of the β-hyperpolarizability extracted from temperature-dependent Kerr studies. It is concluded that these vibrational terms partly account for the difference between β obtained from second-harmonic-generation experiments and from the Kerr constant.     

Calculated sextic centrifugal distortion constants of polyatomic molecules

By a perturbation treatment of the vibration-rotation Hamiltonian, expressions are derived for the sextic centrifugal distortion constants of a polyatomic molecule in terms of the basic molecular parameters. The calculation can be simplified by reordering the terms in the perturbation expansion. The theoretical expressions for the sextic distortion constants contain the cubic anharmonic potential constants, for which they are a possible source of information. The formulas are applied to molecules of various types of symmetry, and numerical results are computed for sulfur dioxide, ammonia and methane from published anharmonic force fields. The agreement with the observed distortion constants is good for SO₂ and reasonable for NH₃, but poor for CH₄. These results probably reflect the present state of knowledge of the cubic potentials of these three molecules.     

The partial structure factors of liquid alloys

The main results of a recent experimental determination of the partial structure factors for liquid Cu₆Sn₅ are outlined. The results are discussed in terms of a hard sphere model and some general comments on the structure of binary alloys are made.     

Quadrupole relaxation in nitrogen nuclear resonances

The ¹⁴N resonance line-widths have been measured for a wide range of nitrogen compounds. The variation of line-width with viscosity of MeCn, EtCN, PrCN and Me₂NCHO in various solvents is discussed in terms of the theories of molecular correlation times. The values of the line-widths in substituted nitrobenzenes are discussed in terms of the quadrupole coupling constants. The relative line-widths in the azide ion are discussed in terms of its electronic structure.     

Dynamics of magnetization of frustrated ising systems

The dynamics of magnetization in triangle lattices of the Ising chains has been investigated in terms of the Glauber theory. The results of three-dimensional numerical simulation of the magnetic structure and magnetization curves of Ca₃Co₂O₆ are presented. The structures of the low-temperature and high-temperature phases differ significantly: the false frustrated low-temperature phase is transformed into a partially disordered antiferromagnetic honeycomb structure. Two additional magnetization steps at low temperatures are formed at the expense of the domain structure and the ferrimagnetic phase. All fundamental hypotheses used in terms of the two-dimensional model have found their confirmation during the three-dimensional simulation.     

Structural and magnetic properties of layer compounds: CoGaInS4

XPS spectra of the layer compound CoGaInS₄ show that CO²⁺ ions are distributed within the sheets of a ZnIn₂S₄-type structure. The magnetic properties are explained in terms of antiferromagnetic uncompensated clusters.     

Effective torsion-rotation Hamiltonian for methanol-type molecules

A fourth-order effective Hamiltonian has been derived for the torsion-rotation problem of a methanol-type molecule, i.e., for a C_3v top attached to a C_s frame. First, symmetry considerations based on a frame-fixed axis system are used to determine allowed terms in the Hamiltonian. These terms are then subjected to a contact transformation to remove the indeterminate ones. This procedure is essentially an extension of Watson's method for semirigid molecules to the torsion-rotation problem. It is demonstrated that the Hamiltonian derived in the present work is capable of improving the fittings of the millimeter and submillimeter absorption frequencies of CH₃OH and CH₃SH.     

Applications of reciprocity to non-linear extended thermodynamics kinetic equations

Reciprocity relations and integrability conditions can be used in non-linear extended irreversible thermodynamics to calculate forces and phenomenological coefficients uniquely in terms of parameters in kinetic equations derived from a model. One assumes a set of n even variables α_i and corresponding η = α_i, with an equation from the model for η_i. η-independent thermodynamic forces terms are assumed known. Comparison of powers of η in the model equation with corresponding powers in the canonical Onsager-Casimir formalism yields equations to determine all quantities in the latter save the higher η-dependence of entropy which is affected by uncertainties in measurement. By introducing a phenomenological ansatz, one can relate these higher entropy terms to corresponding terms in the model equation. A numerical illustration is made for a relaxing scalar structural parameter appropriate to a simple liquid.