Antisymmetrization procedure of identical fermions states

An efficient procedure for antisymmetrization of an arbitrary system of identical fermions is presented. The approach is based on a simple enumeration scheme for antisymmetric A-particle states and an efficient algorithm for calculation of the coefficients of fractional parentage (CFPs) for a single j-shell with isospin. The developed approach is implemented in a new procedure for the calculation of the electric quadrupole moment matrix elements of light atomic nuclei in the isospin formalism.     

Crystal field parameters for Yb ions at orthorhombic centers in garnets—Revisited

The major purpose of this paper is to clarify the deficiencies identified in the recent paper by Liu et al. (J. Lumin. 130 (2010) 103) as well as to reanalyze the available data and provide corrected results for the orthorhombic crystal field parameters (CFPs) for selected rare-earth ions in garnets. It appears that Liu et al., when utilizing the computer package for standardization of CFPs, have inadvertently confused the properties of CFPs expressed in the Wybourne notation with those in the extended Stevens operator notation. This confusion has led to misinterpretations concerning the orthorhombic standardization transformations and incorrect labeling of the CFP sets as supposedly ‘standardized’ for Yb³⁺, Pr³⁺, Nd³⁺, and Er³⁺ ions in various garnets. These deficiencies have prompted us to reconsider the CFP sets determined earlier by matching the experimental data, i.e. the orthorhombic spin Hamiltonian parameters (g factors, g_i, and hyperfine structure constants, A_i; i=x, y, z) and available optical spectral band positions, with the theoretical data calculated using the complete diagonalization method. To further verify the correctness of the present results the CFPs for orthorhombic Yb³⁺ centers in Yb₃Al₅O₁₂ and Yb₃Ga₅O₁₂ garnets are calculated using the superposition model (SPM), which requires adoption of a well-defined symmetry-adapted axis system (SAAS). Hence, the SPM calculations enable reanalysis of available CFP sets based on the correct standardization procedure and establishing the correspondence between the SAAS and the ‘nominal’ axis systems assigned to fitted CFP sets. Using the proper SAAS and general transformations of the axis systems, the relations between the calculated g_i and/or A_i values and the respective principal values determined by EPR experiments can be established. The consistent methodology utilized here may be helpful for proper reanalysis of spectroscopic data for rare-earth and transition-metal ions at orthorhombic symmetry sites in various crystals.     

Method simplifying calculation of coefficients of fractional parentage for translationally invariant shell-model

A new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator $P_{N_1 ,N}$ in a subspace where N ₁ and N ₂ = N ? N ₁ nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators $P_{N_1 ,N}$ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.     

Scattering theory with different state spaces of perturbed and free system

A new method of the time-dependent approach to the scattering problem is presented. For the main initial objects we take a pair of nonnegative bilinear functionals β_j (j = 1,2) (instead of a pair of selfadjoint operators H_j). In the particular case β_j and H_j are connected by the Green's functions of the corresponding Schrödinger equations. In the general case β₂ may be rather arbitrary. The method proposed here can apply to the scattering problem with a non-operator perturbation. This method essentially uses a pair of different state spaces for the free and perturbed physical system respectively.     

Feasibility study of power engineering secondary equipment protection methods from static electricity

The paper presents feasibility study of power engineering secondary equipment protection methods from static electricity basing on calculation and experimental procedure. Method was applied for newly constructed objects and modernized objects as well. The procedure includes calculation of expected electrostatic potential at human body considering environment characteristics (relative humidity, dimensions and electrophysical characteristics of flooring and footwear). Calculated potential was compared to acceptable value. Acceptable value represents immunity test level of secondary equipment (relay protection and automation, communication equipment, PCs) presented in standards [1], [2], [3], [4], [5]. In calculations electrostatic charging current density j₀ = 10 μA/m² was taken as in domestic applications. Calculation result analysis showed optimal methods to limit human electrostatic charge accumulation for designed objects and objects in operation.     

Poly(4-vinylpyridinium)hydrogen sulfate: a novel and efficient catalyst for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes under conventional heating and ultrasound irradiation

A simple and convenient procedure for the synthesis of 14-aryl-14H-dibenzo[a,j]xanthenes is described through a one-pot condensation of 2-naphthol with aryl aldehydes in the presence of poly(4-vinylpyridinium)hydrogen sulfate as an efficient, cheap, readily synthesized and eco-friendly catalyst in a solvent free media using conventional heating and ultrasound irradiation.     

Fast approximate technique for the cumulative wavenumber model to modeling radiative transfer in a mixture of real gas media

In the cumulative wavenumber (CW) model, the total range of the absorption cross-section Cη is subdivided into the supplementary absorption cross-section of gray gases C_j, j=1,…,n, where n is the number of gray gases; and the wavenumber region is subdivided into intervals Δ_i=[η_i−1, η_i], i=1, 2,…,p, where p is the number of intervals. The intersection of the two spectral subdivisions is used to define the modeling of the fractional gray gas D_ij. In the CW model, we solve the radiative transfer equation (RTE) in every subinterval D_ij; then it is necessary to solve n x p times the spectral form of the RTE for complete spectral integration. In this work, the CW model is used with a numerical approximation technique based on additive properties of radiative intensity to reduce the solution of RTE to n new fractional gray gas D_j for complete spectral integration. The CW model was first coupled with the discrete ordinates method and the accuracy of the simplified technique and the algorithm was first examined for one-dimensional homogeneous media; results are compared with line-by-line calculations and it is found that the CW model with the simplified technique is exact for the homogeneous media examined. Also, the fast approach is tested in the diffuse reflecting boundaries case. The CW model is implemented in a bi-dimensional enclosure containing real gases in isothermal cases. Afterwards, this approximate technique is extended to non-isothermal and non-homogeneous cases; the results are compared with line-by-line calculations taken from literature and good agreement was found. The results obtained using the acceleration technique for the CW model agree with the results of original CW model. With this acceleration technique the CPU time decreases p times. Spectral database HITRAN and HITEMP are used to obtain the molecular absorption spectrum of the gases.     

Modeling Spectroscopic Properties of Ni2+ Ions in the Haldane Gap System Y2BaNiO5

Modeling of spin Hamiltonian parameters enables correlation of crystallographic, spectroscopic, and magnetic data for transition ions in crystals. In this paper, based on the crystallographic data and utilizing the point-charge model and superposition model, the crystal field parameters (CFPs) are estimated for Ni²⁺(3d ⁸) ions in the Haldane gap system Y₂BaNiO₅. The CFPs serve as input for the perturbation theory expressions and the crystal field analysis package for microscopic spin Hamiltonian modeling of the zero-field splitting parameters (ZFSPs) D and E. Results of an extensive literature search of the pertinent crystallographic data, experimental ZFSPs, and model parameters are briefly outlined. The modeling aims at verification of the experimental ‘single ion anisotropy’ parameters and explanation of the controversy concerning the maximal rhombic distortion |E/D| ≈1/3 reported for Ni²⁺ ions in Y₂BaNiO₅. The preliminary results call for reanalysis of some magnetic studies of the Haldane gap systems.     

Analytic description of distortionless propagation in a resonant absorbing medium with overlapping Q(j) transitions

Analytic closed form solutions are obtained for distortionless propagation of ultra-short optical pulses through a resonant medium with overlapping Q(j) transitions for j = 2. Apart from the expected 2π solutions, we also found 0π solutions in contrast to conclusions based on numerical calculations.     

Orientation of O(3) and SU(2)⊗CI representations in cubic point groups (Oh,Td) for application to molecular spectroscopy

We propose a detailed method for the symmetrization of the standard O(3) or SU(2)⊗C_I basis |j_τ,m〉 (τ=g or u) into the O_h or T_d point group. This is realized by means of an orientation matrix called G. The oriented basis obtained in this way allows matrix element calculations for rovibronic spectroscopic problems concerning octahedral or tetrahedral molecules. Particular attention has been put on careful phase choices. A numerical calculation of all the G matrix elements for both integer and half-integer j values up to 399/2 has been performed. Such high angular momentum values are necessary for the case of heavy molecules with high rotational excitation. To calculate the G coefficients with high precision at high j values we pre-calculated the necessary Wigner functions using symbolic MAPLE software and made then the numerical calculations with quadruple precision. The complete list of these coefficients can be obtained freely at the URL: http://www.u-bourgogne.fr/LPUB/group.html. As an illustration, we also present briefly an application to two typical spectroscopic calculations: the pure rotational levels of SF₆ in its ground vibrational state and the ν₃ band of ReF₆ (an open-shell molecule with an odd number of electrons and a fourfold degenerate electronic ground state).     

Nonplanar contribution to the four-loop universal anomalous dimension of the twist-2 Wilson operators in the $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

The result of the direct component calculation of the nonplanar contribution to the four-loop anomalous dimension of the Konishi operator in the \(\mathcal{N}\) = 4 supersymmetric Yang-Mills theory is reported. The result contains only the ζ(5) term proportional to the ζ(5) contribution in the planar case, which comes only from wrapping corrections. The previous calculations of the leading transcendent contribution to the anomalous dimension of the twist-2 operators for first three even moments are also expanded to the nonplanar case and the same results as in the planar case are obtained up to a general factor. These two results imply that the nonplanar contribution of the four-loop universal anomalous dimension of the twist-2 Wilson operators with an arbitrary Lorentz spin j is proportional to S ₁ ² (j)ζ(5). This result provides a nonstandard square logarithmic asymptotic behavior ln² j for large Lorentz spins j of the operators.     

Effect of Nucleon Pairing in the Spectra of <Emphasis Type="Italic">N</Emphasis> = 50 Isotones

The emergence of the pairing effect of identical nucleons in the j = 9/2 state in low-lying excited states of nuclei near ⁹⁰Zr (N = 50, Z = 40) is discussed. Multiplets of states with seniority s ≥ 2, the splitting of which is determined by the proton pairing energy, are clearly visible in the nuclear spectra for a chain of N = 50 isotones. A comparison of the spectra of ground state multiplets, calculated in the δ-interaction approximation, with experimental data and results from other theoretical calculations shows this approach can be used to describe the structure of spectra and level positions with high J values.     

A novel method for extracting oscillator strength of select rare-earth ion optical transitions in nanostructured dielectric materials

A new technique to obtain the oscillator strength of select rare-earth optical transitions in nanostructured dielectric materials (nanophosphors) is presented. It is based on the experimentally observed nanophosphor lifetime dependence on the embedding medium. A constant oscillator strength and parity-allowed electric dipole transitions of the RE ion emission are assumed. The oscillator strength is obtained from the slope of the 1/τ_ij vs. n(n²+2)² plot, where τ_ij is the radiative lifetime of transition between states i and j, and n is the index of refraction of the embedding medium. The use of the technique is illustrated for the Y ₂SiO₅:Ce nanophosphor.     

Strongly coupled bands as “effectively” decoupled bands

We present experimental evidence which suggests that almost all the strongly coupled bands in the rare-earth region may also be treated as “effectively” decoupled bands. In contrast to the usual decoupled bands, the strongly coupled bands seem to arise from a system where a particle carrying an “effective” angular momentumj′ is aligned to an even-even core having an “effective” rotational angular momentumR′ which is not necessarily zero for the band head but may even haveR′=2 or, 4 or, 6?etc. We attempt to explain these observations in a simple physical picture whereinJ _R, the projection ofj, the particle angular momentum, on the rotation axis, is taken as the effectively aligned spin of the last particle. Preliminary results from schematic bandmixing calculations forh _9/2 andf _5/2 orbitals with the Fermi energy lying near the highK single particle levels indeed reveal the existence of “effectively” decoupled bands which seem to agree with this physical picture.     

Numerical solution of radiative and conductive heat transfer in concentric spherical and cylindrical media

A new technique is presented to improve the performance of the discrete ordinates method when solving the coupled conduction-radiation problems in spherical and cylindrical media. In this approach the angular derivative term of the discretized one-dimensional radiative transfer equation is derived from an expansion of the radiative intensity on the basis of Chebyshev polynomials. The set of resulting differential equations, obtained by the application of the S_N method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the Chebyshev transform method compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order S_N calculations.     

Relative entropy of entanglement of rotationally invariant states

We calculate the relative entropy of entanglement for rotationally invariant states of spin- and arbitrary spin-j particles or of spin-1 particle and spin-j particle with integer j. A lower bound of relative entropy of entanglement and an upper bound of distillable entanglement are presented for rotationally invariant states of spin-1 particle and spin-j particle with half-integer j.     

A variational adiabatic hyperspherical finite element R matrix methodology: general formalism and application to H + H2 reaction

The aim of this paper is to present an efficient numerical procedure for the theoretical study of bimolecular reactions. It is based on the R matrix variational formalism and the p-version of the finite element method (p-FEM) for expanding the wave function in a finite basis set, and facilitates the development of an efficient algorithm to invert matrices that significantly reduces the computational time in R matrix calculations. We also utilise the self-consistent finite element method to optimise the elements mesh and provide faster convergence of results. We apply our methodology to the study of the collinear H + H₂ process and evaluate its efficiency by comparing our results with several results previously published in the literature.     

Influence of the spatial rotation of a polarization plane on the radiative friction force in light fields with polarization gradients

Simple atomic models (1/2→1/2 and 1/2→3/2 transitions) were taken as an example to consider, in the sub-Doppler cooling approximation, influence of the spatial rotation of a polarization plane on the radiative friction force at arbitrary field configurations of dimensionality D<1. Spatial gradients of the angles determining this rotation additionally contribute to the friction force. This contribution is comparable in magnitude with other forces if the detuning δ is on the order of the radiative relaxation constant γ. For the j→j+1 transitions, the contribution promotes sub-Doppler cooling at δ<0, whereas for the j→j transitions (half-integer j) it induces anisotropic heating and cooling processes.     

The residual interaction of bound nucleons-two-nucleon matrix elements deduced from transfer experiments

Matrix elements for the effective two-nucleon interaction have been deduced from the population of multiplets near closed shells as observed in direct transfer reactions. In the evaluation, the limited purity of such multiples was taken into consideration, typically by weighting the observed fractions of the two-nucleon configurations by their spectroscopic strenghts and by using the resulting energy centroids. In a few cases, off-diagonal matrix elements are available from empirical wave funcitons. The systematic errors for particle-particle matrix elements extracted directly and those obtained from Pandya transformations were found to go in opposite directions. In some cases, this feautre of the empirical mehtod could be used to suggest upper and lower “bounds” for the extracted matrix elements. Diagonal matrix elements for the empirical residual interaction show a number of features suggestive of an underlying simplicity in the interaction of bound nucleons. Within experimental uncertainties (of about 10% for T=0 matrix elements) the monopole parts of the matrix elements are fit well with a simple A?0.75 dependence, and the data available to date do not reveal any significant monopole dependence on the quantum numbers of the interacting nucleons. The usefulness of scaling is suggested. Generally, diagonal matrix elements E_J(j₁, j₂) normalized by the extracted A-dependent monopole strength agree within expected experimental uncertainties whether derived from particle-particle or particle-hole multiples and whether extracted from the beginning or the end of a major shell. For values J≠0, the diagonal E_J(j²) matrix elements seem to follow two universal functions which depend on the semi-classical coupling angles θ₁₂, but are otherwise independent on j. For j₁≠j₂ several “typical” functions ?(θ₁₂) can be constructed which fit subsets of the data and differ in a predictable way. The general features of the bound-nucleon interaction appear consistent with those of theoretical matrix elements based on a number of short-range model forces or on calculations using the G matrix approach to deal with realistic free nucleon forces. For the latter, the available theoretical numbers for j₁=j₂ agree well with the T=1 set, but they differ quantitatively from the observed matrix elements for T=0, sometimes by many (experimental) standard deviations.     

Shell structure of new magic nuclei: Systematics of features

Investigation of the structure of the upper shells of new magic nuclei revealed an empirical regularity with the following characteristic feature: closed proton and neutron subshells, with identically large total angular momenta (j = j coupling), are located near the Fermi energy and there is a closed subshell with j = 1/2 above one of them. The properties of the nuclei exhibiting this feature of closed upper proton and neutron subshells have been investigated in detail. Quantitative manifestation of the new magicity effects, depending on the occupancy of the corresponding subshells with nucleons, has been analyzed. Several nuclei have been found, which, obviously, also have magic properties, and all classical, new magic, and nonmagic oxygen isotopes ^14–48O have been considered from the new point of view.