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Quantum Numbers (quantum + number)

Distribution by Scientific Domains

Physics and Astronomy	60%
Chemistry	32%

Kinds of Quantum Numbers

spin quantum number

Selected Abstracts

Elementary Many-Particle Processes in Plasma Microfields

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 3 2006
M. Yu.
Abstract The effect of electric and magnetic plasma microfields on elementary many-body processes in plasmas is considered. As detected first by Inglis and Teller in 1939, the electric microfield controls several elementary processes in plasmas as transitions, line shifts and line broadening. We concentrate here on the many-particle processes ionization, recombination, and fusion and study a wide area of plasma parameters. In the first part the state of art of investigations on microfield distributions is reviewed in brief. In the second part, various types of ionization processes are discussed with respect to the influence of electric microfields. It is demonstrated that the processes of tunnel and rescattering ionization by laser fields as well as the process of electron collisional ionization may be strongly influenced by the electric microfields in the plasma. The third part is devoted to processes of microfield action on fusion processes and the effects on three-body recombination are investigated. It is shown that there are regions of plasma densities and temperatures, where the rate of nuclear fusion is accelerated by the electric microfields. This effect may be relevant for nuclear processes in stars. Further, fusion processes in ion clusters are studied. Finally we study in this section three-body recombination effects and show that an electric microfield influences the three-body electron-ion recombination via the highly excited states. In the fourth part, the distribution of the magnetic microfield is investigated for equilibrium, nonequilibrium, and non-uniform magnetized plasmas. We show that the field distribution in a neutral point of a non-relativistic ideal equilibrium plasma is similar to the Holtsmark distribution for the electrical microfield. Relaxation processes in nonequilibrium plasmas may lead to additional microfields. We show that in turbulent plasmas the broadening of radiative electron transitions in atoms and ions, without change of the principle quantum number, may be due to the Zeeman effect and may exceed Doppler and Stark broadening as well. Further it is shown that for optical radiation the effect of depolarization of a linearly polarized laser beams propagating through a magnetized plasma may be rather strong. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Half-numerical evaluation of pseudopotential integrals

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 9 2006
Roberto Flores-Moreno
Abstract A half-numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two-dimensional angular and one-dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l -quantum number. The radial integrals are calculated by an adaptive one-dimensional numerical quadrature. For the semilocal radial part a pretabulation scheme is used. This pretabulation simplifies the handling of radial integrals, makes their calculation much faster, and allows their easy reuse for different integrals within a given shell combination. The implementation of this new algorithm is described and its performance is analyzed. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1009,1019, 2006 [source]

Spin densities in two-component relativistic density functional calculations: Noncollinear versus collinear approach

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2002
Christoph Van WüllenArticle first published online: 3 APR 200
Abstract With present day exchange-correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar-relativistic calculations, the spin density can be defined conventionally, but if spin-orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the "spin density" is. In many applications, a fixed quantization axis is used to define the spin density ("collinear approach"), but one can also use the length of the local spin magnetization vector without any reference to an external axis ("noncollinear approach"). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange-correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn-Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I and PbF indicate that the error introduced by the collinear approximation is ,0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 779,785, 2002 [source]

Four-sublattice ferrimagnetic systems: II.

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2004
Effects of the spin quantum number
Abstract The effects of the spin quantum number of each sublattice on the quantum fluctuations are discussed for different spin configurations in four-sublattice ferrimagnetic systems. In multi-sublattice ferrimagnets, although the individual sublattice magnetization vectors do not offset each other, but their deviations vectors can cancel out. Namely, the sum of the deviations of magnetization of sites with same initiate spin direction, equals to that of sites with opposite initiate spin direction ,i , = ,j ,, i and j denote respectively the spins along the up and down initiate spin directions). The role of the spin quantum number of each site on magnetic properties of the system is correlative with properties of the exchange couplings surrounding the site. The results show that the proportion of ferromagnetic and antiferromagnetic exchange couplings, the spin quantum number of each sublattice and the magnetically structural symmetry of the system all play important roles on the quantum fluctuations of the systems. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials

ANNALEN DER PHYSIK, Issue 10-11 2009
A. Arda
Abstract The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov,Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q -deformed Rosen,Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number , = 0, or , , 0. [source]

Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

ANNALEN DER PHYSIK, Issue 10-11 2009
B. Vogt
Abstract The physical properties of quantum systems, which are described by the anisotropic Heisenberg model, are influenced by thermal as well as by quantum fluctuations. Such a quantum Heisenberg system can be profoundly changed towards a classical system by tuning two parameters, namely the total spin and the anisotropy field: Large easy-axis anisotropy fields, which drive the system towards the classical Ising model, as well as large spin quantum numbers suppress the quantum fluctuations and lead to a classical limit. We elucidate the incipience of this reduction of quantum fluctuations. In order to illustrate the resulting effects we determine the critical temperatures for ferro- and antiferromagnets and the ground state sublattice magnetization for antiferromagnets. The outcome depends on the dimension, the spin quantum number and the anisotropy field and is studied for a widespread range of these parameters. We compare the results obtained by: Classical Mean Field, Quantum Mean Field, Linear Spin Wave and Random Phase Approximation. Our findings are confirmed and quantitatively improved by numerical Quantum Monte Carlo simulations. The differences between the ferromagnet and antiferromagnet are investigated. We finally find a comprehensive picture of the classical trends and elucidate the suppression of quantum fluctuations in anisotropic spin systems. In particular, we find that the quantum fluctuations are extraordinarily sensitive to the presence of small anisotropy fields. This sensitivity can be quantified by introducing an "anisotropy susceptibility". [source]

Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials

Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

NMR nomenclature: Nuclear spin properties and conventions for chemical shifts (IUPAC recommendations 2001),

CONCEPTS IN MAGNETIC RESONANCE, Issue 5 2002
Robin K. Harris
Abstract A unified scale is recommended for reporting the NMR chemical shifts of all nuclei relative to the 1H resonance of tetramethylsilane. The unified scale is designed to provide a precise ratio, ,, of the resonance frequency of a given nuclide to that of the primary reference, the 1H resonance of tetramethylsilane (TMS) in dilute solution (volume fraction, , < 1%) in chloroform. Referencing procedures are discussed, including matters of practical application of the unified scale. Special attention is paid to recommended reference samples and values of , for secondary references on the unified scale are listed, many of which are the results of new measurements. Some earlier recommendations relating to the reporting of chemical shifts are endorsed. The chemical shift, ,, is redefined to avoid previous ambiguities but to leave practical usage unchanged. Relations between the unified scale and recently published recommendations for referencing in aqueous solutions (for specific use in biochemical work) are discussed, as well as the special effects of working in the solid state with magic-angle spinning. In all, nine new recommendations relating to chemical shifts are made. Standardized nuclear spin data are also presented in tabular form for the stable (and some unstable) isotopes of all elements with non-zero quantum numbers. The information given includes quantum numbers, isotopic abundances, magnetic moments, magnetogyric ratios and receptivities, together with quadrupole moments and linewidth factors (where appropriate). © 2001 IUPAC. Concepts Magn Reson 14:326,346, 2002 [source]

Big Consequences of Small Changes (Non-locality and non-linearity of Hartree-Fock equations)

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-8 2009
M.Ya. Amusia
Abstract It is demonstrated that non-locality and non-linearity of Hartree-Fock equations dramatically affect the properties of their solutions that essentially differ from solutions of Schrödinger equation with a local potential. Namely, it acquires extra zeroes, has different coordinate asymptotic, violates so-called gauge-invariance, has different scattering phases at zero energy, has in some cases several solutions with the same set of quantum numbers, usually equivalent expressions of current and Green's functions became non-equivalent. These features result in a number of consequences for probabilities of some physical processes, leading e. g. to extra width of atomic Giant resonances and enhance considerably the ionization probability of inner atomic electrons by a strong field (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

On the Time-Resolved Optogalvanic Spectra of Neon and Krypton

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 6 2007
N. K. Piracha
Abstract In this work time resolved optogalvanic signals associated with transitions excited from the first metastable state of neon and krypton have been studied. These gases have similar energy state configurations and it is of significant interest to study their time resolved optogalvanic waveforms resulting from transitions belonging to the states of same quantum numbers. The experimentally observed optogalvanic signals recorded for different discharge currents have been fitted to a theoretical model to obtain parameters that determine amplitudes, instrumental time constants and decay rates of the 1s levels. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Double Excited High-n Spin Dependent Atomic Structure Scaling Laws for He I: Application to Radiative Properties for Edge Plasma Conditions

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7-9 2006
E. H. Guedda
Abstract We present our numerical calculations of dielectronic recombination rate coefficients which are spin dependent (2lnl , -1snl1L, 1snl3L ) and develop scaling relations which are converging for all spin (S), angular (L) and main (n) quantum numbers. The influence of atomic data inaccuracies, spin dependent channelling of dielectronic recombination rates and collisions on the atomic/ionic fractions is discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Calculated Electron Impact Ionization Cross Sections of Excited Ne Atoms Using the DM Formalism

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 7 2005
H. Deutsch
Abstract We used the semi-classical Deutsch-Märk (DM) formalism to calculate absolute electron-impact ionization cross sections of excited Ne atoms from threshold to 1000 eV. Excited states of Ne where the outermost valence electron is excited to states with principal quantum numbers up to n = 7 and orbital angular momentum quantum numbers up to l = 2 have been considered and systematic trends in the calculated cross section data are discussed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Evaluation of one-electron molecular integrals over complete orthonormal sets of ,, -ETO using auxiliary functions

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2010
Israfil I. Guseinov
Abstract By the use of expansion and one-range addition theorems, the one-electron molecular integrals over complete orthonormal sets of ,, -exponential type orbitals arising in Hartree,Fock,Roothaan equations for molecules are evaluated. These integrals are expressed through the auxiliary functions in ellipsoidal coordinates. The comparison is made using Slater-, Coulomb-Sturmian-, and Lambda-type basis functions. Computation results are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants, and location of orbitals. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source]

Application of the asymptotic iteration method to the exponential cosine screened Coulomb potential

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2007
O. Bayrak
Abstract We present the iterative solutions of the radial Schrödinger equation for the exponential cosine screened Coulomb (ECSC) potential for any n and l quantum states by applying the asymptotic iteration method (AIM). We show that it is possible to obtain the solution as accurate as the other methods without any perturbation. Furthermore, there are no tedious mathematical difficulties and restrictions on finding the energy eigenvalues for any n and l quantum numbers. Our results are in excellent agreement with the ones published in the literature. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

Exact analytical solutions to the Kratzer potential by the asymptotic iteration method

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 3 2007
O. Bayrak
Abstract For any n and l values, we present a simple exact analytical solution of the radial Schrödinger equation for the Kratzer potential within the framework of the asymptotic iteration method (AIM). The exact bound-state energy eigenvalues (Enl) and corresponding eigenfunctions (Rnl) are calculated for various values of n and l quantum numbers for CO, NO, O2, and I2 diatomic molecules. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source]

Translation of STO charge distributions

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2005
J. Fernández Rico
Abstract Barnett and Coulson's ,-function method (M. P. Barnett and C. A. Coulson, Philos. Trans. R. Soc., Lond. A 1951, 243, 221) is one of the main sources of algorithms for the solution of multicenter integrals with Slater-type orbitals. This method is extended here from single functions to two-center charge distributions, which are expanded at a third center in terms of spherical harmonics times analytical radial factors. For s,s distributions, the radial factors are given by a series of factors corresponding to the translation of s -type orbitals. For distributions with higher quantum numbers, they are obtained from those of the s,s distributions by recurrence. After analyzing the convergence of the series, a computational algorithm is proposed and its practical efficiency is tested in three-center (AB|CC) repulsion integrals. In cases of large basis sets, the procedure yields about 12 correct significant figures with a computational cost of a few microseconds per integral. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 846,855, 2005 [source]

NMR nomenclature: nuclear spin properties and conventions for chemical shifts.

MAGNETIC RESONANCE IN CHEMISTRY, Issue 7 2002
Applied Chemistry., IUPAC Recommendations 2001., International Union of Pure
Abstract An Addendum has been published for this article in Magnetic Resonance in Chemistry 40(9) 2002, 622. A unified scale is recommended for reporting the NMR chemical shifts of all nuclei relative to the 1H resonance of tetramethylsilane. The unified scale is designed to provide a precise ratio, ,, of the resonance frequency of a given nuclide to that of the primary reference, the 1H resonance of tetramethylsilane (TMS) in dilute solution (volume fraction, , < 1%) in chloroform. Referencing procedures are discussed, including matters of practical application of the unified scale. Special attention is paid to recommended reference samples, and values of , for secondary references on the unified scale are listed, many of which are the results of new measurements. Some earlier recommendations relating to the reporting of chemical shifts are endorsed. The chemical shift, ,, is redefined to avoid previous ambiguities but to leave practical usage unchanged. Relations between the unified scale and recently published recommendations for referencing in aqueous solutions (for specific use in biochemical work) are discussed, as well as the special effects of working in the solid state with magic-angle spinning. In all, nine new recommendations relating to chemical shifts are made. Standardized nuclear spin data are also presented in tabular form for the stable (and some unstable) isotopes of all elements with non-zero quantum numbers. The information given includes quantum numbers, isotopic abundances, magnetic moments, magnetogyric ratios and receptivities, together with quadrupole moments and linewidth factors (where appropriate). Copyright 2001 IUPAC. Reprinted with permission from Pure Appl. Chem. 2001; 73: 1795. [source]

Description of band structures of armchair nanotubes using the symmetry-adapted linear augmented cylindrical wave method

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2009
P. N. D'yachkov
Abstract Using a symmetry-adapted linear augmented cylindrical wave method, the total band structures and the densities of states of the armchair single-walled carbon nanotubes (SWNTs) (n,n) with 4 , n , 20, n = 30, 40, 60 and 100 are calculated. The approximations are made in the sense of muffin-tin potentials and density functional theory only. The electronic states are presented as the functions of the two quantum numbers, namely, the continuous wave vector k corresponding to the screw symmetry operations and an integer rotational quantum number L between 0 and n , 1. An account of rotational and helical symmetry properties of the armchair SWNTs and particularly an introduction of the quantum number L permit to elaborate a more detailed classification of the armchair SWNTs electronic states. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Spin-wave spectra and magnetization of ferro,ferrimagnetic double layers

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 6 2008
Wei Jiang
Abstract The spin-wave spectra and magnetization of the ferro,ferrimagnetic double layers are studied by using a linear spin-wave approximation and retarded Green's-function method. We obtain the four branches of the spin-wave spectra. Two energy gaps are found to exist in the energy band. The effects of the interlayer exchange coupling, the intralayer exchange coupling and the spin quantum numbers on the spin-wave spectra and the energy gaps are discussed. The minimum (maximum) value point on the spin-wave spectra and energy gaps correspond to a system that has a high symmetrical magnetic structure and the balance of quantum competitions among the exchange couplings and the spin quantum numbers of the system. There is a crossover between sublattice magnetizations in ferromagnetic layer that is affected by quantum fluctuations, thermal fluctuations and frustration of spins. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Magnon energy gap and the magnetically structural symmetry in a three-layer ferrimagnetic superlattice

PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 8 2006
Rong-ke Qiu
Abstract The magnon energy band in a ferrimagnetic superlattice with three layers in a unit cell is studied by employing retarded Green's functions and the spin-wave method. Two modulated energy gaps ,,13 and ,,23 are evaluated systematically, which exist in the magnon energy band along the Kx -direction perpendicular to the plane of the superlattice. It is revealed that the energy gap ,,13 has a direct relation with the symmetry among the spin quantum numbers and the interlayer exchange couplings, while the energy gap ,,23 relates to the symmetry among these spin quantum numbers only. These symmetries differ from the symmetry of crystallographic point groups. We define the magnetically structural symmetry that is dominated mainly by the magnetic parameters. The absence of the energy gap at a certain condition means that the system has a high magnetically structural symmetry. The magnetically structural symmetry of the superlattice, which is an intrinsic property, strongly affects the magnon energy band structure and thus the magnetic behaviors of the system. Furthermore, two complete bandgaps are observed to extend through the Brillouin zone (referred to as "magnonic crystal") in this superlattice system. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]