bluuebunny/crossref_metadata_2025 huggingface dataset:
Three-dimensional quantum reactive scattering calculations for the nonadiabatic (D+H2)+ reaction system
Authors: Takayanagi Toshiyuki , Kurosaki Yuzuru , Ichihara Akira
Published: July 2002

Three-dimensional quantum reactive scattering calculations have been carried out for the (D+H2)+ nonadiabatic ion–molecule collision. The calculations have been done using the time-independent close-coupling formalism with hyperspherical coordinates. The (3×3) diatomics-in-molecule potential energy surfaces have been employed. The result of the accurate quantum scattering calculations have been compared to the results of the quasiclassical trajectory surface hopping method. Two versions of the method have been used; one uses Tully’s fewest switches algorithm and the other is the trajectory surface hopping method of Tully and Preston, in which electronically nonadiabatic hopping is only allowed at the predefined crossing seams. We have found that the agreement between the quantum result and the result of Tully’s method is generally good, but the Tully and Preston method significantly underestimates the nonadiabatic transition probability.
An ab initio study of spectroscopy and predissociation of ClO
Authors: Toniolo A. , Persico M. , Pitea D.
Published: July 2002

We have computed all the electronic states of ClO arising from the Cl(2P)+O(3P) dissociation limit and several of those connected with Cl(2P)+O(1D). Only two excited states have attractive potentials, A 2Π and 1 4Σ−. The A 2Π state undergoes a well known predissociation, because several as yet unknown potential curves cross the A 2Π one and are coupled to it by nonadiabatic and/or spin-orbit interactions. The calculation of the interaction matrix elements allows to explain the predissociation of A 2Π, due to transitions to the 3 2Π,  12Δ, 2 4Σ− and other less important states, all leading to the Cl(2P)+O(3P) dissociation.
Liquid crystallinity in flexible and rigid rod polymers
Authors: Pickett Galen T. , Schweizer Kenneth S.
Published: July 2002

We apply an anisotropic version of the polymer reference interaction site model (PRISM) integral equation description of flexible polymers to analyze athermal liquid crystallinity. The polymers are characterized by a statistical segment length, σo, and by a physical hard-core thickness, d, that prevents the overlap of monomers on different chains. At small segment densities, ρ, the microscopic length scale d is irrelevant (as it must be in the universal semidilute regime), but becomes important in concentrated solutions and melts. Under the influence of the excluded volume interactions alone, the chains undergo a lyotropic, first-order isotropic–nematic transition at a concentration dependent upon the dimensionless “aspect ratio,” σo/d. The transition becomes weaker as d→0, becoming second order, as has been previously shown. We extend the theory to describe the transition of rigid, thin rods, and discuss the evolution of the anisotropic liquid structure in the ordered phase.
The product rovibrational and spin–orbit state dependent dynamics of the complex reaction H+CO2→OH(2Π;ν,N,Ω, f)+CO: Memories of a lifetime
Authors: Brouard M. , Hughes D. W. , Kalogerakis K. S. , Simons J. P.
Published: July 2002

The product-state-resolved dynamics of the reaction H+CO2→OH(2Π;ν,N,Ω,f)+CO have been explored in the gas phase at 298 K and center-of-mass collision energies of 2.5 and 1.8 eV (respectively, 241 and 174 kJ mol−1), using photon initiation coupled with Doppler-resolved laser-induced fluorescence detection. A broad range of quantum-state-resolved differential cross sections (DCSs) and correlated product kinetic energy distributions have been measured to explore their sensitivity to spin–orbit, Λ-doublet, rotational and vibrational state selection in the scattered OH. The new measurements reveal a rich dynamical picture. The channels leading to OH(Ω,N∼1) are remarkably sensitive to the choice of spin–orbit state: Those accessing the lower state, Ω=3/2, display near-symmetric forward–backward DCSs consistent with the intermediacy of a short-lived, rotating HOCO (X̃ 2A′) collision complex, but those accessing the excited spin–orbit state, Ω=1/2, are strongly focused backwards at the higher collision energy, indicating an alternative, near-direct microscopic pathway proceeding via an excited potential energy surface. The new results offer a new way of reconciling the conflicting results of earlier ultrafast kinetic studies. At the higher collision energy, the state-resolved DCSs for the channels leading to OH(Ω,N∼5–11) shift from forward–backward symmetric toward sideways–forward scattering, a behavior which resembles that found for the analogous reaction of fast H atoms with N2O. The correlated product kinetic energy distributions also bear a similarity to the H/N2O reaction; on average, 40% of the available energy is concentrated in rotation and/or vibration in the scattered CO, somewhat less than predicted by a phase space theory calculation. At the lower collision energy the discrepancy is much greater, and the fraction of internal excitation in the CO falls closer to 30%. All the results are consistent with a dynamical model involving short-lived collision complexes with mean lifetimes comparable with or somewhat shorter than their mean rotational periods. The analysis suggests a potential new stereodynamical strategy, “freeze-frame imaging,” through which the “chemical shape” of the target CO2 molecule might be viewed via the measurement of product DCSs in the low temperature environment of a supersonic molecular beam.
Predissociation in b 1Πu,v (v=1,4,5,6) levels of N2
Authors: Ubachs W. , Velchev I. , de Lange A.
Published: July 2002

In a high-resolution laser spectroscopic study, using a tunable Fourier-transform limited light source in the extreme ultraviolet, the b 1Πu excited valence state of molecular nitrogen is reinvestigated for vibrational levels v=1, 4, 5, and 6. From line broadening of individual rotational levels excited state lifetimes were determined: τ(v=1)=1.1±0.3 ns, τ(v=4)=18±1 ps, τ(v=5)=205±25 ps, and τ(v=6)=350±75 ps. Additionally, the lifetime of the o3 1Πu, v=0 Rydberg state was determined: τ=240±50 ps. For the b 1Πu, v=1 state improved rotational constants were determined.
Potential energy surface for a seven-atom reaction. Thermal rate constants and kinetic isotope effects for CH4+OH
Authors: Espinosa-Garcı́a J. , Corchado J. C.
Published: July 2002

The potential energy surface for the gas-phase CH4+OH→CH3+H2O reaction and its deuterated analogs was constructed with suitable functional forms to represent vibrational modes, and was calibrated by using the experimental thermal rate constants and kinetic isotope effects. On this surface, the forward and reverse thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 200–2000 K, finding reasonable agreement with the available experimental data. We also calculated six sets of kinetic isotope effects and, in general, the theoretical results underestimate the few available experiments, with exception of the C-13 isotopic effect values which are overestimated. Finally, this surface is also used to analyze dynamical features, such as reaction-path curvature and coupling between the reaction coordinate and vibrational modes.
Theoretical study on ammonia cluster ions: Nature of kinetic magic number
Authors: Nakai Hiromi , Goto Touichirou , Okada Yoshiki , Orii Takaaki , Takeuchi Kazuo , Ichihashi Masahiko , Kondow Tamotsu
Published: July 2002

We theoretically investigated collision cross sections due to the attractive forces between NH4+(NH3)n−1 (n=2–8) and ND3. We found that the dependence of the collision cross sections on collision energy and cluster size are comparable to those of measured fusion cross sections. The kinetic magic number, n=5, is related to the structure of the pentamer. Namely, the center ion in the pentamer is surrounded by first-shell ammonia molecules.
Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge5, Ge6, Ge7, and Ge8 by Knudsen effusion mass spectrometry
Authors: Gingerich K. A. , Schmude R. W. , Sai Baba M. , Meloni G.
Published: July 2002

The high-temperature mass spectrometric method was employed to measure the equilibrium partial pressures of small germanium clusters above liquid germanium contained in a graphite Knudsen cell. These data were combined with new thermal functions, calculated from recent theoretical and spectroscopic molecular parameters, to evaluate the atomization enthalpies and enthalpies of formation of Ge5–Ge8. Mass spectrometric equilibrium data available in literature were also reevaluated. The following atomization enthalpies, ΔaH0o(Gen,g) and enthalpies of formation ΔfH298.15o(Gen,g), in kJ mol−1, have been obtained: Ge5, 1313±27 and 548±27, Ge6, 1649±33 and 583±33, Ge7, 2008±42 and 598±42, Ge8, 2359±60 and 618±60. The atomization energies are compared with available theoretical values.
The influence of both coordination number and lattice constant on the nonmetal to metal transition
Authors: Yakovkin I. N. , Dowben P. A.
Published: July 2002

We show that both coordination and lattice constant can have an important influence on the nonmetal to metal transition and the two parameters are not easily separated. Using example theoretical calculations for barium, we provide a compelling case that atomic coordination is a critical factor in determining the critical lattice constant for the nonmetal to metal transition. A comparison between the nonmetal to metal transition three-dimensional and two-dimensional systems is not possible on the basis of the atomic coordination alone. This is discussed in the context of a comparison of the available experimental data for both elemental expanded fluids (three-dimensional) and overlayers (quasi-two-dimensional).
A lattice model Monte Carlo study of coil-to-globule and other conformational transitions of polymer, amphiphile, and solvent
Authors: Jennings Deirdre E. , Kuznetsov Yuri A. , Timoshenko Edward G. , Dawson Kenneth A.
Published: July 2002

A model of polymer-amphiphile-solvent systems on a cubic lattice is used to investigate the phase diagram of such systems. The polymer is treated within the canonical ensemble (T,V,N) and the amphiphile and solvent are treated within the grand canonical ensemble (T,V,μ). Using a range of Monte Carlo moves the phase diagram of polymer-amphiphile-solvent mixtures, as a function of solvent quality (parametrized by χ) and relative chemical potential, μ, is studied for the dilute polymer limit. The effect of increasing the polymer chain length, N, on the critical aggregation concentration (CAC), and the type of polymer-amphiphile complex formed above the CAC are also examined. For some parameters, it is found that the polymer and amphiphile form a polymer-micelle complex at low amphiphile concentrations, and that the polymer coil-to-globule transition point increases with increasing amphiphile concentration. The resulting collapsed globule has a solvent core and is surrounded by a layer of amphiphile. These results are in good qualitative agreement with experimental results for the poly(N-isopropylacrylamide) (PNIPAM)/sodium dodecyl sulfate (SDS) system. At higher amphiphile concentrations, the polymer and amphiphile form several layered structures depending on the strength of the three-body amphiphilic interactions, l. Finally, the effect of the polymer chain length, N, and the strength of the three-body amphiphilic interactions, l, on the stability of the polymer-amphiphile structures is investigated.
Spectroscopic constants and potential energy curves of tungsten carbide
Authors: Balasubramanian K.
Published: July 2002

Spectroscopic constants (Re,ωe,Te,μe) and potential energy curves for 40 low-lying electronic states of the diatomic tungsten carbide (WC) were obtained using the complete active space multiconfiguration self-consistent field followed by the multireference singles+doubles configuration interaction and full first- and second-order configuration interaction calculations that included up to 6.4 mil configurations. Spin–orbit effects were included through the enhanced relativistic configuration interaction method described here for 28 electronic states of WC lying below ∼20 000 cm−1. The spin–orbit splitting of the ground state of WC was found to be very large (4394 cm−1). The ground and excited electronic states of the W atom were also computed and were found to be in good agreement with the experimental data. The nature of bonding was analyzed through the composition of orbitals, leading configurations, Mulliken populations, and dipole moments. The dissociation energy of WC was computed including spin–orbit and electron correlation effects. The recent photoelectron spectra of WC− were assigned on the basis of our computed results.
A theoretical study of ion dissociation of H2O2+
Authors: Nobusada Katsuyuki , Tanaka Kiyoshi
Published: July 2002

Ion dissociation of H2O2+ following the radiationless decay of core-excited H2O is studied theoretically. The detailed mechanisms of the ion dissociation are discussed by using potential energy diagrams for various electronic states of H2O2+ depicted as a function of the internuclear distance of OH and the bending angle of HOH. The dynamics of the ion dissociation is categorized into three types depending on the site where positive holes of H2O2+ are found. The three types are as follows. (i) One or more positive holes are found on the bonding orbital between O and H. (ii) Two positive holes localize on the oxygen 2p orbital (i.e., the lone-paired electrons on the oxygen atom are ejected). (iii) Two positive holes are present on the oxygen 2p orbital and one more hole appears by shake-up excitation. In the case of (i), H2O2+ easily dissociates by the force of Coulomb repulsion between OH+ and H+. A few lowest electronic states of H2O2+ belong to the type (ii). These low-lying potential curves are less steep than those of the type (i) because Coulomb repulsion does not work. Moreover, such potential energy curves have a shallow well. Reflecting these characteristic features, the ion dissociation is relatively depressed. These results are qualitatively in good accord with the experimental observation. In the case of (iii), it is found that a new two-step ion dissociation process of OH2+→O++H+ following H2O2+→H+OH2+ possibly occurs.
State-to-state studies of intramolecular energy transfer in highly excited HOOH(D): Dependencies on vibrational and rotational excitation
Authors: Kuhn B. , Rizzo T. R.
Published: July 2002

We use infrared-optical double resonance excitation, together with laser induced fluorescence (LIF) product detection, to measure rotationally resolved vibrational overtone spectra of hydrogen peroxide at energies up to 4500 cm−1 above the O–O dissociation threshold. The spectroscopic constants obtained from such spectra help characterize the potential energy surface and provide a stringent test for any theoretical representation thereof. Line profiles of individual rovibrational features provide information on the vibrational and rotational dependence of the intramolecular dynamics. Coupling to the manifold of optically inactive background states is independent of the total density of rovibrational states but rather controlled by specific low-order coupling terms in the Hamiltonian. Moreover, we find no significant difference in the IVR dynamics between states with all quanta in a single OH oscillator or distributed between the two local OH stretches. Finally, increasing rotation around the O–O pseudo-figure axis clearly enhances the IVR rate in most vibrational bands of H2O2 due to increased a-axis Coriolis coupling. Comparison to other OH stretch containing molecules allows us to define chromophore specific dynamics of this light atom oscillator.
Stereodynamics of the reactions of O(3P) with saturated hydrocarbons: The dependences on the collision energy and the structural features of hydrocarbons
Authors: Tsurumaki Hiroshi , Fujimura Yo , Kajimoto Okitsugu
Published: July 2002

State-selected differential cross sections (DCSs) have been measured for the OH radicals produced from the reactions of O(3P) with saturated hydrocarbons by utilizing Doppler-resolved polarization spectroscopy. Stereodynamics in the reactions of secondary (c-C6H12) and tertiary (i-C4H10) hydrogen atoms are discussed based on the dependences of the DCSs on the collision energy and the structure of these hydrocarbons. For the c-C6H12 reaction, the DCS of the OH(2Π3/2,v′=1,j′=3.5,A′) shows predominant intensities in the backward hemisphere with reference to the incident O(3P) atom at a mean collision energy of 〈Ecoll〉=12 kJ/mol. When the collision energy is raised to 〈Ecoll〉=33 kJ/mol, the OH radicals scattered in the forward hemisphere grow almost to match those in the backward hemisphere. The observed increase in the forward scattering implies that the collision energy makes the large impact parameter collisions contribute to the reactive scattering. At a similar collision energy of 〈Ecoll〉=31 kJ/mol the forward scattering component in the DCS of the i-C4H10 reaction does not exceed that of the c-C6H12. This shows that the cone of acceptance is not enlarged in the i-C4H10 reaction from that in the c-C6H12 reaction, as opposed to the expectation based on the height of activation barrier. The absence of the enlargement of the cone of acceptance can be attributed to a large steric hindrance caused by the three bulky methyl groups surrounding the reactive tertiary C–H bond of i-C4H10. The difference in the steric hindrance can explain the difference in the temperature-dependent pre-exponential factors of the macroscopic reaction rates between the abstraction of the secondary and tertiary C–H bonds. The collision energy dependence of the DCS as well as the internal excitation of alkyl radical products reveal that the O(3P)+alkane reactions are not always dominated by the simple rebound mechanism, which has long been believed.
Efficient distributed Gaussian basis for rovibrational spectroscopy calculations
Authors: Poirier Bill , Light J. C.
Published: July 2002

We examine the problem of choosing efficient basis sets for the calculation of vibrational states of molecules. An exact quantum functional is derived for optimizing the parameters of distributed Gaussian basis sets (DGBs). For a given Hamiltonian and energy range, the basis is optimized with respect to the accuracy of the computed eigenvalues. This procedure demonstrates that optimized DGBs are remarkably efficient, being essentially exact for the one-dimensional harmonic oscillator, and orders of magnitude more accurate for the 23-state Morse oscillator than previous DGB calculations of comparable size. Contrary to expectations however, the quantum optimized DGBs have large overlaps, resulting in nearly singular overlap matrices that may cause numerical instabilities in larger calculations. On the other hand, the optimized eigenvalue calculation is shown to be fairly robust with respect to DGB parameter variations, implying that accurate results are possible using more numerically stable DGBs.
Population labeling spectroscopy for the electronic and the vibrational transitions of 2-pyridone and its hydrogen-bonded clusters
Authors: Matsuda Yoshiyuki , Ebata Takayuki , Mikami Naohiko
Published: July 2002

The S1–S0 electronic spectra, and the vibrational spectra of jet-cooled 2-pyridone (2PY) and its hydrogen bonded clusters, 2PY–H2O and 2PY dimer, have been investigated by population labeling and various double-resonant vibrational spectroscopies. For bare 2PY, the S1–S0 spectrum was measured by laser-induced fluorescence and population labeling spectroscopy. In addition, IR and Raman spectra of the NH stretching vibration were observed in S0 and S1. The results led to the conclusion that 2PY has two close lying electronic states in the S1 region, whose structures are slightly different with respect to the NH group. It was also found that the NH stretching frequency becomes smaller in S1 than in S0, indicating that the NH bond strength of 2PY becomes weaker in S1. The effect of the electronic excitation on the hydrogen bond strength has also been investigated by measuring the NH and OH stretching vibrations of the hydrogen bonded clusters in the two electronic states, and it was found that the hydrogen-bond strength is weaker in S1 than in S0. For 2PY dimer, the IR and the Raman spectra of the NH stretching bands showed a clear intensity alternation, confirming its C2h symmetric structure.
Comment on “Four-component relativistic density functional calculations of heavy diatomic molecules” [J. Chem. Phys. 112, 3499 (2000)]
Authors: Liu Wenjian , van Wüllen Christoph
Published: July 2002

The present solid analysis shows that the results by Varga et al. [J. Chem. Phys. 112, 3499 (2000)] are not benchmark to calibrate more approximate relativistic approaches. The convergence of the multipolar expansion of the charge density to evaluate the Hartree potential is demonstrated.
Generalization of the diffusion equation by using the maximum entropy principle
Authors: Jumarie Guy
Published: July 2002

By using the so-called maximum entropy principle in information theory, one derives a generalization of the Fokker–Planck–Kolmogorov equation which applies when the n first transition moments of the process are proportional to Δt, while the other ones can be neglected.
Is perturbation theory misleading in general relativity?
Authors: Geroch Robert , Lindblom Lee
Published: July 2002

Two senses in which the perturbation equations of general relativity can be misleading are explored. (i) Under certain circumstances there exist solutions of the perturbation equations that appear to be gauge, in that the metric perturbation is the symmetrized derivative of a vector field, but which nonetheless are not true gauge. (ii) Under certain circumstances there exist solutions of the perturbation equations that cannot, even locally, be extended to higher order in perturbation theory. The latter is a local version of the well-known phenomenon of ‘‘linearization instability.’’
On extensions of supersymmetry algebras in d=4 and 11
Authors: Ahmed E. , Rands B. L. , Taylor J. G.
Published: July 2002

SUSY algebras, in d=4 and 11, are analyzed, extended by the addition of both spinorial and bosonic central charge generators. It is found that only limited extensions are possible, on use of Jacobi identities. Casimirs, irreps, and spin reduction are discussed, and the problems of constructing actions for SUSY and supergravity theories as full superspace actions are considered.
Analytic strong-potential Born approximation cross sections for electron capture from the K shell by fast ions
Authors: Deb N. C. , Sil N. C. , McGuire J. H.
Published: July 2002

The strong potential Born approximation has been applied to evaluate the transition amplitude for the collision process in which a fast ion of charge ZP captures an electron from the K shell of an atomic target with nuclear charge ZT, where ZT ≥ZP. The transition amplitude has been evaluated analytically in terms of Gauss hypergeometric functions. No peaking approximation has been made. We have considered the K-shell capture of electrons by high-energy protons from Li, C, Ne, Na, and Ar. Our results for C, Ne, and Ar are in good agreement with the available experimental data.
On the analysis of relaxation in electrolytes
Authors: Levine Harold
Published: July 2002

Debye and Falkenhagen [Phys. Z. 29, 121 (1928)] analyzed a linear initial/boundary value problem for a differential equation of diffusion type to model the phenomenon of relaxation in electrolytes; specifically, they sought to characterize the disappearance in time of the radially symmetrical and static charge distribution surrounding an individual motionless ion after the latter is instantaneously removed. A detailed reexamination discloses the existence of multiple solutions for the posed problem, with agreement as regards the initial condition and disparity as regards behavior at the central location. A regular solution during the entire relaxation regime is exhibited and offered in place of the classical one, due to Debye and Falkenhagen, which retains a singular nature at the site originally occupied by the reference ion.
Commutation factors on generalized Lie algebras
Authors: Kleeman R.
Published: July 2002

Generalized Lie algebras or color algebras, as we shall call them, are described by an Abelian grading group Γ and a commutation factor ε defined on Γ. In this paper Γ is assumed to be finite. It is shown that color algebras with the pair 〈Γ,ε〉 can also be considered as color algebras with the different pair 〈Γ′,ε′〉 and that as a result a canonical pair 〈Γc,εc〉 is possible. It is further shown that, in fact, a unique ‘‘minimal’’ 〈Γc,εc〉 can be used for all algebras with the pair 〈Γ,ε〉.
On the semiclassical description of N-level systems interacting with radiation fields
Authors: Raggio G. A. , Zivi H. S.
Published: July 2002

It is shown that the dynamics of an N-level quantum system driven by a classical radiation field can be derived rigorously from an associated fully quantum-mechanical model with the help of an asymptotic limit. By formally expanding the full quantum dynamics around the semiclassical limit, quantum corrections to the semiclassical description are systematically constructed. The observables describing these corrections are shown to exist in any order, and explicit expressions for their time dependence are given.
Factors of the Fock functional
Authors: Hegerfeldt Gerhard C.
Published: July 2002

Can the fields φ and π of a representation of the CCR’s be written as φ=1/{φ1×1+1⊗φ2} and similarly for π, such that φi and πi satisfy the CCR’s? What are the possible φi’s and πi’s? This is equivalent to a factorization of the corresponding generating functionals (scaled by 1/). Generalizing this question somewhat we show a noncommutative analog of Cramér’s theorem of probability theory. If φ and π are Fock fields then so are φi, πi, i=1,2; similarly for quasifree representations of the CCR’s. As an application we show that the fields of a representation of the CCR’s whose generating functional differs from a Fock functional by a phase factor only are just shifted Fock fields.
The plane rotations allowed for d-dimensional discrete lattices and their application to the Bravais lattices in three dimensions
Authors: Kim Shoon K.
Published: July 2002

It is shown that the plane rotations allowed for d-dimensional discrete lattices are independent of the dimension d and given by the n-fold rotations Cn with n=2, 3, 4, and 6. The formalism is then applied to formulate the general analytical expressions of the Bravais lattices for three dimensions.
The continuity of dislocations
Authors: Bloomer Iris , Charap John M.
Published: July 2002

Dislocation continuity is derived from the Bilby–Kondo theory of dislocations using exterior calculus. Dislocation density is represented by the torsion vector-valued two-form. Burgers vectors are associated with the vector part of the torsion while dislocation lines are associated with the two-form part. The exterior derivative of the torsion is shown to vanish when the crystal curvature vanishes. This implies two simultaneous continuity conditions: Burgers vector conservation and continuity of dislocation lines. On the other hand, dislocation continuity is violated when the curvature does not vanish. Since this can occur on grain boundaries it is inferred that grain boundaries are regions where crystal curvature is concentrated.
Core size effects, bound states, and scattering states of the Aharonov–Bohm problem
Authors: Gauthier N. , Rochon P.
Published: July 2002

The mathematical solutions of Schrödinger’s equation for an electron which is moving outside a hard cylindrical core which contains a hidden flux is studied and it is shown that there are two possible types of eigenstates or scattering states. The first type of state is cyclic about the hidden flux. Such states give rise to field-induced energy shifts, to probability density shifts, and to a divergent scattering cross section. The second type of state is noncyclic about the above axis but all the physical observables are independent of the hidden magnetic flux. The relationship to gauge invariance is discussed.
Lax-pair operators for squared-sum and squared-difference eigenfunctions
Authors: Ichikawa Yoshi-Hiko , Ino Kazu-Hiro
Published: July 2002

An interrelationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of Lax-pair operators of the sine–Gordon equation and the modified Korteweg–de Vries equation. In particular, it is shown explicitly that there exist Lax-pair operators for the squared-sum and squared-difference eigenfunctions of the Ablowitz–Kaup–Newell–Segur inverse scattering transformation.
On the denominator function for canonical SU(3) tensor operators
Authors: Biedenharn L. C. , Lohe M. A. , Louck James D.
Published: July 2002

The definition of a canonical unit SU(3) tensor operator is given in terms of its characteristic null space as determined by group-theoretic properties of the intertwining number. This definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique (up to ± phases) construction of all SU(3) WCG coefficients (Wigner–Clebsch–Gordan). Using this construction, an explicit SU(3)-invariant denominator function characterizing completely the canonically defined WCG coefficients is obtained. It is shown that this denominator function (squared) is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials. These polynomials, denoted Gtq, are defined over three (shift) parameters and three barycentric coordinates. The properties of these polynomials (hence, of the corresponding invariant denominator function) are developed in detail: These include a derivation of their degree, symmetries, and zeros. The symmetries are those induced on the shift parameters and barycentric coordinates by the transformations of a 3×3 array under row interchange, column interchange, and transposition (the group of 72 operations leaving a 3×3 determinant invariant). Remarkably, the zeros of the general Gtq polynomial are in position and multiplicity exactly those of the SU(3) weight space associated with irreducible representation [q−1,t−1,0]. The results obtained are an essential step in the derivation of a fully explicit and comprehensible algebraic expression for all SU(3) WCG coefficients.
Dielectric description of hadrons with anti-de Sitter symmetry
Authors: van Beveren E. , Rijken T. A. , Dullemond C.
Published: July 2002

In the SO(3,2) symmetric strong curvature and related dielectric description of the quantum chromodynamic vacuum, the classical Maxwell equations are solved for charged particles moving along geodesics. An alternative five-dimensional description of the quark and gluon dynamics is studied in detail. Some interesting features of the anti-de Sitter bag are discussed.
Prolongation structures of nonlinear equations and infinite-dimensional algebras
Authors: Omote Minoru
Published: July 2002

Prolongation structures of the sine–Gordon equation, the Ernst equation, and the chiral model are systematically discussed. It is shown that the prolongation structures generate the Kac–Moody algebra for the sine–Gordon equation and another type of infinite-dimensional algebra for the Ernst equation. This algebra includes the Kac–Moody algebra and the Virasoro algebra as its subalgebra.
Canonical transformations and the equivalence problem
Authors: Moreira D. T. , Werth J.-E.
Published: July 2002

Several equivalence relations for Hamiltonian systems are studied. The relationship to the theory of canonical transformations is analyzed. In the hyperregular case, the results are transformed into the Lagrangian formulation. The gauge group of Lagrangian mechanics is obtained by looking at the generating functions for canonical fiber invariant transformations. An intrinsic proof of a theorem of Henneaux [M. Henneaux, Ann. Phys. (NY) 140, 45 (1982)] is given.
Gravitational mass in an expanding universe
Authors: Sannan Sigurd
Published: July 2002

A test for the Hawking definition of mass is given in a Tolman–Bondi model that asymptotically approaches the open Friedmann universe. An expanding universe filled with dustlike matter of zero pressure is considered. The matter distribution is spherically symmetric but nonhomogeneous. With appropriate boundary conditions, the calculation yields a finite and nonzero value for the Hawking mass, measured as a deviation from a ‘‘renormalized’’ zero mass in the unperturbed Friedmann model. These boundary conditions are more restrictive than those found for a model with gravitational radiation.
A closed form solution of the s-wave Bethe–Goldstone equation with an infinite repulsive core
Authors: Ong Michael K.
Published: July 2002

A closed form s-wave solution of the Bethe–Goldstone equation for the interaction of two nucleons characterized by a potential with an infinite repulsive core is obtained in terms of angular prolate spheroidal wave functions that arise naturally in the analysis of band-limited functions. The asymptotic result for the case of small core radius shows excellent agreement with known results obtained via an approximate iterative procedure.
Current algebra for chiral gauge theories
Authors: Manías M. V. , von Reichenbach M. C. , Schaposnik F. A. , Trobo M.
Published: July 2002

Chiral gauge theories are studied with a special emphasis on the treatment of gauge degrees of freedom so as to obtain a gauge-invariant effective action from which current commutators can be evaluated. It is explicitly shown in a simple example that these commutators are those to be expected in a gauge-invariant theory.
A new self-similar space-time
Authors: Chi L. K.
Published: July 2002

A new self-similar solution of the Einstein field equations is presented. In the new space-time, the density is zero at time zero and follows an inverse square law for large t. The new solution may have interesting astrophysical applications since it has the same reference lengths as that of the Friedmann universe.
The concept of streamfunctions in the Wien effect on a weak electrolyte
Authors: McIlroy Douglas K. , Mason David P.
Published: July 2002

It is shown that streamfunctions g(k), k=1,2, can be defined to describe the two ionic states of a weakly dissociated electrolyte in the presence of a uniform applied electric field. These states comprise the dissociated state and the associated state and the g(k) are shown to be governed by a second-order partial differential equation. By consideration of characteristic numbers describing the two ionic states this equation is solved using similarity solutions. The association rate constant and relative increase in the dissociation constant due to the applied electric field are shown to have simple expressions in terms of the g(k). It is suggested that the streamfunctions are more natural functions with which to describe the mathematical properties of a weak electrolyte than the corresponding distribution functions. Some important mathematical properties of the streamfunctions are discussed.
Finite-dimensional representations of the Lie superalgebra sl(1,3) in a Gel’fand–Zetlin basis. II. Nontypical representations
Authors: Palev Tchavdar D.
Published: July 2002

All nontypical irreducible representations of the special linear Lie superalgebra sl(1,3) are considered. Explicit expressions for the transformation of the basis under the action of the generators are given. The results of this paper together with those obtained in Paper I [T. D. Palev, J. Math. Phys. 26, 1640 (1985)] solve the problem of the finite-dimensional irreducible representations of sl(1,3). The results are compared with those obtained by the Young supertableau technique. A mapping of the supertableau basis on the Gel’fand–Zetlin basis is given.
Path-space formulas for covariant gauges in Krein spaces
Authors: Challifour J. L. , Wood W. A.
Published: July 2002

Path-space representations in terms of Feynman gauge stochastic integrals are given for the free Maxwell field in all covariant gauges interpolating between the Feynman and Landau gauges. These are applied to quantum electrodynamics and Yang–Mills theories with spatial lattice cutoffs.
The Leibbrandt–Mandelstam prescription for general axial gauge one-loop integrals
Authors: Gaigg P. , Kreuzer M. , Schweda M. , Piguet O.
Published: July 2002

It is well known that, in doing light-cone gauge calculations, it is mandatory to regularize the unphysical (q n)−β poles by use of the Leibbrandt–Mandelstam prescription. This technique is also applied to general axial gauges and it is proved that it is a suitable regularization procedure for these gauges as well. In order to find the relation between the Leibbrandt prescription and the more familiar principal value prescription with its simpler Lorentz structure the temporal gauge limit n→0 is performed (within dimensional regularization). Although this limit is found to be singular for multiple poles, the analytically regularized one-loop integrals agree with the results obtained within the principal value technique for the temporal gauge.
A geometric interpretation for the Dirac field in curved space
Authors: Ranganathan D.
Published: July 2002

The imposition of the condition of length invariance on a Weyl manifold that does not lead uniquely to general relativity is shown. Rather, in this limit, the Weyl vector field can be interpreted as a Dirac current. The action is also the same as the Einstein Dirac one, if and only if, the spinor field is anticommuting. The allowed interactions are greatly restricted. They are only minimal gauge couplings and Yukawa interactions with a scalar field transforming according to the rules of Utiyama [Prog. Theor. Phys. 53, 565 (1975)].
On total noncommutativity in quantum mechanics
Authors: Lahti Pekka J. , Ylinen Kari
Published: July 2002

It is shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.
Pedestrian approach to two-cocycles for unitary ray representations of Lie groups
Authors: Krause J.
Published: July 2002

Necessary and sufficient conditions for unitary ray representations of connected Lie groups are reexamined. Thus a systematic constructive method is obtained for calculating the admissible exponent factors (two-cocycles). The gauge freedom of the unitary ray representation formalism is also considered. This introduces the distinction between trivial and genuine ray representations. A special gauge is then adopted, within which the two-cocycle is almost unique. The only prerequisite of the exponent factor calculus is the knowledge of the binary combination rules for the essential parameters of the group. The attained method affords a simple, general, and explicit (i.e., coordinate-dependent) two-cocycle calculus. The aim of this paper is merely instrumental.
Local Green’s function. II
Authors: Wang Renchuan
Published: July 2002

As shown in the preceding paper [J. Math. Phys. 28, XXXX (1987)], the local Green’s function can represent the results of the original general Green’s function. However, it is difficult to find the exact local Green’s function in the general case. In this paper, a special case—‘‘the chain matrix’’—is studied, which is a generalization of the tridiagonal matrice.
In general, the less degeneracy the less transition. A principle for time-dependent Hamiltonian systems in quantum mechanics
Authors: Gingold H.
Published: July 2002

A principle in quantum mechanics is proposed: ‘‘In general, the less degeneracy the less transition.’’ Mathematical support of this principle is given in a setting of a slowly varying time-dependent Schrödinger equation via a theorem of asymptotic decomposition. Formulas that quantitatively relate transition and degeneracy are developed. Ramifications of those formulas are discussed.
Ambiguities in the Debye expansion of the elastic S matrix
Authors: Galvan J. B. , Sesma J.
Published: July 2002

The possibility of expanding the S matrix in a multiple-reflection series (Debye expansion) is shown for an arbitrary-shape short-range potential. Ambiguity in the definition of outgoing and incoming waves inside the potential leads to an infinity of expansions. These are analyzed in a simple example (square well or barrier) in order to characterize the correct choice of outgoing and incoming waves.
On the collision of planar impulsive gravitational waves
Authors: Taub A. H.
Published: July 2002

Exact continuous solutions to the Einstein field equations are determined under the assumption that the subspaces of space-time spanned by the variables XA (A=1,2) admit the three-dimensional group of motions of a two-plane, and the Ricci tensor RAB (A,B=1,2) vanishes. The space-time is assumed to contain two colliding planar impulsive gravitational waves. Each wave may be followed by a distribution of null dust. It is shown that the Cauchy data on a spacelike three-surface does not lead to a unique solution of the Einstein field equations unless additional requirements are imposed on the stress-energy tensor in the region of interaction of the waves.
One-dimensional quantum three-wave interaction model with two fermionic fields and one bosonic field
Authors: Wang Yu-Peng , Pu Fu-Cho
Published: July 2002

The quantum three-wave interaction model (3WI) with two fermionic fields and one bosonic field is studied on the basis of quantum inverse scattering method (QISM). The Hamiltonian for this model is diagonalized and an infinite number of conserved quantities is obtained.
On the classification of vacuum zero Simon tensor solutions in relativity
Authors: Krisch J. P.
Published: July 2002

The Perjes vector is decomposed on a Frenet basis. Geometric insights into the Perjes classification of zero Simon tensor vacuum solutions to the Einstein field equations are obtained. The behavior of the classification under a Killing vector preserving transform is studied.
Lax conjecture about the eigenspeed of the KdV equation
Authors: Qing Xu Bang , Jiu Wang Yong , Gui Shao Chang
Published: July 2002

The Lax conjecture for the KdV equation ut+6uux+uxxx=0 is proved. Let u be the solution of the KdV equation, which is defined for all x and t and vanishes at x=±∞. Then there exist a discrete set of positive numbers c1,...,cN —called the eigenspeeds of u—and sets of phase shifts θ±j such that limt→±∞ u(x+ct,t) ={S(x−θ±j,cj),0, if c=cj,if c≠cj, where S is a solitary wave [P. D. Lax, Commun. Pure Appl. Math. 21, 467 (1968)].
Galilean quantum kinematics
Authors: Krause Jorge
Published: July 2002

The Galilean symmetry of a free particle in one-dimensional space is examined under the scope of non-Abelian quantum kinematics. Within the Hilbert space that carries the regular ray representation of the Galilei group the Schrödinger operator appears as one of the three fundamental invariants of the extended kinematic algebra. By means of a superselection rule the physical Hilbert subspaces of the system are identified, in which a complementary ray representation of the Galilean transformation produces the time-dependent Schrödinger equation, and the Feynman space-time propagator. The quantization approach used in this paper is purely group theoretic and relativistic.
A comparison of solution generating techniques for the self-dual Yang–Mills equations
Authors: Tafel Jacek
Published: July 2002

It is shown that all self-dual Yang–Mills fields generated by the Atiyah–Ward Ansätze 𝒜l can be obtained from the Ansatz 𝒜0 by the ‘‘dressing’’ method of Zakharov and Shabat [Funct. Anal. Appl. 13, 166 (1979)].
Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. I. Typical representations
Authors: Kamupingene Alfred H. , Ky Nguyen Anh , Palev Tchavdar D.
Published: July 2002

In a series of two papers all finite-dimensional irreducible representations and some indecomposible representations of the general linear Lie superalgebra gl(2/2) are constructed in a basis suitable for the decomposition gl(2/2)⊇gl(2)⊕gl(2). In this paper each induced gl(2/2) module W is represented as a direct sum of its irreducible gl(2)⊕gl(2) submodules Vi, 1≤i≤16. The basis Γ in W is chosen to consist of the union of all Γi, where Γi is an appropriate basis in each Vi. Expressions for the transformation of Γ under the action of the generators are written down for all induced and hence, also, for all typical gl(2/2) modules.
On the Hamiltonian dynamics of vortex lattices
Authors: O’Neil Kevin A.
Published: July 2002

The equations of motion for infinite doubly periodic configurations of point vortices are derived. A Hamiltonian for the motion, generalizing that of Kirchhoff for finite configurations, is found and used to deduce an expression for the energy of an arbitrary vortex lattice. The energy of a lattice with periodic defects is computed. Some special stationary lattice configurations are shown to exist and integral curves for some two- and three-vortex lattice motions are exhibited.
Poincaré invariance—classical electrodynamics
Authors: Lozada Abraham , Torres P. L.
Published: July 2002

In a previous paper by the authors [J. Math. Phys. 29, 1361 (1988)] it was shown that, following the standard definition, the angular momentum tensor corresponding to the Coulomb field does not exist (due to the long range of the field). In the present paper, for a general classical field theory, nonconventional definitions for the four-momentum and angular momentum tensor are given. These definitions are applied to the particular case of a charged classical point particle in an external electromagnetic field, showing that the total four-momentum Pμ and the total angular momentum tensor Mλμ of the system exist and are conserved quantities. In this framework, no asymptotic conditions on the four-acceleration of the particle are needed. The problem of extracting an equation of motion for the particle from these conservation laws is discussed. Also, the different parts (such as the radiated one and the bound one) of Pμ and Mλμ, and their corresponding energy momentum tensors and angular momentum density tensors, are considered.
Branching rules for the Weyl group W(D
n)
Authors: Amunátegui G. Iommi
Published: July 2002

Reduction theorems for the decomposition of induced and irreducible characters of W(Dn) in terms of induced and irreducible characters of W(Dn−1), respectively, are given.
Geometry of linear pairs for self-dual gauge fields
Authors: Roiesnel C , Chakrabarti A.
Published: July 2002

A linear pair for self-dual gauge fields is constructed for the metric ds2=gzz̄dzdz̄+gyȳdyd̄. It is shown that for consistency gzz̄ and gyȳ, apart from a possible overall conformal factor, are given in terms of two Liouville fields of equal and opposite curvatures. The null surface corresponding to the pair and the homogeneous solutions, playing a fundamental role, are constructed explicitly. The five-dimensional space of y,ȳ,z,z̄ and the spectral parameter λ is studied. The proper transformation of λ corresponding to holomorphic ones of y and z is found. Known monopole, instanton, and (quasi)periodic solutions are all shown to emerge systematically as particular cases of our formalism. As examples of new possibilities, the case of accelerated observers and that of cosmic string backgrounds are presented.
Stochastic mechanics of a relativistic spinless particle
Authors: De Angelis Gian Fabrizio
Published: July 2002

An extension of Nelson’s stochastic mechanics to the relativistic domain is proposed. To each pure state of a spinless relativistic quantum particle corresponds a Markov process t ]ξt, where the random variable ξt represents, at every time t, the space position of the particle in the sense of Newton and Wigner. The process t ]ξt is not a diffusion but the usual Nelson’s theory is restored in the nonrelativistic limit.