bluuebunny/crossref_metadata_2025 huggingface dataset:
Electronic transitions of C3− above the photodetachment threshold
Authors: Tulej M. , Fulara J. , Sobolewski A. , Jungen M. , Maier J. P.
Published: July 2002

The A 2Δu←X 2Πg, B 2Σu−←X 2Πg, and C 2Σu+←X 2Πg electronic transitions of C3− were observed in a neon matrix and in the gas phase, although the energy of the excited electronic states involved in these transitions is 1–1.5 eV above the photodetachment threshold. The excited Feshbach states are sufficiently long-lived that some of the bands in the gas-phase photodetachment spectrum exhibit rotational structure. Assignment of the transitions is made on the basis of rotational analysis or profile simulations and theoretical calculations. The b 4Πu←X 2Πg transition is also weakly observed. The presence of such discrete bands, though in the continuum, provides a means of detection for anions in the interstellar medium.
Dynamics of the E state of HBr and DBr: Evidence for the role of tunneling
Authors: Hurley S. M. , Zhong Q. , Castleman A. W.
Published: July 2002

The dynamics of the interaction of the Rydberg E(1Σ+) state and the valence state V(1Σ+) of HBr and DBr were investigated using a reflectron time-of-flight mass spectrometer coupled with a femtosecond laser system. Interrogation of the state formed by the avoided crossing of the Rydberg and valence states revealed dynamic behavior that was different for the two isotopes. Pump–probe experiments on HBr showed no change in the lifetime over the range of pump wavelengths of 256.7–254.7 nm. However, the lifetime of DBr decreased as the pump wavelength was tuned bluer. Tunneling is involved in the evolution of the population in photoexcited Rydberg state to the ion-pair state.
Mean-field theory of an electron solvated in molten salts
Authors: Chuev G. N. , Sychyov V. V.
Published: July 2002

A mean-field, microscopic theory of an excess electron solvated in a molten salt is presented. Starting with the grand partition function of the system, we reformulate the problem to evaluate a mean field induced by charges and calculate self-consistently the electron density distribution. We obtain a Poisson–Boltzmann equation for the mean-field and Schrödinger equation for the electron wave functions with a potential dependent on the mean field and a local density of melt. We also derive expressions for electron–ion correlation functions. We demonstrate that the mean field is weak in molten salts and can be analytically evaluated in the Debye–Hückel limit. Using a simple variational treatment, we calculate energetic and structural properties of a solvated electron for a wide range of alkali halide melts. These properties are mainly determined by the polaron effect, while the repulsion between the electron and ion cores leads to a remarkable variance of the properties. The results obtained are in good agreement with path-integral simulations and experimental data on the maximum of the absorption spectrum of an electron solvated in these melts.
First-order wetting transitions of neon on solid CO2 from density functional calculations
Authors: Ancilotto Francesco , Toigo Flavio
Published: July 2002

We have studied the wetting behavior of neon on the surface of solid CO2 by means of density functional calculations. Our results suggest that a wetting transition occurs at a temperature about 5 K below the bulk critical temperature, accompanied by the characteristic first-order prewetting transitions slightly away from coexistence.
Comment on “Positron and positronium chemistry by quantum Monte Carlo. IV. Can this method accurately compute observables beyond energy” [J. Chem. Phys. 111, 108 (1999)]
Authors: Mitroy J. , Ryzhikh G. G.
Published: July 2002

The 2γ annihilation rate for positronic lithium–hydride [LiH,e+] was computed with the quantum Monte Carlo method [Mella, Morosi, and Bressanini, J. Chem. Phys. 111, 108 (1999)]. A model in which the positron and residual ion compete to attract the most loosely bound valence electron provides an explanation of the small annihilation rate (1.2×109 s−1).
Electronic structure and kinetics of K on graphite
Authors: Lou L. , Österlund L. , Hellsing B.
Published: July 2002

The K/graphite adsorption system is studied in a cluster model using ab initio density-functional methods. From the investigation of the potential energy surface a lower bound for the potassium atom binding energy 1.5 eV is obtained, and a surface diffusion barrier of 0.2 eV. To simulate experimentally reported thermal desorption spectra, a two-phase kinetic model is investigated and a desorption energy of 1 eV is found. The thermally activated surface diffusion of K atoms leads to intercalation at defects or steps, which is followed by desorption when further heating the sample. A normal mode analysis yields a K-graphite in-phase and out-of-phase vibrational mode with an energy split of 8 meV, which indicates a relatively strong dynamical coupling between the adsorbed K atom and the graphite substrate. The calculated electron density distribution is verified by an accurate reproduction of the measured dipole moment. From a projected density of state analysis we find a K 4s and an antibonding K 4p resonance located slightly above and 2.6 eV above the Fermi level, respectively. The location of the K 4s resonance, with a lower occupied tail, is consistent with an incomplete charge transfer, and the location of the K 4p resonance is consistent with a proposed hot-electron model to explain recent photodesorption data. The new assignment of the K-induced states near the Fermi level resolves previous apparent discrepancies of the charge state of the dispersed K atom.
Optimized effective potential method for polymers
Authors: Süle P. , Kurth S. , Van Doren V.
Published: July 2002

The optimized effective potential (OEP) method allows for calculation of the local, effective single particle potential of density functional theory for explicitly orbital-dependent approximations to the exchange-correlation energy functional. In the present work the OEP method is used together with the approximation due to Krieger, Li, and Iafrate (KLI). We present the first application of this method to polymers. KLI calculations have been performed for the insulating polyethylene and the results have been compared to those from other orbital-dependent potentials. Various properties of the band structure are also calculated. The single-particle band gap strongly depends on the basis set with larger basis sets yielding narrow gaps. For certain physical quantities such as the total energy and the exchange energy, the various orbital-dependent Kohn–Sham exchange-only and Hartree–Fock results differ only slightly. For the highest occupied orbital energy the difference is more significant than expected. In order to get the right band gap in OEP the exchange contribution to the derivative discontinuity is calculated and added to the Kohn–Sham gap. The corrected gap obtained by the KLI approach is 12.8 eV compared with the Hartree–Fock and experimental values of 16.6 and 8.8 eV, respectively. We observe, however, the strong dependence of the derivative discontinuity on the basis set.
Iterative determination of several interior eigenstates of large matrices: Application to the determination of light-induced resonances in H2+
Authors: Durand Philippe , Paidarová Ivana , Jolicard Georges , Gemperle František
Published: July 2002

The determination of several interior eigensolutions of large non-hermitian matrices is still an open problem for research. This paper brings significant improvements to the perturbative iterative methods. The theory is developed in the framework of Bloch formalism of wave operators and effective Hamiltonians. The progresses rely on two factors. First, the full Hilbert space is partitioned into three subspaces to improve the convergence and stability properties of the iterative processes. Second, the quasi-quadratic algorithms are well-defined approximations of the exact quadratic Newton–Raphson solution. The addition of these two factors brings the computational efficiency far beyond standard perturbation theory. An application is presented to the determination of the Floquet resonances arising from the ten lowest vibrational states of the molecular ion H2+ for laser intensities up to 1.6×1015 W cm−2. These Floquet states provide the relevant basis of the dynamics of H2+ submitted to intense laser pulses.
Rydberg states of propyne at 6.8–10.5 eV studied by two-photon resonant ionization spectroscopy and theoretical calculation
Authors: Shieh Jau-Chin , Chang Jia-lin , Wu Jen-Chieh , Li Runhua , Mebel A. M. , Handy Nicholas C. , Chen Yit-Tsong
Published: July 2002

The vibronic spectra of jet-cooled propyne at 6.8–10.5 eV have been observed using 2+1 resonance-enhanced multiphoton ionization (REMPI) spectroscopy. The ns (n=4–13), np (n=3–4), and 3dz2 Rydberg states of propyne have been identified, of which seven are newly discovered. The symmetries of the excited vibronic states have been determined directly from polarization-ratio experiments applying linearly and circularly polarized lasers. Under a C3V group, the observed s Rydberg series are of E symmetry and the p Rydberg states belong to A1 or E. Clear doublet splittings in the ns Rydberg states (n=4–9) are observed for the first time. The splittings, 306 cm−1 at 4 s, decrease with increasing n. The doublets of A′ and A″ symmetries, identified from the polarization-ratio measurement, are that due to CS molecular geometry, rather than C3V, for the ns Rydberg states. The term values for the ns Rydberg series (n=6–13) converge to an adiabatic ionization energy of 83 625±2 cm−1 with a quantum defect of δ=0.95. Comparing with one-photon absorption spectrum of propyne, the absence of π→π*, np (n⩾4) and nd (n⩾3, except 3dz2) Rydberg states in the REMPI spectra suggests a strong predissociation character for these states. Calculations for the vertical excitation energies of π→π*, ns, np, and nd (n=3,4) Rydberg states of propyne were performed using time-dependent density functional theory and ab initio methods to compare with experimental results and to test the computational accuracy.
Diffusion-limited coalescence and annihilation in random media
Authors: Mandache Catalin , ben-Avraham Daniel
Published: July 2002

We study the kinetics of diffusion-limited coalescence, A+A→A, and annihilation, A+A→0, in random media consisting of disconnected domains of reaction. Examples include exciton fusion and annihilation in porous matrices and along polymer chains. We begin with an exact analysis of A+A→A in a finite segment. This result is applied to coalescence in a random distribution of segment lengths, and the implications for coalescence and annihilation in percolation clusters and other confined geometries are then derived by means of scaling techniques.
Shannon information entropies of molecules and functional groups in the self-consistent reaction field
Authors: Hồ Minhhuy , Clark B. James , Smith Vedene H. , Weaver Donald F. , Gatti Carlo , Sagar Robin P. , Esquivel Rodolfo O.
Published: July 2002

The Shannon information entropies in position and momentum space of H2O, HCN, HOOH, NH3, CH2O2, CH3NH2, CH3OH, CH3CHO, CH3OCH3, CH3COCH3, NH2OH, NH2COH, and CH3NHCOH at the RHF/6-31++G** level in vacuo and in the Onsager aqueous field, were calculated and correlated with various properties. The local entropy of atoms and functional groups in these molecules were also investigated. The results show that the response of the electron density of the groups to solvation is such as to minimize electron transfer to or from the group, and its associated entropy change, which implies a stability of the functional groups within the molecular framework. The effect of solvent fields with increasing dielectric constant on the Shannon entropy of water was studied. The relationships between position and momentum densities through the Shannon entropy are discussed.
Identification of CH3OH2+ and H3O+-centered cluster isomers from fragment-dependent vibrational predissociation spectra of H+(CH3OH)4H2O
Authors: Chaudhuri C. , Jiang J. C. , Wang X. , Lee Y. T. , Chang H.-C.
Published: July 2002

Cluster isomers of H+(CH3OH)4H2O have been identified by vibrational predissociation spectroscopy in combination with mass-selected detection of photofragments. Ab initio calculations indicate that the cluster ion can exist in either CH3OH2+(CH3OH)3H2O or H3O+(CH3OH)4 isomeric forms. They can dissociate via a methanol loss or water loss channel, depending on the structure of the isomers. While water loss is the dominant channel of the dissociation, the methanol loss channel is readily accessible by the H3O+-centered cluster isomer. We demonstrate in this study that mass-selected detection of photofragments produced by vibrational excitation is an effective way of identifying cluster isomers in the gas phase.
Analysis of stability of macromolecular clusters in dilute heteropolymer solutions
Authors: Timoshenko E. G. , Kuznetsov Yu. A.
Published: July 2002

We study the formation of clusters consisting of several chains in dilute solutions of amphiphilic heteropolymers. By means of the Gaussian variational theory we show that in a region of the phase diagram within the conventional two-phase coexistence region mesoglobules of equal size possess the lowest free energy. Monte Carlo simulation confirms that the mesoglobules are stabilized due to microphase separation, which introduces a preferred length scale. The very existence of such mesoscopic structures is related to a delicate balance of the energetic and entropic terms under the connectivity constraints. The issue of size monodispersity and fluctuations for mesoglobules is investigated.
Some peculiarities of proton transport in quasi-one-dimensional hydrogen-bonded chains
Authors: Pavlenko Natalie I.
Published: July 2002

The protonic conductivity in the hydrogen-bonded chains is investigated theoretically in the framework of the two-stage transport model. The strong interactions with optical phonon stretching mode are considered. We obtain the phonon-induced transition from the insulator to the metal-type behavior from the temperature dependencies of the hopping conductivity and analyze the influence of the specific Grotthuss mechanism on the transition character. We investigate also the main peculiarities in the frequency dependencies of the band and hopping conductivity parts which appear due to above-mentioned two-stage mechanism of the proton migration along the chain.
An inelastic incoherent neutron scattering study of water in small-pored zeolites and other water-bearing minerals
Authors: Line Christina M. B. , Kearley G. J.
Published: July 2002

Inelastic neutron scattering spectra of the zeolites natrolite Na2Al2Si3O10 2H2O, wairakite CaAl2Si4O12 2H2O, scolecite CaAl2Si3O10 3H2O, and bikitaite Li2Al2Si4O12. 2H2O, together with the sheet silicate apophyllite KCa4Si8O20(F, OH) 8H2O, are shown here. We show clear trends across these minerals, illustrating the relative influence of hydrogen bonding and cation bonding. For some of these spectra, the bands are clearly separated, permitting a discussion of their assignments. In particular, we can identify librational bands (L) or librational edge (LE) and translational (cation-water stretch) bands (C), and by elimination can tentatively assign bands as hydrogen-bond stretch bands (H), as follows (frequencies given in meV): Natrolite: 13,18 (C) 26 (H), 64,68,87 (L); Apophyllite 17,26 (C), 35 (H) 64,79,98 (L); Scolecite 10 (C), 22,29,36,41 (H), 46 (LE); Wairakite 12 (C), 30 (LE); Bikitaite 13 (C), 22 (H), 34 (LE), 70(L). The results are compared with those for ice and are explained in terms of the nearest-neighbor environment of the water molecule.
The νCC+3νCH rovibrational manifold of acetylene. II. Intramolecular perturbations and symmetry-breaking processes
Authors: Milce Angela P. , Orr Brian J.
Published: July 2002

We identify perturbing rovibrational states that are responsible for local J-dependent interactions in the νCC+3νCH rovibrational manifold of acetylene (C2H2) at ∼11 600 cm−1, observed by infrared-ultraviolet double resonance (IR–UV DR) spectroscopy. These comprise: firstly, the set of vibrational eigenstates (0 1 3 0 0)II0 that are involved in an avoided crossing with the primary (0 1 3 0 0)I0 states, as designated in a previous report [Milce and B. J. Orr, J. Chem. Phys. 106, 3592 (1997)]; secondly, a Πu state locally perturbing (0 1 3 0 0)I0 in the range J=3–5; the adjacent (0 1 3 0 0)I0, J=6 state, which is locally perturbed but with no obvious mixed-in Π-character; and finally, the local perturber of the (0 4 0 3 3)+0 level at J=12. These three vibrational states are now identified and relabeled, according to their most prevalent zero-order normal-mode basis states, as (0 1 3 0 0)0 [previously (0 1 3 0 0)I0]; (0 4 0 3 3)2 [previously (0 1 3 0 0)II0]; (0 2 1 5 2)1 (previously an unidentified perturbing Πu state); and (0 1 1 8 2)2 [previously the unidentified local perturber of (0 4 0 3 3)+0, J=12]. This analysis is achieved with the aid of the well-established anharmonically coupled polyad model, adapted from a set of generalized quantum numbers for C2H2. The model has been expanded to include rotational structure, first, in the form of l-resonance off-diagonal elements and, second, in the form of a variety of resonant Coriolis-type interactions. We also predict likely identities for the perturber states involved in unusual odd-ΔJ symmetry-breaking effects that have been characterized dynamically. It is now postulated that these effects are due to resonant Stark mixing induced by electric fields arising in either molecular collisions or the infrared excitation pulse itself. Coincident ultraviolet probe transitions from doublet levels of opposite e/f parity also contribute to the observed odd-ΔJ energy transfer ascribed to symmetry breaking.
Femtosecond real-time probing of the ultrafast energy dissipation in the Hg(63P1)–CO van der Waals interaction
Authors: Ohmori K. , Amano K. , Chiba H. , Okunishi M. , Sato Y.
Published: July 2002

We have performed the fs pump–probe experiment on the B̃→ã nonadiabatic transition in the Hg–CO vdW complex. It is found that the transition occurs near the point where Hg and CO come nearest to each other on the B̃-state surface with a probability of 0.07 for their single encounter. This experiment serves as the first observation of the wave packet dynamics associated with an intermolecular energy flow in the vdW interaction.
Simulation and density functional study of a simple membrane. II. Solvent effects using the solvent primitive model
Authors: Boda Dezsö , Henderson Douglas , Patrykiejew Andrzej , Sokołowski Stefan
Published: July 2002

The simple membrane, supporting charge densities σ1 and σ2=−σ1 on its inner and outer surfaces that we studied previously is extended to include solvent molecules, modeled as hard spheres. In addition to the electrostatic potential, the membrane can interact with the surrounding electrolyte by a short-range van der Waals-type potential that can be attractive or repulsive. The fluid beyond the outer surface is four component electrolyte consisting of the hard sphere solvent, two species of cations, and one species of anions. The membrane is impermeable to one of the cation species so that the fluid in the membrane and beyond the inner surface is a three component electrolyte. Monte Carlo simulations and density functional theory are used to study the density profiles of the electrolyte and the charge-electrostatic potential relationship for the membrane surfaces. The presence of the solvent molecules leads to oscillatory profiles. The potential versus charge relationship is strongly influenced by the solvent density. The density functional results are in good agreement with the simulations.
Ferroelectric properties of pyridinium fluorosulfonate
Authors: Pająk Z. , Czarnecki P. , Małuszyńska H. , Szafrańska B. , Szafran M.
Published: July 2002

Pyridinium fluorosulfonate has been synthesized and studied over a wide range of temperatures by differential thermal analysis, differential scanning calorimetry, H1H and F19 nuclear magnetic resonance (NMR) spectra and relaxation, and complex dielectric permittivity. The room temperature crystal structure has been determined by x-ray diffraction as trigonal, space group R3̄m, Z=1 with a=5.762 Å and α=97.96° and confirmed by FTIR spectra. Three solid–solid phase transitions at 235, 272, and 282 K have been disclosed and the dynamics of the pyridinium cation and the fluorosulfonate anion characterized. The polar properties of phase II have been demonstrated. The upper transition temperature 282 K appears to be the Curie point of a new ferroelectric compound.
Phase diagram of C60 from ab initio intermolecular potential
Authors: Ferreira A. L. C. , Pacheco J. M. , Prates-Ramalho J. P.
Published: July 2002

Recently a new intermolecular potential for C60 was derived from ab initio calculations. Using this new interaction potential we numerically study the phase diagram of fullerite. Several numerical techniques are used in order to ascertain the correctness of the results. We predict that C60 can be found in the liquid state for densities between 0.468 and 0.845 nm−3 and temperatures between 1881 and 2012 K.
Binary combination and overtone modes in the C–H stretch region in ethoxy adsorbed on Cu(100): Experimental and calculated vibrational spectra
Authors: Ásmundsson R. , Uvdal P. , MacKerell A. D.
Published: July 2002

The C–H stretch and bend modes of ethoxy adsorbed on Cu(100) are investigated using Fourier transform infrared spectroscopy. Three fundamental stretch modes and four fundamental bend modes are assigned. In addition, five binary bend modes are identified; two combination and three overtone modes. It is demonstrated that by combining quantum mechanical ab initio electronic structure calculations and C13 isotopic labeling, a conclusive assignment of all observed modes is possible. The implications for the determination of surface/adsorbate geometry using vibrational spectroscopy are discussed.
Size-intensive decomposition of orbital energy denominators
Authors: Koch Henrik , Sánchez de Merás Alfredo
Published: July 2002

We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will focus on the coupled-cluster singles and doubles model including connected triples corrections [CCSD(T)], and several numerical examples are discussed.
Infrared spectrum of the CO–N2 van der Waals complex: Assignments for CO-paraN2 and observation of a bending state for CO-orthoN2
Authors: Xia Changhong , McKellar A. R. W. , Xu Yunjie
Published: July 2002

The infrared spectrum of the weakly bound complex CO–N2 has been studied using a pulsed supersonic slit-jet and a rapid-scan tunable diode laser. A mirror system giving 182 passes of the laser through the jet helped to give improved spectra with lower effective rotational temperatures (≈0.5 to 4 K) and less interference by CO dimer transitions. In the case of the CO-paraN2 spin modification, for which only one subband was previously known, over 10 linked subbands were assigned in terms of three ground (vCO=0) state stacks of levels (with K=0 and 1), and 7 excited state (vCO=1) stacks (with K=0, 1, and 2). In the case of the more abundant form, CO-orthoN2, an excited bending state was observed for the first time. The infrared analysis relied on precise ground state energy level differences obtained from microwave data.
Structure and discrimination in chiral fluids: A molecular dynamics and integral equation study
Authors: Cann N. M. , Das B.
Published: July 2002

An analysis of structure and discrimination in simple chiral fluids is presented. The chiral molecules consist of a central carbon bonded to four distinct groups. Molecular-dynamics simulations have been performed on a one-component chiral fluid and on two racemic mixtures. For the racemates, discrimination, as measured by differences in pair distribution functions, is present but found to be small. Intermolecular pair interaction energies are found to be good predictors of the magnitude and the sign (mirror-image pairs favored) of the differences observed in site–site distribution functions. For the one-component fluid, the quality of structural predictions from the reference-interaction-site method and Chandler–Silbey–Ladanyi (CSL) integral equation theories, with the hypernetted chain (HNC) and Percus–Yevick closures, has been examined. These theories generally provide a qualitatively correct description of the site–site distributions. Extensions beyond the HNC level have been explored: Two-field-point bridge diagrams have been explicitly evaluated and included in the CSL theory. The inclusion of these diagrams significantly improves the quality of the integral equation theories. Since the CSL theory has not been used extensively, and bridge diagrams have been evaluated in only a few instances, a detailed analysis of their impact is presented. For racemic mixtures, diagram evaluation is shown to be crucial. Specifically, the differences in site–site distributions for sites on identical and mirror-image molecules are found to originate from bridge diagrams which involve interactions between four-site, or larger, clusters. Discrimination cannot be predicted from an integral equation theory which neglects these diagrams.
Hamiltonian representation for helically symmetric magnetic fields
Authors: Turner Leaf
Published: July 2002

It is proved that one of the two potentials used in a standard representation of helically symmetric magnetic fields is a Hamiltonian that generates the magnetic lines of force. It is proved also that if the other potential is restricted to be proportional to this Hamiltonian, then the radial components of current density and magnetic field are proportional. This restriction applies, for example, to constant-λ, helically symmetric, force-free magnetic fields [j(r)=λB(r)] relevant to both fusion physics and astrophysics.
An electromagnetic inverse problem for dispersive media
Authors: Beezley R. S. , Krueger R. J.
Published: July 2002

The dispersion of transient electromagnetic waves in a homogeneous medium can be characterized by expressing either the complex permittivity as a function of frequency or the susceptibility kernel as a function of time. In this paper, a time domain technique is used to derive a nonlinear integrodifferential equation which relates the susceptibility kernel for a one-dimensional homogeneous slab to the reflection operator for the medium. Thus, the susceptibility kernel (which is a function of time) can be determined from reflection data. A numerical implementation of this technique is shown. The more general case of a medium consisting of a stack of homogeneous dispersive layers is also addressed.
On the connection between Schrödinger and Dirichlet forms
Authors: Albeverio S. , Gesztesy F. , Karwowski W. , Streit L.
Published: July 2002

Relations between Schrödinger forms associated with Schrödinger operators in L2(Ω;dnx), Ω ⊂ Rn open, n≥1 and the corresponding Dirichlet forms are investigated. Various concrete examples are presented.
A note on the multiplicity-free unitary irreps of SL(3,R)
Authors: Weaver L. , Biedenharn L. C.
Published: July 2002

Unitary irreps of ∼(SL(3,R)) which contain a representation D j of SU(2) at most once are known to exist with SU(2) content j=k+2n (n=0,1,2,.. and k=0, 1/2 ,1). Güler, in a recent paper, claims that there also exist multiplicity-free unitary representations with SU(2) content j=k0, k0+1, k0+2,..., for k0>3. We show that such representations do not exist for k0>1.
A general approach to the systematic derivation of SO(3) shift operator relations. II. Applications
Authors: Vanden Berghe G. , De Meyer H.
Published: July 2002

The technique reported on in the preceding paper is applied to construct shift operator relations in the SU(3) and SO(5) Lie algebras. Comments are made concerning the integrity basis for SO(3) scalar operators appearing in their respective enveloping algebras.
The short-range expansion for multiple well scattering theory
Authors: Holden H. , Ho/egh-Krohn R. , Mebkhout M.
Published: July 2002

We expand the scattering amplitude and the scattering matrix around the zero-range limit, i.e., with point interactions, in the case when the potential has a finite number of wells. The lower-order terms are largely independent of the shape of the potentials.
Some remarks on torsion in Kaluza–Klein unification
Authors: Muzinich I. J.
Published: July 2002

The role of manifolds endowed with a parallelizing torsion in Kaluza–Klein theories is examined. In particular the spin connection on such manifolds is demonstrated to be a single pure gauge almost everywhere on the manifold. This follows from the Frobenius integration theorem. As a consequence of this result the computation of the representation of massless fermions follows immediately and trivially. The spectrum of massless fermions on manifolds with a parallelizing torsion is contrasted with the analogous spectrum on manifolds with nontrivial topological configurations. While the remarks are primarily of pedagogic value much of the relevant mathematics is made intuitive.
Canonical transformations theory for presymplectic systems
Authors: Cariñena J. F. , Gomis J. , Ibort L. A. , Román N.
Published: July 2002

We develop a theory of canonical transformations for presymplectic systems, reducing this concept to that of canonical transformations for regular coisotropic canonical systems. In this way we can also link these with the usual canonical transformations for the symplectic reduced phase space. Furthermore, the concept of a generating function arises in a natural way as well as that of gauge group.
Finite-dimensional irreducible representations of the Lie superalgebra sl(1,3) in a Gel’fand–Zetlin basis
Authors: Palev T. D.
Published: July 2002

A concept of a Gel’fand–Zetlin pattern for the Lie superalgebra sl(1,3) is introduced. Within every finite-dimensional irreducible sl(1,3) module the set of the Gel’fand–Zetlin patterns constitute an orthonormed basis, called a Gel’fand–Zetlin basis. Expressions for the transformation of this basis under the action of the generators are written down for every finite-dimensional irreducible representation.
Simple expressions for radial functions appearing in the expansions of 𝒴m1l1 (∇)F m2l2(r) and ∇2n𝒴m1l1(∇)F m2l2 (r)
Authors: Rashid M. A.
Published: July 2002

In this paper, simple analytic expressions for the radial functions r ll1l2( f (r)) and Glnl1l2( f (r)), which appear in the expressions for 𝒴m1l1(∇) fl2(r) Ym2l2(r̂) and ∇2n𝒴m1l1(∇) fl2(r) Ym2l2(r̂) when expressed as linear combinations of Yml(r̂), where 𝒴m1l1(∇) is obtained from the solid harmonic 𝒴m1l1(r) =r l1Ym1l1(r̂), are derived by replacing x, y, and z in its representation as a polynomial of degree l1 by ∂/∂x, ∂/∂y, and ∂/∂z, respectively.

Writing r ll1l2( f (r)) =r ll1l20(r) f (r) and Glnl1l2( f (r)) =Glnl1l20(r) f (r), the expression for r ll1l20(r) (Glnl1l20(r)) is found to be (2/r)l1((2/r)l1+2n) times a product of commuting factors containing the single operator 1/2 r(d/dr) and not two noncommuting operators r and (1/r)(d/dr) in the many equivalent previously obtained results which are thus synthesized in this approach. Also, expressions for these operators manifest the symmetries in the problem. In addition, a simple connection Glnl1l20(r) =r ll1+2nl20(r) between these two operators and the corresponding radial functions Glnl1l2( f (r)) and r ll1l2( f (r)) are found.
On the Bäcklund transformation and Hamiltonian properties of superevaluation equations
Authors: Roy Chowdhury A. , Roy Swapna
Published: July 2002

Bäcklund and Darboux–Bäcklund transformations are deduced for the superevaluation equations recently deduced by Kupershmidt [B. Kuperschmidt, ‘‘A super-K–dV equation—An integrable system,’’ preprint UTSI-Tullahoma, 1984; Phys. Lett. A 102, 213 (1983); J. Phys. A 17, L 863 (1984)] and Gürses [H. Gürses and O. Oguz, Phys. Lett. A 108, 437 (1985)]. By a extension of the technique of BPT [M. Boiti, F. Pempinelli, and G. Z. Tu, Nuovo Cimento B 79, 231 (1984)] to anticommuting variables the bi-Hamiltonian structure and hence the form of the recursion operator for the Lie–Bäcklund symmetry for such equations are deduced. Incidentally some explicit forms of the Lie–Bäcklund symmetry are also deduced.
Matrix operator symmetries of the Dirac equation and separation of variables
Authors: Kalnins E. G. , Miller W. , Williams G. C.
Published: July 2002

The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].
Spinor focus wave modes
Authors: Hillion Pierre
Published: July 2002

New solutions of the homogeneous spinor wave equation are obtained. They are similar to the focus wave mode solutions of Maxwell’s equations leading to a Gaussian pulse energy. A weighted superposition of these modes may supply finite energy pulses. The particular case of Bessel weight functions is discussed.
Direct and inverse scattering in the time domain for a dissipative wave equation. III. Scattering operators in the presence of a phase velocity mismatch
Authors: Kristensson G. , Krueger R. J.
Published: July 2002

The direct scattering problem for an inhomogeneous lossy medium is examined for the one-dimensional case in which the phase velocity profile is discontinuous at the boundaries of the medium. Scattering operators (or impulse responses) and propagation operators are defined and equations that govern their behavior are developed. Knowledge of the scattering kernels for one round trip in the medium implies that the scattering kernels can be determined on any time interval. Numerical examples are presented. It is also shown that this scattering problem is reducible to one in which there are no phase velocity mismatches. This reduction provides considerable numerical advantage in the solution of the direct scattering problem. The inverse problem is examined in a companion paper.
Evaporation of nonzero rest mass particles from a black hole
Authors: Diaz Bejarano J. , Miro Rodriguez C.
Published: July 2002

Analytic expressions for the transmission coefficient and the emission and the absorption rates for scalar particles with mass and a chargeless, nonrotating black hole are calculated by using Jacobian elliptic functions and integrals in the Jeffreys–Wentzel–Kramers–Brillouin (JWKB) approximation.
A case study of degeneracy in quantum statistics. I
Authors: Barker William A. , Raney Daniel , Sy John
Published: July 2002

In quantum statistics there are four categories of quantum degeneracy: nondegenerate, weak, intermediate, and strong. These are associated with the Fermi–Dirac and Bose–Einstein integrals, which are difficult to evaluate over the entire range of the activity parameter r defined as the particle density divided by the quantum concentration. In this paper (I), four classical systems with r≪1, and four weakly degenerate systems with r≲1 are examined. In the former, the Maxwell–Boltzmann distribution is sufficient. In the latter, the treatment of Landau and Lifschitz is extended. Physically realistic systems, like electrons in intrinsic and impurity semiconductors, and noble gases at different pressures and temperatures, are investigated. The neutrino and neutral pion systems are illustrative, albeit esoteric. Expressions for the quantum concentration for different dimensions and particle velocities are useful in predicting the onset of degeneracy. In the companion paper (II), intermediate and strong degeneracies are studied for r≥1.
Electrohydrodynamic stability of two superposed elasticoviscous liquids in plane Couette flow
Authors: Eldabe Nabile T. M.
Published: July 2002

The electrohydrodynamic stability of two superposed elasticoviscous liquids (Oldroyd’s liquid B) in plane Couette flow is studied. The system is stressed by a normal electric field. The analysis includes all possible modes of perturbations. The eigenvalue problem governing the stability of the flow against wave formation is formulated and solved for small values of wave numbers. It is found that the electric field cannot only destabilize the flow but it can also stabilize the flow for certain values of dielectric ratio, depth ratio, viscosity ratio, elasticity ratio, density ratio, Froude number, Reynolds number, and the electric potential of the plate.
Totally symmetric irreducible representations of the group SO(6) in the principal SO(3) subgroup basis
Authors: Vanthournout J. , Van der Jeugt J. , De Meyer H. , Vanden Berghe G.
Published: July 2002

Explicit matrix elements are found for the generators of the group SO(6) in an arbitrary totally symmetric irreducible representation, using the physical principal SO(3) subgroup in the chain SO(6)⊇SO(5)⊇SO(3). The internal one missing label problem is solved through the definition of intrinsic states associated to the SU(2)×SU(2) subgroup in the chain SO(6)⊇SO(5)⊇SU(2)×SU(2) and out of which is projected a complete set of states in the physical basis by integrations over the physical rotation group manifold. The matrix elements of the SO(6) generators in the SU(2)×SU(2) basis are themselves obtained by the intermediate use of an SU(2)×SU(2)×U(1) basis, the latter group being a subgroup of SO(6) but not of SO(5).
On generalized Kerr–Schild transformations
Authors: Nahmad-Achar E.
Published: July 2002

The geometric properties of generalized Kerr–Schild metric transformations (KST’s) are studied in detail, and the energy and momentum induced by the transformation are calculated explicitly. A characterization is given of all algebraically special metrics, obtained via a KST, that satisfy the weak energy condition.
Variational nature of dispersion equations revisited
Authors: Schwarzmeier J. L. , Lewis H. R.
Published: July 2002

Corrections and clarifications are made of some past treatments of the variational nature of the eigenfrequency calculation for dispersion equations and new results are presented. The main conclusions are the following: (1) Any relation between a normal mode and its dual must be consistent with the fact that the boundary conditions satisfied by the normal mode may differ from the adjoint boundary conditions satisfied by the dual. This will affect whether or not a given bilinear form will yield a variational result for the eigenfrequency. (2) If a dispersion matrix is constructed from the dispersion operator by using left and right basis functions that satisfy homogeneous boundary conditions on the dual eigenfunction and the eigenfunction, respectively, then generally a second-order accurate eigenfrequency is obtained by solving the matrix form of the dispersion equation. (3) When solving for the normal modes in terms of perturbation potentials, the adjoint boundary conditions are gauge dependent. For cases where the adjoint boundary conditions allow only the trivial solution for the dual eigenfunction, it may be possible to obtain variational results for the eigenfrequency by requiring that the trial functions for the normal mode and its dual satisfy variational boundary conditions.
A remark concerning canonical commutation relations
Authors: Reeh Helmut
Published: July 2002

An elementary quantum mechanical example of canonical commutation relations not equivalent to the Schrödinger representation is discussed. It demonstrates that the ‘‘Nelson phenomenon’’ occurs in a natural situation.
Correlation inequalities for multicomponent ferromagnets
Authors: Kondo Kei-ichi , Sugiyama Yūki
Published: July 2002

A systematic method to obtain a series of new correlation inequalities for a class of two-component vector spin systems is presented. These correlation inequalities are applied to lattice scalar field models with two-body, anisotropic or isotropic ferromagnetic interactions and interaction potential of even polynomials, especially the λ(‖Φ‖2)2 model, which includes the plane rotator model as a special case. Here an external field h=(h,H), h≥0, H≥0, is present. The possible way to extend our method to the N-component (N≥3) case is also discussed.
Studies in space-times admitting two spacelike Killing vectors
Authors: Halilsoy M.
Published: July 2002

Some properties of the space-times admitting two spacelike Killing vectors are studied. In particular, using harmonic maps the degree of freedom on the M′ manifold is exploritd to add scalar and electromagnetic fields to Bonnor’s nonsingular solution. It is also shown that for vacuum space-times the noncommutativity of two spacelike Killing vectors is incompatible with the self-similarity requirement and such a self-similar vacuum space-time has no Taub–NUT equivalent extension.
Finite-dimensional representations of the special linear Lie superalgebra sl(1,n). II. Nontypical representations
Authors: Palev Tchavdar D.
Published: July 2002

All nontypical irreducible representations of the special linear Lie superalgebra sl(1,n) are constructed for any n. 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 [J. Math. Phys. 28, 2280 (1987)] solve the problem of the finite-dimensional irreducible representations of sl(1,n).
Resonant interval action transfer between coupled harmonic oscillators
Authors: Dendy R. O.
Published: July 2002

A formula is obtained for the action transferred between two weakly coupled harmonic oscillators, where the time-dependent frequency of one oscillator passes through resonance with the fixed frequency of the other. The analysis employs an action-angle Hamiltonian that is the classical analog of an earlier wave-mechanical description of linear mode conversion. It represents a link between generalized Hamiltonian approaches to linear mode conversion, and those based on wave dispersion relations.
Exact behavior of Jost functions at low energy
Authors: Klaus Martin
Published: July 2002

For Schrödinger operators with central potential q(r) and angular momentum l, the behavior of the Jost function Fl(k) as k→0 is investigated. It is assumed that ∫∞0dr (1+r)σ‖q(r)‖<∞, where σ≥1. Situations where q is integrable with 1≤σ<2, but not with σ≥2 are of particular interest. For potentials satisfying q(r)∼q0r−2−ε (0<ε≤1) and l=0, the leading behavior of F0(k) and the phase shift δ0(k) as k→0 is derived. Also comments are made on the differentiability properties of the Jost solutions with respect to the variable k at k=0. For σ=1 Levinson’s theorem is proved, thereby clarifying some questions raised recently by Newton [J. Math. Phys. 27, 2720 (1986)].
Irreducible finite-dimensional representations of the Lie superalgebra gl(n/1) in a Gel’fand–Zetlin basis
Authors: Palev Tchavdar D.
Published: July 2002

All finite-dimensional irreducible representations of the general linear Lie superalgebra gl(n/1) are studied. For each representation, a concept of a Gel’fand–Zetlin basis is defined. Expressions for the transformation of the basis under the action of the generators are written down.
Separable coordinates and particle creation. II: Two new vacua related to accelerating observers
Authors: Costa Isaias
Published: July 2002

An exactly solvable example of quantum field theory in a nonstationary system is presented, which has an inertial and a uniform accelerated asymptotic region. Two sets of solutions are constructed that are quasiclassical in each of these regions and they are compared. The Bogoliubov coefficients have thermal character and show a temperature of a∞/2π, where a∞ is the asymptotic acceleration. This result is indeed what one would expect on the grounds of the Hawking effect.
Equivalence of higher-order Lagrangians. II. The Cartan form for particle Lagrangians
Authors: Hsu Lucas , Kamran Niky , Olver Peter J.
Published: July 2002

It is shown how Cartan’s method of equivalence may be used to obtain the Cartan form for an r th-order particle Lagrangian on the line by solving the standard equivalence problem under contact transformations on the jet bundle J r+k for k≥r−1.
Scalar concomitants of a metric and a curvature form. II
Authors: Noriega R. J. , Schifini C. G.
Published: July 2002

The general form of a Lagrangian concomitant of a metric and a curvature form is found, improving substantially a previous result.
Complex manifold methods in quantum field theory in curved space-time
Authors: Meister A.
Published: July 2002

A real analytic space-time 𝒩 can be embedded as a real slice in a complex Riemannian manifold (M,g). A theorem due to Woodhouse [Int. J. Theor. Phys. 16, 671 (1977)], stating that real slices are necessarily totally geodesic submanifolds of (M,g), is used to find all real slices of the complexified sphere cSnr of dimension n and radius r, and of complexified Robertson–Walker space-time cℛ. The real slices 𝒩 of cSnr are n-dimensional spaces of constant curvature (±r−2) of all possible signatures. cℛ is determined by a holomorphic radius function r(x), the x-constant hypersurfaces being isometric to cSnr(x). In general, all real slices of cℛ are Robertson–Walker-type spaces (of various signatures). The interesting case that a Robertson–Walker space-time with radius function 𝓇(t) intersects a Euclidean real slice in an n-dimensional hypersurface, can only occur if 𝓇(t) is time reflection symmetric. Finally, propagators to the scalar wave operator (□–m2) on real slices 𝒩1 of cS4r are considered and their analytic continuations to other real slices 𝒩2 are discussed. There are useful continuations only if 𝒩1, 𝒩2 are isometric either to the sphere and de Sitter space-time, or to the hyperbolic plane and anti-de Sitter space-time. In this case the continuation does not depend on the relative position of 𝒩1 and 𝒩2 in cS4r. For instance, it also works if the intersection 𝒩1∩𝒩2 is one dimensional.
Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. II. Nontypical representations
Authors: Palev Tchavdar D. , Stoilova Nedjalka I.
Published: July 2002

All finite-dimensional irreducible representations of the general linear Lie superalgebra gl(2/2) are written down in matrix form. The basis within each representation space is chosen in such a way that it makes evident the decomposition of gl(2/2) into irreducible representations of its even subalgebra gl(2)⊕gl(2). Special attention is devoted to the analysis of all nontypical representations and some indecomposible representations.
Fermionic determinants for chiral-bag-like two-dimensional systems
Authors: Falomir H. , Muschietti M. A. , Santangelo E. M.
Published: July 2002

This paper evaluates the determinant of a Dirac-like operator, for a system of fermions confined to a region of two-dimensional Euclidean space and subject to bag-like boundary conditions. In the framework of the ζ-function regularization method, use is made of Seeley’s developments for the resolvent of such operators. A relation is derived between the Green’s function and the finite part of the diagonal element of the kernel of the power z of the operator for z=−1, which amounts to having information about the whole Seeley’s series.