bluuebunny/crossref_metadata_2025 huggingface dataset:
Scattering of a plane longitudinal elastic wave by a large convex rigid object with a statistically corrugated surface. I. Perturbation solutions
Authors: Fan W. , Chen Y. M.
Published: February 2004

The scattering of time-harmonic plane longitudinal elastic wave by a large convex rigid object with statistical surface irregularities is considered. The maximum deviation of the corrugated surface from the smooth one is assumed to be small, and hence the boundary-perturbation technique is utilized in this study. First, the scattering of longitudinal wave by a large rigid sphere with statistical surface irregularities is treated as a canonical problem in the general discussion. It is found that the higher-order solutions can be obtained from the zeroth-order solution in a straightforward manner. Due to the complexity of the problem, only the first-order solution and its asymptotic expansion are explicitly computed and carried out. A general recipe based on the zeroth-order solution is given for the treatment of the general problem. The asymptotic expressions of mean values of the scattered wave function and the scattered intensity are also given for the general problem.
Representations of the coordinate transformation group
Authors: Altschul Martin S.
Published: February 2004

In this paper we deal with the Lie (pseudo-) group of coordinate transformations in four dimensions. We discuss the detailed structure of the corresponding Lie algebra, especially including Theorem II, which states a limited set of structure relations that uniquely determine the structure of the algebra. Using Theorem II, we attack the problem of finding unitary representations of the pseudogroup. Finally we discuss some physical implications of these representations.
Tachyons and gravitation
Authors: Raychaudhuri A. K.
Published: February 2004

This note presents the following results: (1) In the weak field approximation, the tachyon apparently experiences a repulsion due to ordinary matter; (2) a tachyon turns back from a black hole after penetrating the Schwarzschild singularity; (3) in ever expanding isotropic universes the tachyon velocity becomes arbitrarily large at a finite time; (4) between tachyons themselves, there is apparently an attraction.
On the theory of plasma turbulence
Authors: Marcuvitz N.
Published: February 2004

Microscopic to macroscopic transitions in classical, nonequilibrium, particle-field systems pose a class of stochastic perturbation problems that can be solved via the formal theory of scattering. Such solutions permit the nonlinear microscopic equations descriptive of a turbulent plasma field to be ensemble averaged into macroscopic particle- and wave-kinetic equations. The method is essentially operator theoretical. The original microscopic operator is first conventionally decomposed into deterministic and stochastic parts and then via scattering theory its inverse is evaluated in terms of explicit, formally exact, operator expressions that admit rapidly convergent, nonsecular, series representations. These results may be obtained by either operator algebra or diagram methods, the former being preferred. The derivation appears to be more physically and analytically transparent than in most existing procedures and has the virtue of exhibiting explicitly higher order terms, some of which are novel. The theory is illustrated for the case of a simple isotropic electron plasma by the derivation of kinetic equations for particles and for waves.
Quantum field theory on a seven-dimensional homogeneous space of the Poincaré group
Authors: Boyer C. P. , Fleming G. N.
Published: February 2004

Field theories over the homogeneous space of the Poincaré group consisting of the direct product of ordinary Minkowski space M and a three-dimensional timelike hyperboloid H3 are investigated in an effort to provide a description of a relativistic extended body. The locality properties of such fields are investigated, and it is found that such fields are in general nonlocal with the nonlocal behavior governed by the type of representations used. It is also found that an internal O(4) symmetry arises quite naturally and is used to construct a model describing an infinite number of particles with an almost linear mass spectrum. This model provides no unphysical solutions, decreasing electromagnetic vertex functions, positive definite field energy, and weak nonlocality. All the vertex functions are calculated and discussed.
Poincaré analytic vectors in axiomatic quantum field theory
Authors: Snellman Håkan
Published: February 2004

It is demonstrated that in a Wightman quantum field theory with a denumerable set of field operators over the test function space SR, transforming covariantly among themselves under a unitary representation U(Λ, a) of the covering group of the Poincaré group, the domain D0 of vectors generated by the polynomial ring over the field operators applied on the vacuum state contains a dense invariant set of analytic vectors for U(Λ, a).
The Hamiltonian and generating functional for a nonrelativistic local current algebra
Authors: Menikoff Ralph
Published: February 2004

The nonrelativistic current algebra with conserved current consisting of ρ(x), the particle number density, and J(x), the flux density of particles, is studied. The Hamiltonian for any time reversal invariant system of spinless particles, interacting via a two-body interaction potential, is expressed as a Hermitian form in the currents. This leads to a functional equation for the generating functional, which is the ground state expectation value of exp[i ∫d xρ(x)f(x)]. In the N / V limit an expression for the generating functional in terms of correlation functions is given. Representations of the exponentiated current algebra which are translation invariant satisfy the cluster decomposition property, and those which have different Hamiltonians are shown to be unitarily inequivalent.
Scalar waves in the exterior of a Schwarzschild black hole
Authors: Persides S.
Published: February 2004

Using the method of separation of variables, we study rigorously scalar waves due to a point source in the exterior of a Schwarzschild black hole. First, a Fourier analysis gives general formulas for the interior and exterior radial wave functions and their relations to solutions of special cases, the Green's function, and the frequency spectrum. Three special cases are examined. Second, Laplace transforms of the field are obtained and their properties are studied. Using the results of the Laplace transformation and some general properties of timelike curves, we prove the following theorem: The time-dependent scalar field of a point source goes to zero outside the horizon as the source falls into the black hole.
Rigged Hilbert space formalism as an extended mathematical formalism for quantum systems. I. General theory
Authors: Melsheimer Olaf
Published: February 2004

Roberts' proposal of a rigged Hilbert space Φ⊂G⊂Φ× for a certain class of quantum systems is reinvestigated and developed in order to exhibit various properties of this kind of rigged Hilbert spaces which might be of interest for the application of this formalism to special quantum systems. It is shown that on the basis of this proposal one also obtains a satisfactory solution for a rigged Hilbert space for composite systems. Another part is concerned with topological properties of the so-called eigenoperators γ(t) belonging to an A-eigen-integral decomposition of Φ with respect to a self-adjoint operator A on G. We derive a representation of γ(t) in terms of the generalized eigenvectors of A and in the same context give a rough topological characterization of these eigenvectors.
Mackey-Moore cohomology and topological extensions of Polish groups
Authors: Cattaneo U. , Janner A.
Published: February 2004

Topological group extensions with Abelian kernels are analyzed using factor sets and following the pattern of the work of Eilenberg and MacLane on extensions of groups without topology. In this analysis, the Eilenberg-MacLane cohomology is replaced by the Mackey-Moore one, whose cochains are Borel mappings and which is especially suitable in the case of Polish groups (Hausdorff second countable complete groups). The connection between cohomology groups of degree 2 and equivalence classes of topological group extensions with Abelian kernels is established. A fundamental sequence of cohomology groups and group homomorphisms is proven to be exact, and it is shown that, in some interesting cases, the low degree cohomology groups of topological semidirect products are determined by the corresponding cohomology groups of the factors.
Behavior of distribution functions in the thermodynamic limit
Authors: Klein William
Published: February 2004

Ruelle has proven that the solutions of the Kirkwood-Salsburg equation for a finite volume Λ become, in the limit as Λ → ∞, the solutions to the Kirkwood-Salsburg equation for an infinite volume, i.e., limΛ→∞ρΛ→ρ+limΛ→∞ε(Λ), limΛ→∞ε(Λ)→0. The form of ε is not obtained. We show that for the first order contribution to the solution of the Kirkwood-Salsburg equations obtained via a perturbation scheme developed in an earlier paper that ε(Λ)⩽limR→∞ε−k′aR,where k′a is a positive real constant which can be specified and R is the minimum distance from the container walls to the particles of the system.
Exact nearest neighbor degeneracy for dumbbells on a one-dimensional lattice space
Authors: McQuistan Richmond B.
Published: February 2004

Relationships are developed which describe exactly the degeneracy associated with nearest neighbor pairs of occupied sites (1–1), mixed sites (0–1), and vacant sites (0–0) for dumbbells distributed on a one-dimensional lattice space. The first moments of these statistics are calculated, thereby permitting an evaluation of the error inherent in the use of the Bragg-Williams approximation for this situation.
Irreducible tensorial sets within the group algebra of a compact group
Authors: Kasperkovitz P. , Dirl R.
Published: February 2004

For compact topological groups (discrete or continuous) a basis of the group algebra is defined which consists of irreducible tensors only. This tensor basis is generally discussed and compared with similar constructions for finite groups and SU (2).
On analytic nonlocal potentials. III. Local correlations
Authors: Yao Te Hai
Published: February 2004

We give examples of ``analytic nonlocal potentials'' which show local correlations for a finite range of the distance, bounded below and above.
Representations of the Jost solutions and the S matrix for a class of analytic nonlocal potentials
Authors: Yao Te Hai
Published: February 2004

We derive representations of the Jost solutions, the Jost functions, and the S matrix, for analytic nonlocal potentials belonging to a double Laplace transform class, for the s-wave case, in terms of the spectral function for the potential.
Lie theory and separation of variables. 4. The groups SO (2,1) and SO (3)
Authors: Kalnins E. G. , Miller Willard
Published: February 2004

Winternitz and coworkers have shown that the eigenfunction equation for the Laplacian on the hyperboloid x02−x12−x22=1 separates in nine orthogonal coordinate systems, associated with nine symmetric quadratic operators L in the enveloping algebra of SO (2,1). Corresponding to each of the operators L, we employ the standard one-variable model for the principal series of representations of SO (2,1) and compute explicitly an L basis for the Hilbert space as well as the unitary transformations relating different bases. We also compute the associated results for realizations of these representations on the hyperboloid. Three of our bases are related to well-known subgroup reductions of SO (2,1). Of the remaining six, one is related to Bessel functions, two to Legendre functions, and three to Lamé functions. We show that there is virtually a perfect correspondence between the known theory of the Lamé functions and the representation theory of SO (2,1) and SO (3).
Null electromagnetic fields in spaces of high symmetry
Authors: Raychaudhuri A. K. , Dutta A. K.
Published: February 2004

The paper investigates the solutions of Maxwell-Einstein equations for null electromagnetic fields with or without matter in case of spaces of high symmetry. For the spherically symmetric space no such solution exists, while for cylindrically symmetric spaces, there arises a wide variety of situations. In reality, for the solutions that emerge, the spaces should more appropriately be termed plane symmetric. Some solutions are exhibited.
Superpropagators as boundary values of analytic distributions
Authors: Lazarides G. , Patani A. A.
Published: February 2004

In this paper we give a rigorous analysis for defining a class of superpropagators as boundary values of analytic distributions and discuss the ambiguities connected with this definition.
Generalized covariance principles and neutrino physics
Authors: Flato M. , Piard A.
Published: February 2004

The zero-mass Dirac equation admits a simple generalized covariance group which is an inhomogeneous Lorentz group G different from the Poincaré group. Its mathematical structure and unitary irreducible representations have been studied by Flato and Hillion [Phys. Rev. D 1, 1667 (1970)]. Physical consequences concerning neutrino physics were then obtained by introduction of the Stokes parameters. The present article is divided into three parts: (1) Introduction, in which we present briefly the idea of generalized convariance, summarize the main results obtained by Flato and Hillion, and introduce the 14-dimensional unification group proper for the generalized convariance of the free neutrino equation. (2) In the second part, we study by the well-known method of induced representations all the strongly continuous unitary irreducible representations of the 10-dimensional Dirac group G as well as of the 14-dimensional unification group G′. (3) Physical applications: in this chapter, we concentrate on particular zero-mass representations of G′ which are of interest at least for the study of the neutrino free-field theory. These classes of unitary irreducible representations of G′ permit us to have two possible physical alternatives which are discussed.
Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. II
Authors: Mukunda N. , Radhakrishnan B.
Published: February 2004

Following the approach of a previous paper, the Clebsch-Gordan problem for the group SU(1,1) for products of the form D+⊗D− is related to properties of the pseudo-orthogonal O(2,2). A new understanding of the Clebsch-Gordan series for this case is achieved by analyzing the properties of O(2,2) spherical harmonics. The Clebsch-Gordan coefficients in a continuous basis are also calculated.
C*-algebraic formalism for coarse graining. III. Momentum coarse graining for Fermi systems in infinite free space
Authors: Wolfe John C. , Emch Gérard G.
Published: February 2004

The C*-algebraic formalism developed by the authors for the coarse-graining operations in quantum statistical mechanics is adapted to the case of an infinite Fermi system in free space.
Weak gravitational fields
Authors: Lerner D. , Porter J. R.
Published: February 2004

We consider the set of Ck bounded tensor fields of type (r,s) on R4 in the topology of uniform Ck convergence. For each k≥2, the map sending a metric to its curvature tensor is shown to be analytic at the Minkowski metric. The same is true of the map sending a metric to its Einstein tensor. The well-known linearized theory of gravitation amounts to studying the directional derivatives of these maps. An iterative method for solving the full field equations along an analytic curve of Einstein tensors passing through zero is proposed.
Structure of the 12j and 15j coefficients in the Bargmann approach
Authors: Huang Cheng-Sheng , Wu Alfred C. T.
Published: February 2004

Generating functions of the 12j and 15j angular momentum recoupling coefficients are computed explicitly in the Bargmann formalism. Symmetry properties are deduced therefrom. A geometrical Möbius strip representation (originally due to Ord-Smith for the 12j case), which can be generalized to all n, suggests a 4n-fold symmetry for the 3nj coefficients (n ≥ 4).
Quasiperiodic pointwise solutions of the periodic, time-dependent Schrödinger equation
Authors: Okuniewicz Joyce M.
Published: February 2004

For Hamiltonians periodic in time, we obtain under certain assumptions a condition which is necessary and sufficient for the existence of quasiperiodic pointwise solutions to the Schrödinger equation. Orthonormality and completeness of these functions in L2(Rn) are investigated, and the time-displacement operator is considered as a sum of quasiperiodic terms.
Vacuum-Ultraviolet Photochemistry. VIII. Photolysis of Hydrazine–15N in the Presence of 14NO at 1470 Å
Authors: Stief L. J. , DeCarlo V. J.
Published: February 2004

The relative contributions of direct molecular elimination and radical disproportionation reactions to the formation of nonrandomized nitrogen in the photolysis of hydrazine and hydrazine–15N have been determined by examining the production of 30N2 in the photolysis of hydrazine–15N at 1470 Å in the presence of 14NO. The limiting value of the ratio H2/30N2 in close to two and suggests that the mechanism of the molecular elimination processes is best represented by the sequence N2H4→N2H2 + H2, N2H2→N2 + H2. The ratio of disproportionation to combination of radicals in the system (N2H3 and NH2) is approximately five. The formation of 29N2 is attributed to the reaction of 15NH2 with 14NO while the formation of 28N2 is discussed in terms of the reaction of atomic hydrogen with 14NO.
Gaseous Metal Nitrides. II. The Dissociation Energy, Heat of Sublimation, and Heat of Formation of Zirconium Mononitride
Authors: Gingerich Karl A.
Published: February 2004

The ZrN molecule has been identified in the vapor phase over a ZrN–BN mixture at temperatures above 2400°K using a combination of effusion and mass spectrometric techniques. Its apprearance potential was measured as 7.9 ± 0.4 eV. From the experimentally determined partial pressures the equilibrium constants and the enthalpy for the gaseous reaction ZrN = Zr + 0.5 N2 have been calculated. The reaction enthalpy was obtained as ΔH°298 = 22.0 ± 5.0 kcal/mole. Combined with published thermodynamic data this reaction enthalpy yields the following thermodynamic properties for gaseous ZrN: ZrN(g) = Zr(g) + N(g) D°298 = 135.0 ± 6.0 kcal ZrN(s) = ZrN(g) ΔH°s, 289 = 211.4 ± 9.0 kcal Zr(s) + 0.5N2(g) = ZrN(g) ΔH°f, 298 = 123.5 ± 7.0 kcal.
Electrical Properties of Thorium Borides
Authors: Auskern A. B. , Aronson S.
Published: February 2004

The electrical resistivity, Hall coefficient, thermoelectric power, and magnetic susceptibility of polycrystalline samples of thorium tetraboride and thorium hexaboride have been measured over a range of temperatures. Both compounds exhibit metallic properties. The carrier concentration, about 2 electrons per thorium atom, is that predicted by the bonding model of Lipscomb and Britten.
Vibrational Spectra of Single Crystals. Polymorphic Solids of Cyclohexane
Authors: Obremski Robert J. , Brown Chris W. , Lippincott E. R.
Published: February 2004

Polarized infrared spectra of a single crystal of cyclohexane solid II and the infrared and laser Raman of polycrystalline solid II at 90°K have been measured. The observed splittings and the infrared polarization results indicate a unique site and factor group for this phase. The suggested crystal structure is orthorhombic D2h. The infrared spectrum of a single crystal of the solid I phase has also been recorded and the results are found to agree with previous x-ray and Raman studies. Pressure techniques employing miniaturized instrumentation were used to grow single crystals of solids I and II.
Luminescent Properties of Hexafluoroacetone. II. Fluorescence Quenching by Oxygen, Nitric Oxide, and Unsaturated Hydrocarbons
Authors: Ware William R. , Lee Sai K.
Published: February 2004

It has been observed that oxygen, nitric oxide, olefins, and benzene quench the fluorescence of hexafluoroacetone. Fluorescence lifetime measurements were used to evaluate rate constants for quenching. Quenching efficiencies were found to follow the order piperylene > isobutylene > propylene > benzene > ethylene > oxygen. Olefin quenching efficiencies decreased with increasing temperature. These results suggest a mechanism involving an unstable intermediate, perhaps a complex with some charge-transfer character, for quenching by olefins, dienes, and benzene.
Membrane Transport Characteristics of Ultrafine Capillaries
Authors: Gross R. J. , Osterle J. F.
Published: February 2004

A detailed study and further development of the capillary model for charged wide-pore membranes is presented. Previous work on this model has either linearized the Poisson–Boltzmann equation and/or assumed a small Debye length-to-tube-radius ratio, or ignored axial concentration gradients. None of these simplifications are made here. The problem is characterized by a set of nine coefficients coupling the various transport phenomena. We establish these coefficients and combine them to form “figures of merit” which describe the energy conversion capability of the membrane in its various conversion modes. The capillary membrane is found to be considerably more efficient in electrodialysis than in either osmosis or electro-osmosis.
CH and CD Stretching Anharmonicities and Radiationless Decay of Triplet Benzene
Authors: Martin T. E. , Kalantar A. H.
Published: February 2004

The near-ir spectra of liquid chloroform and benzene have been analyzed to evaluate the CH and CD diagonal and cross anharmonicity constants. For HCCl3 and DCCl3, the diagonal anharmonicities (−124 and −66 cm−, respectively) and the rate of intensity decrease of successive overtones show an isotope effect. The more complex C6H6, C6H5D, C6HD5, and C6D6 spectra yield both diagonal and cross terms which are −116 and −150 for C6H6 and −63 and −87 cm−1 for C6D6, respectively) and show the same isotope effects. The analysis indicates that the only CH stretching progression arises from a combination-overtone, ν20(e1u) + nν2(a1g), and is due to the considerable anharmonicity associated with an asymmetric potential function. The pattern of anharmonicity in C6D6 is greatly changed by replacing one D by an H. The relationship of the CH stretching anharmonicity to the radiationless rate constants derived from phosphorescence lifetimes is discussed.
Vibrational Spectra and Structure of XeO2F2
Authors: Claassen Howard H. , Gasner Earl L. , Kim Hyunyong , Huston J. L.
Published: February 2004

The Raman spectra of liquid and solid XeO2F2 and the infrared spectrum of XeO2F2 in an argon matrix at liquid-helium temperature are reported. They are interpreted in terms of C2υ molecular symmetry which can be associated with a molecule of pseudobipyramidal structure, where the two F atoms are axial to the Xe and the two O atoms with a lone electron pair are equatorial. The vibrational spectra support the existence of primarily monomeric XeO2F2 molecules in the liquid state and quite probably in the solid. The nine fundamentals assigned are: 848 (ν1), 490 (ν2), 333 (ν3), 198 (ν4), 224 (ν5), 905 (ν6), 324 (ν7), 585 (ν8), and 317 (ν9).
Magnetic Nonequivalence in the High-Resolution NMR Spectra of Diborane
Authors: Farrar T. C. , Johannesen R. B. , Coyle T. D.
Published: February 2004

Proton and boron-11 nuclear magnetic resonance spectra of 11B-enriched neat diborane have been measured over the temperature range from −7° to −60°C. The terminal-proton resonance and the 11B spectrum exhibit partially resolved fine structure which arises from the magnetic nonequivalence of the terminal protons and of the boron nuclei due to long-range spin coupling. Spectra were calculated which agree quite well with the observed spectra and result in a reasonably accurate determination of the magnitudes and most of the relative signs of the various coupling constants. These values are: JBB = ∓5 Hz, JBHb = +46.2 Hz, JBHt = +133 Hz, J′BHt = +4 Hz, | JHtHb | = 7.2 Hz, JHtHb (trans or cis) = ±14 Hz, JHtHt (cis or trans) = ±6 Hz, | JHtHtgem | < 3 Hz, δ(Ht − Hb) = −4.50 ppm.
Competitive Unimolecular Decomposition in Chemically Activated Radical Systems. Propyl Rupture
Authors: Larson C. W. , Tardy D. C. , Rabinovitch B. S.
Published: February 2004

The study of the competitive unimolecular decomposition of chemically activated alkyl radicals is extended to cases of rupture of a propyl fragment vs a methyl or ethyl fragment. A study of the decomposition at room temperature of the octyl-4, heptyl-3, and 3-methyl-hexyl-2 radicals, formed by addition of H atoms to trans-octene-4, trans-heptene-3, and 3-methylhexene-1, is reported. The value of D0°(n-Pr–H) is deduced to be within −0.8 kcal of the value of D0°(Et–H). Comparison of the results are made with values obtained on a theoretical model for the absolute and relative rates; good agreement was found.
Question of Energy Migration in Liquid Benzene and Some of Its Derivatives. I. Self-Quenching Studies
Authors: Ludwig P. K. , Amata C. D.
Published: February 2004

The luminescence of benzene, toluene, p-xylene, and mesitylene and their solutions in n-nonane is studied under conditions of steady-state and nonsteady-state uv excitation. It is shown that the often-used simple reaction mechanism involving only excited monomers cannot account for the results under nonsteady-state excitation. An analysis of the data, which includes formation and reactions of excimers in these systems, is presented.
Rotational Isomers of the 1-Fluoro-2-haloethanes
Authors: Bermani M. F. El , Jonathan Neville
Published: February 2004

The infrared spectra of 1-chloro-2-fluoroethane, 1-bromo-2-fluoroethane, and 1-fluoro-2-iodoethane have been obtained in the solid, liquid, and vapor states. Raman spectra of the liquids are also presented. A complete vibrational-frequency assignment has been made for each of the molecules. The results indicate that the gauche isomer is the more stable in the liquid state whereas the trans form is more stable in the vapor. Enthalpy differences have been determined for each of the molecules in the liquid and vapor states except for gaseous 1-fluoro-2-iodoethane.
Analysis of the Charge-Transfer Spectra of Some First-Transition-Series Tetrahalide Complexes
Authors: Bird B. D. , Day P.
Published: February 2004

The charge-transfer spectra of 10 tetrahalide complexes of the first transition series have been measured at 77°K in the form of evaporated films or rigid glassy solutions. To assign the spectra in detail, theoretical expressions are developed, using vector coupling methods, to describe the first-order effect of spin–orbit coupling at both the metal and the ligand nucleus on the terms arising from each of the excited charge-transfer configurations. Theoretical expressions for the intensities of charge-transfer transitions are also derived by the same method and tested by substituting approximate LCAO eigenvectors. The assignments established by these arguments lead to the conclusion that the highest occupied orbitals of mainly ligand character occur throughout in the order 1e < 3t2 < t1 with a total energy spread of about 15 kK.
Improved Theoretical Ground-State Energy of the Hydrogen Molecule
Authors: Kolos W. , Wolniewicz L.
Published: February 2004

The potential-energy curve for the electronic ground state of the hydrogen molecule has been calculated for 1 ≤ R ≤ 3.2 a.u. in double precision and using a 100-term expansion for the electronic wavefunction. Accuracy of the previously computed diagonal corrections for nuclear motion has been tested. The vibrational equation has been solved for all isotopes of the hydrogen molecule and for the rotational quantum number J ≤ 10. The calculated adiabatic dissociation energy of H2, corrected for relativistic and radiative effects, is by 3.8 cm−1 larger than the experimental value, hence the theoretical total energy is by the same amount lower than the experimental value. The calculated vibrational quanta for H2 are by 0.5–0.9 cm−1 larger than the experimental ones.
Effect of Temperature on the Rotational and Vibrational Relaxation Times of Some Hydrocarbons
Authors: Hill G. L. , Winter T. G.
Published: February 2004

Ultrasonic velocity and absorption measurements in methane, ethylene, ethane, and propane are reported. The temperature range is from room temperature to 800°C, and the frequency/pressure range encompasses both the vibrational and the apparent rotational relaxation. In methane and ethylene the vibrational relaxation time of the lowest frequency mode varies with exp (T−1/3), while the apparent rotational relaxation time increases with temperature. Evidence is presented that the vibrational and rotational degrees of freedom are excited independently, even when the time constants are within a factor of 15 of each other.
Semiempirical Method for the Determination of Localized Orbitals in Molecules
Authors: Trindle Carl , Sinanoǧlu Oktay
Published: February 2004

A semiempirical procedure, based on the minimum-exchange-repulsions criterion, but convenient for large molecules, is developed. It is compared with the population-localization criterion and found preferable. The possibility of the transfer of local orbitals among molecules is discussed. Localization of the sigma subsystems of planar molecules without the pi systems is seen to be justified. The CH2, NH3, H2O, C2H6, C2H4, HCHO, and butadiene molecules are treated as examples.
Monte Carlo Trajectories: The Dynamics of Harpooning in Alkali–Halogen Reactions
Authors: Blais Normand C.
Published: February 2004

An analysis is presented of the dynamical properties of a model meant to represent the “harpooning,” or electron-jump mechanism that has been proposed to describe the alkali-metal–halogen-molecule reactions (M + X2→MX + X). Individual trajectories are computed from classical equations of motion with the starting conditions chosen by Monte Carlo procedures. With 500 or so trajectories for each trial, a comparison can be made with available observations from molecular-beam experiments; the way in which the reaction energy is distributed between kinetic energy of translation and the internal modes of the product, along with a measure of the differential cross section, are of particular concern. The trajectories include a sudden crossing from an initial homopolar surface to a final surface with the long-range forces required of an M+X− bond to simulate electron transfer. Two different potential functions are used as the final surface: one has a phenomenological form to include various types of X–X forces after transition, and the other has a simple induced-dipole term as an interaction of the departing X with the resulting charges (M+,X−). Except for an extreme trial closely approximating pure stripping, nine trials of the first potential failed to agree with experiment. The last potential gave good results for trials of K + Br2,K + I2,Rb + Br2,Rb + I2, and Cs + Br2.
Pressure Broadening and Shift of 3.39-μ Absorption in Methane Perturbed by Noble Gases
Authors: Goldring Hanna , Szöke A. , Zamir E. , Ben-Reuven A.
Published: February 2004

High-resolution tuned-laser spectroscopy was used to study pressure broadening and shift of a 3.39-μ methane absorption line perturbed by noble gases. Measurements were carried out in the low-pressure region where collisions influence the line shape both by pressure broadening and by narrowing the Doppler width. The Galatry line shape was found best suitable for determining the linewidth. In order to account for the observed ratio of line width to line shift, it was found necessary to modify Foley's phase-shift theory by adding a “hard-core” term to the collision cross section.
LCAO–MO–SCF Calculations Using Gaussian Basis Functions. II. BeH2
Authors: Kaufman Joyce J. , Sachs Lester M. , Geller Murray
Published: February 2004

Results of extensive LCAO–MO–SCF calculations on BeH2 utilizing Gaussian basis functions are presented. It is established that BeH2 is linear in its ground state, and the equilibrium bond distance has been determined. Force constants and normal frequencies were obtained. Utilizing an accurate estimate of the correlation energy, the dissociation energy of BeH2 was determined to within the experimental error of the National Bureau of Standards measurement.
Raman and Infrared Spectral Data for CH2Br2, CHDBr2, and CD2Br2
Authors: Dennen Robert S. , Piotrowski Edward A. , Cleveland Forrest F.
Published: February 2004

Raman displacements, relative intensities, and depolarization ratios have been observed for CH2Br2, CD2Br2, and CHDBr2 in the liquid phase, and the wavenumbers and relative intensities for the infrared bands from 400–4000 cm−1 have been obtained for both the liquid and vapor phases. All but five of the 90 bands observed for the liquid phases of these methanes have been assigned to fundamentals, first overtones, and binary combinations. The assignments for the fundamentals of CH2Br2 are in agreement with previous assignments of Plyler, Smith, and Acquista, but the assignment for the b1 fundamental of CD2Br2 at 2313 cm−1 differs from that of Dowling. The assignments for CD2Br2 were made by comparison with those for CH2Br2, and those for CHDBr2 were made with the aid of the Brodersen and Langseth complete isotopic rule. The present assignments are in better agreement with that rule than are the previous assignments.
Proton Magnetic Resonance and Hindered Rotation in Phosphonium Halides and Ammonium Iodide
Authors: Tsang Tung , Farrar T. C. , Rush J. J.
Published: February 2004

Proton spin–lattice relaxation times T1 and second moments have been measured as a function of temperature for the phosphonium halides and ammonium iodide. Correlation times τc derived from the relaxation data were used to obtain activation energies for the reorientation of the phosphonium and ammonium ions. The activation energies for PH4Cl, PH4Br, and PH4I are (35 ± 1) × 103, (29.4 ± 0.6) × 103, and (30.7 ± 0.8) × 103 J/mole, (8.3 ± 0.2, 7.1 ± 0.1, 7.3 ± 0.2 kcal/mole), respectively, indicating little change in barrier with halide ion. The frequency factors, however, do appear to vary significantly from crystal to crystal. These results are in marked contrast with previous results for the ammonium halides and suggest that nonelectrostatic repulsive forces are important in the phosphonium salts. The activation energy for NH4+ ion reorientation in the tetragonal phase (Phase III) of NH4I is found to be (13.4 ± 0.4) × 103 J/mole (3.2 ± 0.1 kcal/mole). The present results are compared with previous spectroscopic and structural results.
Spectral Intensities of the Trivalent Lanthanides and Actinides in Solution. II. Pm3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, and Ho3+
Authors: Carnall W. T. , Fields P. R. , Rajnak K.
Published: February 2004

We have correlated the experimentally determined band intensities in the solution absorption spectra of the trivalent lanthanides with a theoretical expression derived by Judd. The spectra were measured in a single medium, dilute acid solution, and, in most cases, in the range ≈6000–50 000 cm−1. In general, the correlation between calculated and observed intensities was very good, even at higher energies. The variation of the intensity parameters over the series is discussed as is the somewhat unexpected degree of correlation obtained in the ultraviolet region.
Electronic Energy Levels in the Trivalent Lanthanide Aquo Ions. I. Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+
Authors: Carnall W. T. , Fields P. R. , Rajnak K.
Published: February 2004

The free-ion energy-level schemes of the Pr3+, Nd3+, Pm3+, Sm3+, Dy3+, Ho3+, Er3+, and Tm3+ aquo ions have been determined from their absorption spectra in dilute acid solution at 25°. Energy-level assignments were made by comparison with crystal spectra, and on the basis of correlations between calculated and observed band intensities. For most of the ions, it was possible to identify several transitions giving rise to bands at energies as high as 45 000–50 000 cm−1. Sufficient numbers of assignments were made to justify inclusion of the effects of configuration interaction in the calculation of the energy-level parameters. Variation of the electrostatic, spin–orbit coupling, and configuration-interaction parameters across the lanthanide series is examined.
Electronic Energy Levels of the Trivalent Lanthanide Aquo Ions. II. Gd3+
Authors: Carnall W. T. , Fields P. R. , Rajnak K.
Published: February 2004

The free-ion energy level scheme of Gd3+ (aquo) to ∼52 000 cm−1 has been determined from the absorption spectrum of Gd3+ in dilute acid solution at 25°C. Several new absorption bands near 50 000 cm−1 have been ascribed to transitions from the ground state to components of the 6G multiplet. Energy level assignments were made on the basis of correlations between calculated and observed intensities. The resulting parameters were: E1 = 5761, E2 = 28.02, E3 = 582.0, ζ4f = 1450, α = 22.55, β = − 103.7, γ = 997.
Ionization Potentials of Molecules and Free Radicals and Appearance Potentials by Electron Impact in the Mass Spectrometer
Authors: Williams James M. , Hamill William H.
Published: February 2004

An improved method of measuring ionization efficiency (I.E.) curves by the retarding potential difference technique in the mass spectrometer (to ∼one ion/sec at onset) gives ionization potentials which agree within ± 0.02 eV of spectroscopic values and ± 0.03 eV of photoionization. Ionization potentials I have been measured for the following free radicals (eV): CH3, 9.87; C2H5, 8.34; n-C3H7, 8.13; i-C3H7, 7.57; n-C4H9, 8.01; C2H5O, 9.11; n-C3H7O, 9.20; i-C3H7O, 9.20; n-C4H9O, 9.22. Appearance potentials V have been measured for R+/RX, where R=CH3, C2H5, n-C3H7, n-C4H9 and X=H, Cl, Br, I, and OR; also for RO+/ROX where R=C2H5, i-C3H7, n-C4H9 and X=H, NO, and R; also for I+/n-C4H9I, NO+/C2H5ONO, NO+/n-C4H9ONO, and C3H6D+/CH3CD2CH3. Values of ΔHf(R+), ΔHf(RO+), D(R−X), and D(RO−X) are reported as well as electron affinities of NO, C2H5O, n-C3H7O, i-C3H7O, and n-C4H9O. Whenever two or more independent measurements of V provide the same ΔHf or D, agreement is satisfactory. The linearity of onsets does not correlate with photoionization efficiency curves according to present threshold theory. The “breaks” in I.E. curves do yield thermochemically consistent results.
Nonpairwise Additivity in the Exchange Energy for a Trio of Carbon Atoms in an Equilateral Triangle
Authors: Williams Denis R.
Published: February 2004

In order to gauge the importance of deviation from pairwise additivity in the intermolecular potential, a calculation of the exchange energy of a model system consisting of three carbon atoms arranged in a triangle has been performed. The calculations were carried out using both Slater and SCF functions as a basis set. Each of these functions are expanded in terms of Gaussian orbitals, so that the appropriate three-center integrals can be evaluated. It has been shown that deviations are considerable at distances that are normally taken to be nonbonding, the deviation calculated using SCF functions being about twice as large as that calculated using Slater functions.
Perturbed Morse Oscillator Approximation in Reactive Collisions. II. A Repulsive Potential
Authors: Pirkle J. C. , McGee H. A.
Published: February 2004

The H+Br2→HBr+Br reaction has been considered to form a linear collision intermediate and detailed reactive scattering cross sections have been computed quantum mechanically using a perturbed Morse oscillator approximation. These computations employed a diatomics-in molecules potential-energy surface distorted to make it moderately repulsive, i.e., the potential energy of the collision intermediate was made to be closer to that of the reactants than to that of the products. The resulting cross sections are peaked about the lower allowed vibrational quantum numbers of product HBr for a wide range of initial conditions corresponding to temperatures from 300° to 1000°K. This appearance of the heat of reaction as relative translation rather than as internal excitation is in agreement with both experiment and semiclassical calculations. Specific rate coefficients and pre-exponential factors calculated from the computed cross sections are also in satisfactory agreement with experiment.
Classical Mechanics of Rotational–Translational and Other Energy Transfer. I. A Hamilton–Jacobi (Action-Angle) Treatment
Authors: Cohen Audrey O. , Marcus R. A.
Published: February 2004

The classical-mechanical equations of motion describing collisional energy transfer are converted to a form involving constants of the elastic collision, using a Hamilton–Jacobi formalism. These constants frequently vary only slowly during an inelastic collision. An approximate version of the transformed equations, related to a variation of constants procedure, is next introduced. The collision of an atom with a rigid linear diatomic molecule is considered in some detail. Several desirable features of the approximation are that the change in rotational angular momentum is obtained directly, all initial orientations of particles and angular momenta occur outside the integrals, an approximate error estimate can be made, results can be calculated relatively quickly, and further insight is obtained into the energy-transfer process. Because of the close relationship of Hamilton–Jacobi and Schrödinger formalisms, a comparison of exact and approximate classical results is also expected to provide estimates of range of validity of some commonly used approximations in the quantum case.
Liquid Viscoelasticity under Rare-Gas Infusion
Authors: Knollman G. C. , Hamamoto A. S. , Miles D. O.
Published: February 2004

Experimental measurements have been made of the complex frequency-dependent shear modulus for hexachlorobiphenyl (Aroclor 1260) both with and without, in turn, helium- and argon-gas infusion to capacity, over the temperature range 5°–25°C and the pressure range ambient atmospheric to 4000 psi. Static viscosity results derived from the data are presented and analyzed with the aid of the Macedo–Litovitz hybrid equation to find changes in relative free volume brought about by rare-gas impregnation. Limiting high-frequency shear-compliance data are also presented, to which a phenomenological formulation for shear compliance in molecular-bonded liquids is applied as a means for assessing the additional equilibrium number of intermolecular bonds that are bent or broken under rare-gas infusion. Changes are noted in dynamic shear rigidity, loss modulus, and viscoelastic relaxation times brought about by the presence of each rare-gas impregnant in the recipient liquid, all as influenced by temperature and applied static pressure. Some effects on the dynamic shear spectra that are directly related to evaluated changes in free volume and intermolecular bond density are cited. We find that, except at low pressure, an increase in relative free volume is manifest upon Aroclor infusion with helium or argon gas over our temperature and pressure range. This added free-volume characteristic applies for all pressures at low temperatures where the free volume is small. The effect is found to be larger the higher the pressure (greater infusion) at all temperatures. Additional equilibrium numbers of broken bonds occurring upon infusion are enhanced with increasing temperature and, in general, with decreasing pressure. Viscoelastic relaxation times are decreased in Aroclor upon rare-gas impregnation, the reduction being more pronounced the lower the temperature or the higher the applied pressure. Infusion with the larger argon molecule has over all a more prominent impact on changes in free volume, bond density, and shear-rigidity spectra than has impregnation with helium molecules. However, no appreciable differences are detected between the two gas-infusion cases insofar as their impact on the relaxation time is concerned.
Diagonalization of a Molecular-Exciton Hamiltonian for an Impure Crystal
Authors: Philpott M. R.
Published: February 2004

The molecular-exciton Hamiltonian derived by Agranovitch {Zh. Eksp. Teor. Fiz. 37, 430 (1960) [Sov. Phys.—JETP 10, 307 (1960)]} has been diagonalized for a crystal containing a single isotopic impurity molecule. Unlike previous treatments, terms corresponding to the coupling of one-exciton and many-exciton states are not neglected. The results are compared with a classical theory.
NMR Subspectral Analysis Applied to Polyfluorobenzenes C6HnF6−n. III. Pentafluorobenzene
Authors: Lustig Ernest , Moniz William B. , Diehl Peter , Bodmer Bernhard
Published: February 2004

The nuclear magnetic resonance spectra (1H and 19F) of pentafluorobenzene at ν0 = 6.14, 94.1, and 100.0 MHz have been analyzed. Subspectral analysis, perturbation theory, and direct analysis were applied to the low-frequency spectra in order to obtain all the magnitudes and relative signs of the parameters. It was demonstrated that although at high frequencies a loss of information due to weak coupling should in principle arise, it is still possible to obtain the same results by exploitation of high-precision measurements through computer iteration and by double irradiation (tickling).
Second Virial Coefficients and the Force Constants, ε and r, of Six Halogen-Substituted Methanes
Authors: Hajjar Raja F. , MacWood George E.
Published: February 2004

The second virial coefficients of six halogen-substituted methanes were determined in the temperature range 40°–130°C, using a modified gas balance in conjunction with a reference gas, carbon tetrafluoride. It was found that the Lennard-Jones 12–6 potential describes the interaction of CClF3, CCl2F2, and CCl3F adequately, while the Stockmayer potential describes the interaction of the more polar CHF3, CHClF2, and CHCl2F. The force constants ε0 and r0 were calculated for these six halogen-substituted methanes. It was also found that the r0 values of nine halogen-substituted methanes, including the six compounds investigated here, may be expressed as a linear combination of the r0 values of CH4, CCl4, and CF4. This relationship was found to hold within 5.5% for seven out of the nine compounds.
Theory of Nonequilibrium Distribution Coefficients during Crystallization
Authors: Jindal B. K. , Tiller W. A.
Published: February 2004

A phase transformation in a multicomponent system is described in terms of a set of coupled reactions of the transformation type and the redistribution type. The interface region is considered as an open thermodynamic system undergoing irreversible changes. The nonequilibrium partitioning of impurities is calculated for nonionic systems and the nonequilibrium partition coefficient is found to depend on the interface temperature Ti and the growth velocity V of the new phase. Whether the equilibrium partition coefficient ke is greater than, less than, or equal to 1, for an ideal solution the actual partition coefficient k is greater than, less than, or equal to 1 dependening on Ti and V. Using a “large departure from equilibrium” approximation, it is shown that k → 1 as V → ∞ independent of whether ke is less than or greater than 1, and a mathematical relationship is derived to give k as a function of V.
Charge-Transfer Cross Sections for N2+ Ions Incident on H2 and D2 between 20 and 1000 eV
Authors: Haugsjaa Paul O. , Amme Robert C. , Utierback Nyle G.
Published: February 2004

Absolute cross sections for slow-ion production have been measured for beams of N2+ incident on H2 and D2 targets. The beam energy was varied from 20 to 1000 eV. A sharp maximum in the cross section was observed for the case of D2 at a beam energy of about 100 eV. A more gentle maximum, lying close to 200 eV, was found for the H2 target gas. These results are very similar to those found for argon ions on H2 and D2. The observed cross sections were found to vary only slightly with ionizing electron energy, which was varied between 16 and 25 eV. As an instrumental check, the intensity of the resulting neutral N2 beam was examined and found to be consistent with that formed by symmetric charge transfer.