bluuebunny/crossref_metadata_2025 huggingface dataset:
Dielectric Relaxation of Nonrigid Molecules at Lower Temperature
Authors: Matsumoto Akio , Higasi Keniti
Published: January 2005

The complex dielectric constants of supercooled, branched alkyl halides, if plotted on the complex plane, are described by the skewed-arc expression of Davidson and Cole. Contrary to this, dielectric properties of a great majority of straight-chain alkyl halides at room temperature are in fair accord with the circular-arc rule of Cole and Cole. Glarum considered the former behavior as an anomaly and presented a defect diffusion model. In the present paper another new mechanism is proposed. According to this, the dielectric properties of all these nonrigid molecules at lower temperatures are explainable from the same principle which explains the dielectric properties of the same substances at higher temperatures. In this mechanism a distribution of relaxation times between two limits is assumed. Skewed arcs similar to the Davidson-Cole type are to be observed at low temperatures, because the ratio of two limiting relaxation times becomes considerably larger with decrease in temperature.
Application of Rayleigh-Schrödinger Perturbation Theory to the Hydrogen Atom
Authors: Gray B. F.
Published: January 2005

A complete solution to all orders of perturbation theory is obtained without recourse to numerical approximation and it is shown that all corrections to the energy of higher order than the second do in fact vanish although the corrections to the wave function do not.
Analysis of Valence-Bond Wave Functions for LiH
Authors: Browne J. C.
Published: January 2005

Several LiH valence-bond wave functions of nonorthogonal structure are analyzed in terms of the ``natural orbitals'' and the ``structure projections.'' These wave functions are shown to agree well among themselves and to be closely similar to molecular orbital wave functions which give similar total energies.
Resonance Absorption in Solid Cyclohexane
Authors: Rasmussen Robert A.
Published: January 2005

According to the resonance absorption theory recently proposed by L. N. Liebermann, large acoustic attenuations can occur in molecular crystals as the result of weak coupling among lattice and intramolecular oscillators near resonance. Theoretical and experimental investigations have been undertaken for the purpose of testing this theory. A refinement of the original theory is presented and employed to calculate the absorption coefficient for crystalline cyclohexane. The close agreement between calculated and experimentally observed attenuations in cyclohexane together with Liebermann's results for benzene is interpreted as strong evidence of the resonance absorption mechanism.
Multicomponent Polyelectrolyte Solutions. Part I. Thermodynamic Equations for Light Scattering and Sedimentation
Authors: Eisenberg Henryk
Published: January 2005

Equations are derived, in terms of the derivative of the osmotic pressure with respect to concentration, for light scattering and sedimentation (transport and equilibrium) of polyelectrolyte systems comprising a solvent component 1, a macromolecular component 2, and an added simple electrolyte component 3. It is shown by thermodynamic arguments that, when suitable restrictions are applied to the chemical potential of component 3, the equations for the three-component systems become formally identical with the equations for two-component systems. A striking similarity is achieved between the equations for light scattering and sedimentation, by direct use in the latter of the derivative of the solution density with respect to concentration, instead of the more familiar buoyancy terms. The extension of the equations to more than one supporting electrolyte is immediate, and the extension to a macromolecular component inhomogeneous with respect to molecular weight may be achieved by known methods.
Interaction Energies from Scattering Cross Sections of Hydrogen Ions in CH4, CF4, C2H6, and C2F6
Authors: Cloney Robert D. , Vanderslice Joseph T.
Published: January 2005

The potential energy curves for the interactions between hydrogen ions (H+, H2+) and CH4, C2H6, CF4, and C2F6 have been determined from the elastic scattering cross section measurements of Simons and co-workers. The scattering measurements indicate no minimum in the H+–CH4 potential curve as one might expect from the fact that mass spectrographic results indicate a proton affinity of 5 ev for CH4. Reasons are suggested why no minimum is indicated. Various crude semiempirical schemes are suggested for correlating the potential curves for the different interaction systems. All suggested schemes are tested on the experimental results and are found to reproduce the measured potentials to within a factor of 2.
Shock-Tube Measurement of Dissociation Rates of Hydrogen
Authors: Patch Richard W.
Published: January 2005

The rate of dissociation of hydrogen was measured in a shock tube by following the absorption of ultraviolet light by the H21Πu—1Σg+ Werner transition. Dissociation was observed in mixtures of from 1.00 to 30.1% hydrogen over the temperature range from 2950° to 5330°K. A digital computer program was used to calculate reaction profiles behind a normal shock wave for arbitrary reaction rate coefficients assuming that the reaction proceeded by the mechanism H2+M⇄ lim krkd2H+M,where the third body, M, may be Ar, H2, or H. By varying the reaction rate coefficients, it was possible to match the computed reaction profiles with the observed profiles for all experiments; however, the temperature range covered was not sufficiently wide to permit an accurate determination of the temperature dependence of kr. Consequently, a T−1 dependence was arbitrarily chosen. The recombination rate coefficients in cm6 mole−2 sec−1 were 7.5×1017 T−1 for argon as the third body, 7.5×1018 T−1 for H2, and 5×1019 T−1 for H, where T is in °K.
Rates of Reaction of Hydrogen with Iodine. II
Authors: Sullivan John H.
Published: January 2005

The rate of reaction of hydrogen with iodine was measured at 666.79° and 799.77°K. The elementary reactions were considered to be  ⇀   ↼H2+I2⇌2HI,            (1)  (2) I+H2⇌HI+H,            (3)  (4) H+I2⇌HI+I,            (5)  (6)     I2=2I,                  where the left-hand equation number applies when the reaction proceeds to the right and the right hand number when the reaction proceeds to the left.

Our previous measurements over a shorter and lower temperature range had given E4∼0 kcal and an apparent temperature dependence for k4/k5 which suggested a negative temperature coefficient for k5. The present more extensive and more precisely treated data show that k4/k5 is temperature independent and E4=0 kcal, E5=0 kcal. The specific rate [(mole/cc)−1 sec−1] of (3), which at 800°K accounts for about 95% of the HI production, is given by log(k3/T12)=12.55±0.07−(32 800±250)/4.575T. The close agreement of our rates with those calculated from data in the literature leads to the conclusion that the experimentally determined values of k4/k5 are equal to values of k4/k5 for thermal energy distributions of H atoms.
Vacuum Ultraviolet Photolysis of Methane
Authors: Mahan Bruce H. , Mandal Robert
Published: January 2005

The photolysis of CH4—CD4 mixtures, CH2D2, and CHD3 with 1236 Å light shows that molecular elimination of hydrogen from methane is an important but not an exclusive primary photochemical process. The photolysis products are principally those expected from the insertion reaction of the methylene radical.
Rotational Freedom of Ammonium Ions and Methyl Groups by Cross-Section Measurements with Slow Neutrons
Authors: Rush J. J. , Taylor T. I. , Havens W. W.
Published: January 2005

The slope Δσs/Δλn of a plot of the scattering cross section per proton vs the wavelength of subthermal neutrons is shown to increase with increasing freedom of rotation of ammonium ions. For ammonium iodide, the slope increases from 6.2 b/Å—H in phase II to 11.2 b/Å—H in phase I, where the ammonium ions are rotating relatively freely. Measurements on five liquid methylbenzenes indicate greater hindrance to rotation of methyl groups in o-xylene (slope=9.5±0.3 b/Å—H), than in toluene, m-xylene, p-xylene, and mesitylene (slopes=11.4±0.3 b/Å—H).

From an empirical plot of slopes vs barriers to rotation of ammonium ions in several ammonium salts, slopes of 5.5 and 5.8 b/Å—H for (NH4)2CrO4 and NH4CNS indicate a barrier of about 4 kcal mole−1 for both these salts, while a high slope of 13 b/Å—H for NH4ClO4 predicts a barrier of only about 0.1 to 0.2 kcal mole−1. Assuming a similar type curve for methyl groups, the barrier to rotation of the methyl groups in o-xylene is estimated to be about 1 kcal mole−1, and a value of 0.1 to 0.4 kcal mole−1 is predicted for the other methylbenzenes.
Electron Magnetic Resonance of an Oriented Allyl-Type Free Radical
Authors: Heller C. , Cole T.
Published: January 2005

It has been found that x-irradiation of a single crystal of glutaconic acid (HOOC)CH=CH–CH2(COOH) produces the oriented allyl-type free radical (HOOC)C(1)H=C(2)H–C(3)H(COOH). A detailed analysis of the electron magnetic resonance spectra of this radical confirms that the spin density on carbon 2 is opposite in sign to the spin densities on carbons 1 and 3. Additional structural features determined are: (a) The unpaired electron occupies a delocalized π molecular orbital extending over carbon atoms 1, 2, and 3; (b) spin densities ρii for carbon p orbitals on carbon atoms 1, 2, and 3 are ρ11=ρ33=+0.57, ρ22=−0.19; (c) principal values of the hyperfine tensors for protons 1 and 3 are −53, −36, and −18 Mc, and for proton 2 are +17, +12, +7 Mc; (d) all C–H bonds in the radical are nearly parallel. The parallelism of all C–H bonds indicates that the undamaged parent molecule is the trans isomer of the acid.
Evaluation of Molecular Integrals by Solid Spherical Harmonic Expansions
Authors: Pitzer Russell M. , Kern C. William , Lipscomb William N.
Published: January 2005

The use of expansions of solid spherical harmonics, which are the functions (rn or r−n−1) Pnm (cosθ)(cosmφ or sinmφ),is discussed with respect to molecular integrals, and it is found that terms of the delta function type must be included in the expansion for the r−n−1 case if n—m≥2. These expansions are especially useful for operators involving inverse powers of r such as electromagnetic interaction operators. General formulas are given for integrals in which two atomic orbitals, e.g., Slater orbitals, are on one center, and one of these operators is on the other center. Formulas are also given for the corresponding one-center integrals, and methods of evaluating three-center integrals and other two-center integrals are discussed briefly.
Matrix Isolation of High-Temperature Vapors: Boric Oxide
Authors: Weltner W. , Warn J. R. W.
Published: January 2005

The matrix isolation technique has been extended to allow molecules which are in equilibrium with solids at high temperatures to be trapped and studied at low temperatures. A beam of the hot vapor issuing from a Knudsen cell or a heated surface is premixed with a large excess of argon or xenon just prior to condensation at 20°K. The method was applied to boric oxide vapor which was vaporized from the liquid at 1400°K. The infrared absorption spectrum of the B2O3 molecule in a solid inert gas matrix was measured between 280 and 3600 cm−1 and compared with the known vapor emission spectrum. Several new bands were found near 500 cm−1 which led to a considerable alteration in the vibrational assignment and the thermodynamic properties of the gaseous molecule. The infrared spectrum of B2O2 (produced by heating boron plus boric oxide) isolated in a matrix yielded one absorption band which agreed with the emission spectrum. An extensive normal coordinate treatment of B2O3 was made utilizing the observed spectra of the B10 and B11 substituted molecules.
Contribution of Octopole—Octopole Interactions to the Excess Properties of Mixtures of Tetrahedral Molecules
Authors: Parsonage N. G. , Scott R. L.
Published: January 2005

The contribution to thermodynamic properties of the interaction between bond dipoles of adjacent tetrahedral molecules (such as CF4) has been estimated by calculating the octopole—octopole effect (a) between molecules in an isolated pair and (b) in a rigid lattice. The effect is small and cannot account, at best, for more than a small part of the anomalous excess free energies of systems such as CF4+CH4.
Spin Resonance Spectra of Substituted Aromatic Ions; Superposition Model
Authors: Schug John C. , Brown Thomas H. , Karplus Martin
Published: January 2005

A simplified model is developed for the extension of the valence-bond method to certain types of substituted aromatic ions. The model assumes that the ground-state wave function can be decomposed into quasi-independent charge distributions whose interactions can be analyzed by perturbation theory. The resulting formulation permits the approximate superposition of the results of electron spin resonance measurements of monosubstituted species to estimate hyperfine constants of polysubstituted ions. By this very simple averaging technique, reasonable agreement with experiment is obtained in certain cases and significant deviations occur in others. Also a number of relationships (e.g., constancy of a 2H+a3H in para-substituted nitrobenzene anions) are predicted or explained by the model.
Radiation Damage in Organic Crystals. III. Long Polyene Radicals
Authors: Hanna M. W. , McLachlan A. D. , Dearman H. H. , McConnell H. M.
Published: January 2005

The distribution of electronic spin in a series of linear odd-alternant polyene radicals is calculated using valence-bond, Hückel, and the ``extended'' Hartree—Fock methods. These theoretical results are compared with the spin distributions in a series of free radicals produced by irradiation of polyene acids, CH3 (CH=CH)m-1COOH, m=2–5, 7. The experimental spin distributions are deduced from the line shape of the ESR spectra of polycrystalline samples by making use of a method relating the second moments of the ESR spectra to the spin distribution. Experimental evidence is adduced for the presence of negative spin density on the ``unstarred'' atoms of these radicals. The relation between these results and the problem of bond alternation in long polyene radicals is discussed.
EPR Study of Tetracene Positive Ion
Authors: Hyde James S. , Brown Harmon W.
Published: January 2005

The EPR response of tetracene positive ion formed by dissolving tetracene in concentrated sulfuric acid has been investigated in detail. The splittings of the hyperfine lines have been carefully measured and the spectrum analyzed. Relaxation processes (T1 and T2) have been investigated over a range of experimental conditions. At low temperatures anisotropic hyperfine interactions determine linewidths and result in asymmetric spectra. This asymmetric interaction differs for the various classes of protons and depends on the form of the hyperfine tensor for each class. A second broad resonance of integrated intensity equal to that of the tetracene positive ion has been detected. In one experiment deuterated sulfuric acid was used, and it was found that the deuterium exchanged with the tetracene protons.

Considerable attention has been paid to experimental techniques useful in investigating narrow line spectra. Both 100-kc field modulation, where modulation sidebands were encountered, and superheterodyne detection have been employed. Linewidths as narrow as 35 mG have been obtained.
Fermi Resonance in Linear Triatomic Molecules in Π Electronic States
Authors: Hougen Jon T.
Published: January 2005

The effect of Fermi resonance on the vibronic energy levels of linear triatomic molecules in Π electronic states has been considered, for states in which both the spin-orbit interaction and the Renner interaction are small compared to the frequency of the bending vibration. The essential difference between the results below and those for Fermi resonance in nondegenerate electronic states is the introduction of two Fermi interaction parameters W1 and W2, rather than one. Specific results are presented for the Fermi diad (100)—(020). The only experimental data available, those for the vibronic states of the A2Π electronic state of BO2, can be nicely fitted with the results of this paper.
Intensities of Crystal Spectra of Rare-Earth Ions
Authors: Ofelt G. S.
Published: January 2005

Magnetic and electric dipole transitions between levels of the 4fx configuration perturbed by a static crystalline field are treated. The expression obtained for the pure-electronic electric-dipole transition probability involves matrix elements of an even-order unit tensor between the two 4fx states involved in the transition. The contributions to the transition probability from interactions, via the crystalline field, with the nd94fx−1, 4fx−1nd, 4fx−1ng configurations are shown to add linearly, in such a manner as to multiply each odd k crystal-field parameter Akq by a constant. If ``J mixing'' in the 4fx configuration is neglected ΔJ between the upper and lower 4fx levels is restricted to six units or less. If ``L mixing'' is neglected then ΔL is also restricted to six units or less. Application is made to the fluorescence spectra of PrCl3 and EuCl3. Many of the missing and weak transitions are explained.
Cleavage of Alkali Halide Single Crystals in High Vacua. Analysis of Evolved Gases
Authors: Vanderslice T. A. , Whetten N. R.
Published: January 2005

The gas evolved on cleavage of alkali halide single crystals in a high vacuum has been analyzed with an ultrasensitive mass spectrometer. The gas is primarily H2O in the case of NaCl, and primarily CO in the case of KCl, KI, NaF, and KBr. The evolved gas appears to come at least in part from the interior of the crystal, rather than from only the surface and from sliding parts in a vacuum. The amount of gas evolved from NaCl was found to depend on the source of the crystal, with less gas coming from the purer crystals. The total contamination of the freshly cleaved surfaces as a result of the gas is probably less than one-hundredth of a monolayer coverage. The sensitivity of this method of detecting certain impurities in solids is shown to be high.
Note on Absorption Coefficients of Hot CO2 at 4.40 μ
Authors: Tourin Richard H. , Babrov Harold J.
Published: January 2005

The infrared absorption of CO2–N2 mixtures, enclosed in a furnace-heated gas cell, was studied for optical depths of 0.10 to 2.5 cm-atm at 1273°K. The results of these measurements were compared to results for shock-heated CO2–N2 mixtures, obtained for the range 0.10 to 0.40 cm-atm. The results did not appear to depend upon the method of heating, whether furnace or shock tube. However, the results did depend strongly upon pressure. Two types of Beer's law failure were found: (1) When the ratio of CO2 pressure to total pressure was kept constant, plots of reciprocal transmittance vs optical depth were straight lines through the origin, of slope (absorption coefficient) dependent on the pressure ratio; (2) similar plots for constant total pressure were concave toward the optical depth axis. These effects are due to varying pressure broadening of unresolved spectral lines.
d Orbitals in Compounds of Second-Row Elements. I. SF6
Authors: Craig D. P. , Zauli C.
Published: January 2005

Optimum exponent values for 3s, 3p, and 3d orbitals of sulfur in SF6 have been calculated in an electrostatic approximation. The sulfur electrons are perturbed by fluorine potentials appropriate to self-consistent field wave functions for the fluorine orbitals, and the energy minimized with respect to wave-function exponents. The optimum values are k3s=2.0, k3p=1.6, and k3d=1.2, corresponding to expansion of 3s and 3p orbitals, and contraction of 3d, compared with free-atom values. The values are remarkably stable to changes in valence-orbital configurations as between SF6, S+F6−, S++F6=, and even S−F6+. They are also little affected by change in hybridization at fluorine, and should therefore be suitable for use in the construction of molecular wave functions.

Although the calculated energies include no exchange terms they are still of some interest. They suggest for example that the promotion energy to the configuration sp3d2 of sulfur (estimated to be 25–31 eV) can be compensated by the energy of molecule formation.
Structure of the Ground State of HCN
Authors: McLean A. D.
Published: January 2005

A wave function is presented for the ground state of HCN calculated in the LCAO MO SCF approximation. All integrals needed to compute the expectation value of the energy of the molecule were computed accurately. The results of a population analysis on the wave function are reported.
Infrared Spectrum and Thermodynamic Functions of the NF2 Radical
Authors: Harmony Marlin D. , Myers Rollie J.
Published: January 2005

The three fundamental vibrational frequencies for the NF2 radical have been measured in an N2 matrix at 20°K. They are ν1 = 1069.6±0.5, ν2 = 573.4±1.0, and ν3 = 930.7±0.5, all in cm−1. The infrared spectrum of N2F4 was also examined and good evidence is presented to confirm that N2F4 dissociates into NF2 at low pressures. This dissociation was found under the conditions in our spray-on line to have a half-life of 100 sec or more at room temperature and about 1 sec near 100°C. The thermodynamic functions of NF2 are tabulated.
Heat Capacity of MnBr2 between 1.7 and 20°K. Magnetic Ordering in MnBr2
Authors: Hadley Wayne B. , Stout J. W.
Published: January 2005

The heat capacity of MnBr2 has been measured between 1.7 and 20°K. The calorimeter and carbon resistance thermometer—heater are described. There is an anomaly in the heat capacity of MnBr2, arising from the ordering of the spins of the manganous ions. The maximum heat capacity, in excess of 30 cal mole−1 deg−1, occurs at 2.16±0.01°K. The entropy associated with the magnetic ordering is R ln6 and the corresponding enthalpy is 10.84 cal mole−1.
Primary Reactions in the Mercury-Photosensitized Decomposition of 1-Butyne, Propyne, and Acetylene at Low Pressures
Authors: Kebarle P.
Published: January 2005

The mercury-photosensitized decomposition of 1-butyne, propyne, and acetylene was studied at very low pressures in a flow system attached to a mass spectrometer.

The primary decomposition of 1-butyne was found to proceed by the reactionsC4H6*→HC≡C–CH–CH3+H50%→HC≡C–CH2+CH3    25%→1,2 and 1,3 butadiene.7%

The primary decomposition of propyne was C3H4*→HC≡C–CH2+H80%→allene.15%

The presence of C2H radicals was detected in the decomposition of acetylene. These probably originate from the primary decomposition. The primary quantum yield for acetylene appears very much lower than that of the butyne and propyne. It is concluded that acetylene forms an excited molecule, but that the primary decomposition does not necessarily occur by this process but from reactions involving the formation of HgH and HgC2H.
Spectroscopic Study of the Effect of High Pressures on Organic Charge-Transfer Complexes in Solution
Authors: Gott J. Robert , Maisch William G.
Published: January 2005

The charge-transfer solution spectra of tetracyanoethylene with benzene, hexamethylbenzene, diphenyl, and naphthalene have been observed as a function of pressure up to a maximum of 10 000 atm. The association constants and charge-transfer transition oscillator strengths have been determined for pressures up to 4000 atm in the case of the benzene—tetracyanoethylene complex. A large increase in transition oscillator strength with pressure is observed for the benzene complex; this is in accord with the theoretical predictions of Mulliken. A small decrease in association constant with pressure for this complex is tentatively interpreted in terms of complexing between the tetracyanoethylene and the solvent, methylene chloride. The observed frequency shifts with pressure, and the band splitting of the charge-transfer spectra of the diphenyl and naphthalene complexes are discussed. It has previously been suggested that solutions of charge-transfer complexes contain orientational isomers of those complexes; this theory receives a measure of support from the pressure measurements.
Two Assumptions in the Theory of Attractive Forces between Long Saturated Chains
Authors: Zwanzig Robert
Published: January 2005

A recent calculation by Salem of the attractive forces between two long parallel hydrocarbon chains was based on two assumptions: (1) pairwise additivity of dispersion forces between individual groups on each chain, and (2) isotropy of the polarizability of a group on the chain. The validity of these assumptions is examined here by means of a Drude model calculation of the interaction between two parallel linear lattices of dispersion oscillators. We describe an exact calculation on this model, and also a calculation based on applying Salem's assumptions to the same model. We conclude that the assumptions are not valid for the Drude model, because of strong induced-dipole interactions between neighbors along the lattice. Salem's procedure leads to essentially correct numerical results, however, due to use of an experimentally determined bond polarizability at a crucial stage of the calculation. This allows for the effects of interactions between neighbors. Our results are applicable to real hydrocarbon chains only to the extent that the Drude model is valid.
Semiempirical Calculation on the Lower Electronic States of the Benzene Molecule
Authors: Anno Tosinobu , Sado Akira
Published: January 2005

Within the semiempirical ASP—LCAO—MO—CI framework proposed by Pariser and Parr, the lower excited levels of the benzene molecule are calculated by considering CI up to and including doubly excited configurations. This calculation has three purposes: (i) a check on the value of the core resonance integral βCC, (ii) the symmetry assignment of the controversial absorption system around 2000 Å and (iii) the elucidation of the change of the ring-breathing vibrational frequency due to electronic excitation. From the condition that the calculated value of the lowest 1 B2u−1 A1g transition energy agree with experiment, the core integral βCC is found to be −2.7217 eV, which is to be compared with −2.39 eV suggested originally by Pariser and Parr without considering CI. By using this new value of βCC, CI calculations for the lower singlet levels are carried out. The theoretical energy levels are compared with the experimental data as well as the calculated values with nonempirical and the other semiempirical methods. The present calculation favors the 1 B1u←1 A1g assignment for the 2000-Å absorption system. The wavefunctions as approximated by linear combinations among the ground and the singly and doubly excited configurational functions are, also, obtained for the ground 1 A1g and the lowest-excited 1 B1u, 1 B2u and 1 E2g states. From these wavefunctions the bond orders of the CC bonds in these states are obtained. By using the values of the CC bond order, the changes in the CC bond length and the ring-breathing frequency are estimated for the 1 B1u←1 A1g, 1 B2u←1 A1g and 1 E2g←1 A1g transitions and compared with the available experimental values.
Determination of the Geometry of Lithium Oxide, Li2O(g), by Electric Deflection
Authors: Büchler Alfred , Stauffer James L. , Klemperer William , Wharton Lennard
Published: January 2005

A conventional Inghram-type mass spectrometer has been adapted to permit the study of the polarity of high-temperature species by electric-deflection methods. The molecule Li2O has been found to be nonpolar and therefore to have an equilibrium angle close to 180°, as shown by the absence of deflection of a molecular beam by an inhomogeneous electric field. The species LiO, which was found by Berkowitz, Chupka, Blue, and Margrave, has been confirmed to form a small percentage of the vapor in equilibrium with solid Li2O. Gaseous lithium molybdate, Li2MoO4, has been observed. It is readily formed by the reaction of lithium oxide with molybdenum above 1150°C.
Emission and Dissociation of NO2 in Shock Waves
Authors: Hiraoka Hiroyuki , Hardwick R.
Published: January 2005

When compared with other kinetic data, the time dependence of the emission of NO2 in shock waves at ∼2000°K supports the conclusion that the intensity follows [NO2] in this system. Study of the emission from the system of CH3NO2–Ar shows that NO2 appears following the shock, but that it has a very short lifetime, presumably reacting according to CH3+NO2→CH3O+NO.
Charge Densities in Atoms
Authors: Steiner Erich
Published: January 2005

A corollary to a theorem by Kato is derived which relates the charge density and its derivative at the nucleus of an atom. For nuclear charge Z it is (∂ρ/∂r)r=0=−2Zρ(0).
Asymptotic Solutions of Differential Equations with Transition Points or Singularities
Authors: Erdélyi A.
Published: January 2005

Asymptotic solutions of d2y/dx2+[λ2p(x)+r(x,λ)]y=0 are found when λ is a large parameter and r is ``small'' in comparison with λ2p, except at a single point where either p has a simple zero, or p a pole of the first order and r a pole of the second order. The results are applied to Bessel functions, and to Hermite and Laguerre polynomials. The resulting asymptotic forms are valid uniformly in x.
Ergodicity Conditions in Quantum Mechanics
Authors: Prosperi G. M. , Scotti A.
Published: January 2005

In this paper ergodicity conditions for a quantummechanical system are investigated in the line of thought of recent papers of Bocchieri and Loinger and of authors themselves. More precisely, the averaging a over all the initial states used in the paper by Bocchieri and Loinger is here substituted by an averaging B over the initial states belonging to a given cell; that is to say, over all the microscopic states corresponding to a given macroscopic state. Restrictions to be imposed on the Hamiltonian in order that relation ∑ ν = 1NB(Muν(t)−sν/S)2sν2/S2≪1be satisfied are then looked for. These restrictions could be obtained only in an implicit form.
Double Commutator in Quantum Field Theory
Authors: Streater R. F.
Published: January 2005

A representation is obtained for the most general function with the properties of the double commutator, including nonzero mass thresholds but not the Jacobi identities. The thresholds are proved to satisfy triangular inequalities (without using any more information) which are always true physically. The problem of incorporating a discrete level at the mass of a stable particle is not solved.
Decomposition of Direct Products of Representations of the Inhomogeneous Lorentz Group
Authors: Lomont J. S.
Published: January 2005

The direct products of the physically significant, irreducible, unitary representations of the proper, orthochronous inhomogeneous Lorentz group are reduced. It is shown that Γm1s1⊗Γm2s2 contains only irreducible components of the form ΓmJ, and that ΓmJ occurs with nonzero multiplicity only if J − (s1+s2) is an integer. For such J's the multiplicity of Γm, J for J≥s1+s2 is (2s1+1) (2s2+1) for each positive m. Γm1s1⊗Γs2(±) contains only irreducible components of the form ΓmJ, where J − (s1+s2) is an integer. The multiplicity of such Γm, J for J≥s1+s2 is (2s1+1) for each positive m. Γs1(ε1)⊗Γs2(ε2) contains irreducible components of the form Γs(∈) and ΓmJ, where s = | ∈1s1+∈2s1 |, ∈ = sign (∈1s1+∈2s2) and J − (s1+s2) is an integer. The multiplicity of Γm, J is one for J≥(s1+s2) and for each positive m. The multiplicity of Γs(∈) is infinite. The symmetrized squares are also analyzed. Numerous examples are given.
New Theorem in the Classical Ensemble Theory
Authors: Albertoni S. , Bocchieri P. , Loinger A.
Published: January 2005

In the framework of the classical ensemble theory a theorem is proved which is sufficient to justify the classical statistical mechanics.

Our result can be stated as follows. Let us consider a fixed and otherwise arbitrary subdivision in cells Iν (ν = 1, 2, …, N) of the energy shell I of an isolated dynamical system: Having introduced a suitable definition of functional average, we prove that for ``almost all'' the initial Liouville density functions ρ(p′,q′; 0) we have lim lim T→∞1T ∫ 0Tdt{[ ∫ Iνρ(p′,q′;t)dp′dq′−σνσ]2}=0,where σν and σ are the measures of Iν and I, respectively. The unitarity of the Koopman-von Neumann time-evolution operator is the only dynamical property needed to establish this theorem. On the basis of our result, it can be shown that systems with very many degrees of freedom satisfy the laws of statistical mechanics.
On the Analytic Properties of Partial Wave Amplitudes in Yukawa Potential Scattering
Authors: Fivel Daniel I. , Klein Abraham
Published: January 2005

A new proof is given of the dispersion relation for the lth partial wave amplitude when the potential is of the Yukawa form or (by obvious extension) a suitable linear combination of such forms. The requisite analyticity properties are obtained by rewriting the integral equation for the quantity fl(k,r), which is related to the l-wave amplitude, as a Volterra equation on a finite interval in which the contribution from the asymptotic part of the integral is absorbed into the inhomogeneous term. The Born series for the inhomogeneous term is analytically continued termwise into the cut complex-wave-number plane and the uniform convergence of the series is then established utilizing approximations which apply in the asymptotic region. The properties of fl(k,r) then follow from a well-known theorem on Volterra equations.
Statistical Dynamics of Simple Cubic Lattices. Model for the Study of Brownian Motion
Authors: Rubin Robert J.
Published: January 2005

The system considered is an n-dimensional cubic crystal with nearest-neighbor central and noncentral harmonic forces in which the mass M of one of the lattice particles is relatively large. It is assumed that the velocities and positions of the light particles in the system (mass m) are normally distributed, at time t=0, as in thermal equilibrium. The conditional velocity distribution for the heavy particle at time t is then a normal distribution with a time-dependent mean value. This mean value is the velocity autocorrelation function. The dispersion of the distribution is shown to be a simple function of the autocorrelation. In the limit M/m≫1 in the one- and two-dimensional lattices, the autocorrelation function is, respectively, a damped exponential and a damped oscillating exponential. These different types of statistical behavior are related to the different dynamic properties of the medium with which the heavy particle interacts.
Liouville Equation and the Resolvent Formalism
Authors: Teitler S. , Wallis R. F.
Published: January 2005

With the use of the Prigogine and Balescu representation for the description of relaxation starting from the Liouville equation, we apply Van Hove's resolvent formalism to obtain higher-order contributions for classical weakly coupled homogeneous gases. These results confirm Van Hove's observation that, for appropriate representations, persistent (long time) effects are determined by diagonal matrix elements of operators consisting of products of perturbative operators separated by diagonal operators. The mechanism of relaxation is also discussed.
Phenomenological Distinction between Unitary and Antiunitary Symmetry Operators
Authors: Wigner Eugene P.
Published: January 2005

It is well known that one always can find as many orthogonal states (i.e., states between which the transition probability is zero) as the Hilbert space has dimensions which are invariant under a given unitary transformation. The corresponding vectors are characteristic vectors of the unitary operator. In contrast, most antiunitary operators leave not more than one state invariant. However, if there are two orthogonal invariant states, a consideration of the states for which the transition probability is ½ into both invariant states surely provides a distinction. In the antiunitary case, one of these states is also invariant, another one is transformed into an orthogonal state, the rest are in between. In the unitary case, the transition probability between original state and transformed state is the same for all states for which the transition probability is ½ into two orthogonal states. This provides a ``directly observable'' distinction between unitary and antiunitary transformations.
Algebraic Characterization of the TCP Operation
Authors: Grossmann A.
Published: January 2005

If an ``operation'' 𝔐 is real and preserves Lorentz covariant relations, then 𝔐 is either a proper Lorentz operation or the product of a proper Lorentz operation and the TCP operation.
Symmetry-Adapted Functions Belonging to the Symmetric Groups
Authors: McIntosh Harold V.
Published: January 2005

Young's factorization of idempotents belonging to the symmetric groups is given a necessary and sufficient characterization, by means of a lemma due to Burrow. The use of these idempotents is contrasted with Yamanouchi's representation, and finally the equivalence of Löwdin's path diagram method to the group-theoretical treatment of the angular momentum states arising from the coupling of an assemblage of spin ½ particles is demonstrated.
On the Calculation of the Inverse of the Overlap Matrix in Cyclic Systems
Authors: Löwdin P. O. , Pauncz R. , De Heer J.
Published: January 2005

The inverse of the overlap matrix of a cyclic system has been computed in three different ways, each of which throws light on a different aspect of the subject and has its own range of applicability to related problems. In all these derivations extensive use has been made of the properties of the Chebyshev polynomials. The results hold for every cyclic symmetric matrix.
Quantization of Nonlinear Systems
Authors: Segal I. E.
Published: January 2005

A direct method of quantization, applicable to a given nonlinear hyperbolic partial differential equation, is indicated. From such classical equations alone, without a given Lagrangian or Hamiltonian, or a priori linear reference system such as a bare or incoming field, a quantized field is constructed, satisfying the conventional commutation relations. While mathematically quite heuristic in part, local products of quantized fields do not intervene, and there are grounds for the belief that the formulation is free from nontrivial divergences.
On the Nonexistence of a Class of Static Einstein Spaces Asymptotic at Infinity to a Space of Constant Curvature
Authors: Buchdahl H. A.
Published: January 2005

It is known that there exist no nontrivial static regular solutions of the Einstein vacuum equations Rkl=0 which are asymptotically Galilean at infinity. One may ask correspondingly whether there exist static solutions of the equations Rkl=λgkl(λ<0) which are regular at all finite points and asymptotic (in a sense to be defined) to a space of constant curvature at infinity. The answer to this question is here shown to be in the negative. The proof rests upon the possibility of writing a certain quadratic invariant density of the Riemann tensor in the form of an ordinary divergence.
Galvanomagnetic and Thermomagnetic Effects in Isotropic Materials
Authors: Pipkin A. C. , Rivlin R. S.
Published: January 2005

Invariant-theoretical considerations are employed to obtain constitutive equations for the current density vector, the heat flux vector, and the magnetic intensity field in isotropic materials (both holohedral and hemihedral) when an electric field, a magnetic induction field, and a temperature gradient are simultaneously present in the material. Certain of the interaction effects which are indicated by these constitutive equations are discussed.
Quantization of Fields with Infinite-Dimensional Invariance Groups
Authors: DeWitt Bryce S.
Published: January 2005

A general approach to the problems of quantizing fields which have infinite-dimensional invariance groups is given. Space and time are treated on a completely equal footing. A Poisson bracket is defined by means of Green's functions, independently of the discovery or recognition of canonical variables, and is shown to satisfy all the usual identities. In accordance with the measurement theoretical foundations of the quantum theory, the Poisson bracket (i.e., commutator) is defined only for physically measurable group invariants. The Green's functions give a direct description of the propagation of small disturbances arising from a pair of mutually interfering measurements.

In order to establish a correspondence between this approach and conventional canonical theory, a motivation for the adopted definition of the Poisson bracket is outlined with the aid of the fundamental theorem of canonical transformation theory. The rest of the discussion is logically independent of this, however. The general theory of ``wave operators'' and their associated Green's functions is briefly reviewed. Specific details connected with the group theoretical side of the theory are handled in such a way that problems of constraints are completely avoided. In the last section the general method is applied to the Yang-Mills field, as a nontrivial example. The problem of factor ordering is not studied.
Generalized Retarded Functions and Analytic Function in Momentum Space in Quantum Field Theory
Authors: Araki Huzihiro
Published: January 2005

The analytic n-point function in momentum space in quantum field theory is studied. Its different boundary values for real value of the argument are determined, and a necessary and sufficient condition for them to be obtainable from the Wightman functions is given. The conditions are relativistic covariance, support properties in coordinate space (retardedness), two-term identities for momentum below threshold (corresponding to spectrum conditions) and four-term identities (Steinmann relations). The first three conditions are translatable into a statement about the domain of analyticity of the n-point function: it is analytic in a union of various extended tubes plus the points of contact of two neighboring tubes for real part of one momentum below threshold.
Integral Representation for the Nonrelativistic Coulomb Green's Function
Authors: Wichmann Eyvind H. , Woo Ching-Hung
Published: January 2005

Although the radial Green's function for the Schrödinger equation in a Coulomb field can be obtained in the usual way in terms of the two linearly independent solutions to the radial equation for a particular angular momentum state, the sum over angular momentum states does not seem to have been carried out. In this note this sum is carried out and a ``closed form'' obtained in the form of a double integral. The result is believed to be useful for perturbation calculations where the ``intermediate states'' involve many angular momentum states.
Almost Periodicity and the Quantal H Theorem
Authors: Percival Ian C.
Published: January 2005

It is proved that the H theorem for an ensemble of isolated quantal systems with a discrete energy spectrum is false provided the systems satisfy certain broad conditions: the theorem is false for bounded many-particle systems with potential interaction, provided that interaction contains no repulsive singularities stronger than r−2 and no attractive singularities stronger than r−1. Ensembles of such systems behave almost periodically, in the sense of H. Bohr. The entropy and the probability of finding an observable in a given range are both almost periodic functions of time.
Free Quantized Lorentzian Fields
Authors: Schwartz J.
Published: January 2005

A systematic classification is made of all local Lorentz-invariant quantized field theories which are free in the sense that [ψ(x),ψ(x′)] is a c number. It is shown that none exist except those given in the classical paper of Fierz, and that, in fact, certain of the fields listed by Fierz are redundant.
Free Propagator Expansion in the Evaluation of the Lamb Shift. II
Authors: Layzer Arthur J.
Published: January 2005

The results of the preceding paper are extended and applied to the calculation of the new Lamb shift orders of αw3 ln2w and αw3 lnw [w≡(αZ)2]. The final result for the 2S−2P½ shift due to the ln2 and ln terms, which has been previously published, is ΔE(2S−2P½) = −Lw[¾ ln2w+lnw(4 ln2+1+7/48)] where L is Z4 times the Lamb unit. In megacycles this is −0.25 for H and −9.5 for He+. The corresponding new values for the total theoretical shift are 1057.70±0.15, 1059.08±0.16, and 14047.2±3.0 for H, D, and He+, respectively. These values incorporate more up to date estimates for the nuclear finite size effect in D and He+ than those previously reported.
Absolute Definition of Phase Shift in the Elastic Scattering of a Particle from Compound Systems
Authors: Temkin A.
Published: January 2005

The projection of the target wave function on the total wave function of a scattered particle interacting with the target system is used to define an absolute phase shift including any multiples of π. With this definition of the absolute phase shift, one can prove rigorously in the limit of zero energy for s-wave electrons scattered from atomic hydrogen that the triplet phase shift must approach a nonzero multiple of π. One can further show that at least one π of this phase shift is not connected with the existence of a bound state of the H− ion.
Theories of Transport in Fluids
Authors: Green H. S.
Published: January 2005

The object of this paper is to establish the equivalence of the Kubo-type transport coefficients with those obtained by the method of Chapman and Enskog. Kubo-type coefficients are derived by a simple method, based on classical mechanics, and these are found to be in general agreement with those found by Mori, who has, however, discarded some important relaxation terms. The neglect of these terms by Kubo and other authors has the effect of leaving their coefficients of diffusion and electrical conductivity divergent. It is shown quite generally that the computation of the corrected Kubo-type coefficients for dilute gases leads to the same results, and even the same calculations, as the method of Chapman and Enskog. The equivalence of the two methods for dense systems is also briefly discussed.
Nonequilibrium Processes in Isotopically Disordered Crystals
Authors: Maradudin Alexei A. , Weiss George H. , Jepsen Donald W.
Published: January 2005

The equations of motion of the atoms in an isotopically disordered crystal, which contains a fraction p of atoms of mass M1, and a fraction 1−p of atoms of mass M2, are expanded in terms of the normal coordinates of a monatomic lattice whose atoms all have mass M=pM1+(1−p)M2. The equations of motion of these normal coordinates are derived and are then solved by Laplace transform methods. The perturbed normal coordinates are found to decay exponentially into the future and into the past until an inverse power dependence on time becomes dominant. Calculations of the mean lifetime and frequency shift of each normal coordinate are carried out for the one-dimensional case. A theory of the optical absorption spectrum of an isotopically disordered ionic crystal is obtained, and the distribution function for the energies of the normal modes and the mean energy in a normal mode are found. The generalization of the methods of this paper to three-dimensional lattices is discussed.
Statistical Dynamics of Simple Cubic Lattices. Model for the Study of Brownian Motion. II
Authors: Rubin Robert J.
Published: January 2005

New results concerning the statistical dynamics of a heavy particle in an n-dimensional (nD) cubic lattice are presented. It is demonstrated that this model exhibits many properties which are familiar in the phenomenological theory of Brownian motion. In a well-defined sense, the random thermal motions of a heavy particle in a 1D lattice and a 3D lattice are accurately described by Kramers' equation for a free particle and a harmonically bound particle, respectively. A related, but not independent, result is that the velocity v(t) and position u(t) of a heavy particle in a 1D lattice and a 3D lattice constitute two-dimensional stationary Gaussian Markoff processes. It is definitely established that in the case of a 2D lattice the stationary Gaussian process {v(t),u(t)} is non-Markoffian. In the course of the analysis, several interesting connections between solutions of the discrete lattice equations of motion and solutions of the corresponding continuum equation of motion (the nD wave equation) are uncovered.