bluuebunny/crossref_metadata_2025 huggingface dataset:
Exact Statistical Mechanics of a One-Dimensional System with Coulomb Forces. II. The Method of Functional Integration
Authors: Edwards S. F. , Lenard A.
Published: January 2005

The statistical mechanics of a one-dimensional system of charged sheets is studied in the formalism of the grand canonical ensemble. It is shown that the grand partition function may be expressed as a Wiener integral, i. e., as an average of a certain functional of Brownian motion paths. This functional integral is then expressed in terms of the fundamental solution of a partial differential equation of diffusion type. This depends on a theorem of Kac whose proof is also given. The generality of this method is discussed. When all charges are integral multiples of a common unit the problem is reduced to the determination of the largest characteristic value of an ordinary differential operator with periodic coefficients. An invariance property of the thermodynamic potential is shown to imply charge neutrality in the infinite system limit. A theorem is proven which, in certain cases, excludes the possibility of a thermodynamic phase transition. The method is generalized to yield exact expressions for the n-particle reduced density functions. Some properties of the two-particle functions are discussed.
Structure of a Bloch Wall
Authors: Muller M. W. , Dawson S.
Published: January 2005

The standard form of a domain wall in a ferromagnetic medium is the result of a one-dimensional variational principle and is valid only for an unbounded medium. In a bounded ferromagnetic body two- or three-dimensional dipolar fields arise wherever a Bloch wall meets a surface of the body, and the form of the wall is distorted by these fields. If the fields and the corresponding distortions are small, they can be calculated approximately. We carry out the calculation for 180° walls in a ferromagnetic film with uniaxial anisotropy, and with the easy axis of magnetization either parallel or perpendicular to the surfaces of the film. Numerical results are not obtained but formulas are presented ready for evaluation.
Exact Solution for the Vibrations of a Nonlinear Continuous Model String
Authors: Zabusky Norman J.
Published: January 2005

An exact solution is given for the partial differential equationytt=[1+εyx]αyxx,which describes the standing vibrations of a finite, continuous, and nonlinear string. The nonlinearity studied, [1 + εyx]α, was motivated by the work of Fermi, Pasta, and Ulam (1955), where they reported on numerical studies of the ``equipartition of energy'' in nonlinear systems. To obtain the solution, the above equation is transformed into a linear equation by inverting the roles of the dependent (u = yx and v = yt) and independent (x and t) variables. Riemann's method of integration is applied to the problem and the solutions for t and x are written as integrals. The nature of the ``inverse Riemann plane,'' how it is related to the initial conditions, and how one unfolds it, are discussed in detail. A general procedure is described for reinverting the solution, so that y can be written as a function of x and t. It is illustrated to order ε for the above problem. It is demonstrated that yxx becomes singular, that is, yx develops a discontinuity after an elapsed time or order (1/ε). The methods described are applicable to any nonlinear string where the coefficient of yxx is a function of yx only. The effect of higher spatial derivatives on the formation of the singularity is discussed.
Proof of a Conjecture by Dyson
Authors: Wilson Kenneth G.
Published: January 2005

We prove a mathematical conjecture by Dyson which he used in a study of the statistical distribution of energy levels in complex nuclei.
Analytic Functions of Continuant Matrices
Authors: Abraham Phillip B. , Weiss George H.
Published: January 2005

It is shown that the Fourier method which was developed by us for the calculation of analytic functions of circulant matrices can also be applied to calculate analytic functions of continuant matrices. Similar calculations are developed for generalized continuant matrices which arise in connection with problems in greater than one dimension.
On Feynman Quantization
Authors: Schweber S. S.
Published: January 2005

The observation by Klauder that in the space of the a = (1/√2) (p + iq) variables, the Feynman integral can be defined in terms of a Gaussian measure, forms the basis of a presentation of the Feynman formulation of nonrelativistic quantum mechanics. The extension of this formulation to the case of a Bose field is sketched.
Dynamical Mappings of Density Operators in Quantum Mechanics. II. Time Dependent Mappings
Authors: Jordan Thomas F. , Pinsky Mark A. , Sudarshan E. C. G.
Published: January 2005

The most general continuous time-dependent evolution of a physical system is represented by a continuous one-parameter semi-group of linear mappings of density operators to density operators. It is shown that if these dynamical mappings form a group they can be represented by a group of unitary operators on the Hilbert space of state vectors. This proof does not assume that the absolute values of inner products of state vectors or ``transition probabilities'' are preserved but deduces this fact from the requirement that density operators are mapped linearly to density operators. An example is given of a continuous one-parameter semi-group of dynamical mappings which is not a group.
The Primitive Domains of Holomorphy for the 4 and 5 Point Wightman Functions
Authors: Manoharan A. C.
Published: January 2005

A method is given for estimating the dimensions of different types of boundary surfaces which are relevant for the domains of holomorphy, without using local commutativity, of the 4 and 5 point Wightman functions in scalar product space. The procedure is a straightforward application of the explicit parametrization given by Källén and Wightman for vectors on the boundary. The DANAD and other hypersurfaces for the 4 point function are deduced. For the 5 point function, in addition to generalizations of hypersurfaces corresponding to lower point functions, a new type of hypersurface appears which can be denoted in a matrix form Z = DUMUD but not in the form Z = DANAD.
Heisenberg Fields which Vanish on Domains of Momentum Space
Authors: Greenberg O. W.
Published: January 2005

If a local Heisenberg field vanishes, or where appropriate has an infinite zero, on one of the momentum space domains A, p2 = —a2; B, 0 ≤ p2 < m2, and p = 0; or C, p2 > M2, then the field is a generalized free field. Counter examples show that this conclusion cannot be drawn if the field vanishes on the momentum space domains D, 0 ≤ M12 < p2 < M22, p ≠ 0; or E, p = 0. It follows that if two fields in the same Borchers class are equal on one of the domains A, B, or C, then the fields differ at most by a generalized free field in their Borchers class.
Complex Angular Momenta in Potential Scattering
Authors: Froissart Marcel
Published: January 2005

The S matrix associated with a central potential is shown to be meromorphic in the energy and angular momentum variables under very broad conditions. The domain of meromorphy contains the product of a domain in the energy variable by a domain in the angular variable. The former (latter) domain has a very simple connection with the domain of meromorphy of the Laplace (Mellin) transform of the potential with respect to the radius.
Asymptotic Properties of the Wave Function for a Bound Nonrelativistic Three-Body System
Authors: Slaggie E. Leo , Wichmann Eyvind H.
Published: January 2005

The asymptotic properties of a Schrödinger wave function which represents the bound ground state of a system of three interacting particles are examined. It is assumed that the interaction can be described by a static potential which is the sum of three two-body potentials and one three-body potential, where the potentials have the property that if any one of the particles is separated from the other two by a distance which tends to infinity, then the part of the potential energy which depends on the position of that particle tends to zero. The problem is treated nonrelativistically. Decreasing exponential bounds on the ground-state three-body wave function are established in configuration space. It is shown that these bounds depend only on the masses of the three particles, on the ground-state energy of the three-body system, and on the lower bounds on the spectra of the Hamiltonians for the three two-body systems arising when one of the three particles is removed and the remaining two interact through the corresponding two-body potential.

It is furthermore shown that the three-body wave function in momentum space admits of analytic continuation into a tube-region in complex momentum space, which tube-region is the product of real momentum space and a convex bounded region in imaginary momentum space. The tube-region is explicitly determined.

The implications of the results for the theory of the vertex function in quantum field theory are discussed. The relevancy of the results obtained in this paper to the variational computation of energy levels and wave functions of three-body systems is also briefly discussed.

In the course of the derivation some generalizations are pointed out; in particular, the final results remain valid for a class of more general interactions, which cannot be described by static potentials. Likewise, the results remain valid for a class of spin-dependent interactions.
Charged Spheroid in Cylinder
Authors: Smythe W. R.
Published: January 2005

The problem of a charged conducting spheroid within a coaxial conducting cylinder is solved by a slight variation of the method in J. Appl. Phys. 31, 553 (1960). Errors in the terminal digits of Table I in that paper have been corrected and the table extended. The charge density on the spheroid, the potential between it and the cylinder, and its capacitance are given for ratios of the spheroid equatorial radius to cylinder radius of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 0.95. Tables give numerical results for five cases: the disk, the oblate spheroid with 2 to 1 axial ratio, the sphere, and the prolate spheroid with axial ratio 1 to 2. The thin prolate spheroid requires special treatment.
Dielectric Constants of Liquefied Noble Gases and Methane
Authors: Amey Ralph L. , Cole Robert H.
Published: January 2005

Dielectric constants of argon, krypton, xenon, and methane have been measured in the liquid and in the solid near the melting point. Values of the derived Clausius—Mossotti function are in all cases less than for the gas, indicating a decreased effective polarizability attributed to overlap effects.
Determination of Nuclear Quadrupole Coupling Constants from Nuclear Magnetic Resonances in Polycrystalline Solids
Authors: Casabella P. A.
Published: January 2005

The line shape of a nuclear magnetic resonance in a polycrystalline solid under the influence of an axially symmetric second-order nuclear quadrupole perturbation has been calculated for 20 values of the quadrupole coupling constant. From these calculations the frequency difference between the peaks in the derivative of the resonance line has been found as a function of the quadrupole coupling constant. This relationship has been shown to be useful in two cases. First, a procedure is described for determining the quadrupole coupling constant by studying the resonance as a function of magnetic field, when it is known that the electric-field-gradient asymmetry parameter is zero. Second, when both first- and second-order quadrupole effects can be observed in a polycrystalline solid, a method is described for determining both the quadrupole coupling constant and the electric field gradient asymmetry parameter for small values of the asymmetry parameter.
Optical Rotation of Oriented Helices. IV. A Free Electron on a Helix
Authors: Tinoco Ignacio , Woody Robert W.
Published: January 2005

The absorption and rotation of light is derived for a free electron constrained to move on a helix. This model is probably the simplest optically active system for which exact wavefunctions can be obtained. It is found that a randomly oriented right-handed helix has a positive rotational strength for the longest wavelength absorption band. As expected, this free electron model gives results very similar to an exciton model in which only nearest-neighbor interactions are considered.
Infrared Absorption of the v3 Fundamental of Liquid and Solid CH4 and CD4
Authors: Ewing George E.
Published: January 2005

The v3 fundamental of CH4, CD4, and solutions of CD4 in CH4 has been studied in the liquid and solid state from 105° to 28°K. The broad liquid-state absorption approximates the gas-phase vibration—rotation envelope in the wings, but has significantly more absorption at the band center. This deviation is consistent with the assumption that molecules in the liquid can undergo hindered rotation. One consequence of this model is that rotatory motion of molecules is in part librational in character and selection rules predict an intense Q branch and weaker P, R, S, and O branches. Another consequence is that the liquid environment may induce molecular dipoles causing Raman selection rules to be operative which contribute further to an intensification of the Q branch. The bandwidth decreases gradually with temperature but undergoes no discernable discontinuous change on passing through the freezing point, which suggests that rotatory motion persists in this solid phase. The bandwidth of the fundamental of liquid and solid CD4 is narrower than CH4 but behaves in a similar fashion with temperature. The band shape and position of v3 of CD4 in solution with CH4 is indistinguishable from that of pure liquid CD4, and suggests that resonance broadening or coupling of rotatory motion is not important for this phase. In the solid state, however, the v3 bandwidth of CD4 in the CD4—CH4 solution is slightly larger than the v3 bandwidth of pure CD4.
Vapor Pressures of Zinc Chloride and Zinc Bromide and Their Gaseous Dimerization
Authors: Keneshea F. J. , Cubicciotti Daniel
Published: January 2005

The absolute vapor pressures of zinc chloride and zinc bromide have been measured by a quasistatic method. In addition, transpiration experiments have been made to determine the vapor density of the gas. Mass spectrometric observations of the gas over the liquid salts have indicated that the gas consists mainly of zinc halide monomer with some dimer also present. The individual partial pressures of the zinc halide monomers and dimers calculated from the results of the pressure and density measurements can be represented by the equation logp(mm)=(−A/T)−BlogT+C.Constants A, B, and C are: for zinc chloride monomer, 8415.2, 5.034, 26.420, respectively; for dimer, 4698.8, 0, 5.891; for zinc bromide monomer 7784.5, 5.034, 26.112; and for dimer 5612.5, 0, 7.915. The various thermodynamic functions have also been calculated and are discussed. The zinc halides are unique among salts that have polymeric gaseous species in that the heat of vaporization of the monomer is greater than the heat of vaporization of the dimer whereas the monomer is the predominant species in the temperature range investigated.
Sudden Approximation Applied to Rotational Excitation of Molecules by Atoms. I. Low-Angle Scattering
Authors: Kramer K. H. , Bernstein R. B.
Published: January 2005

The sudden approximation is applied to the calculation of transition probabilities and cross sections for rotational excitation and scattering of homonuclear diatomic molecules by atoms. The present analysis is restricted to a consideration of the influence of the anisotropy and strength of the long-range attractive part of the interaction potential on the scattering at low angles. Nevertheless, the results illustrate the main features of the method applied to inelastic molecular collisions in general, and demonstrate its advantage over the first-order perturbation approximation. Measurements of low-angle differential inelastic scattering cross sections would yield directly the anisotropy of the long-range attractive potential.
Electronic Energy of the Hydrogen Molecule Ground State by the Local-Energy Method
Authors: Harriss D. K. , Frost A. A.
Published: January 2005

The least-squares local-energy method is applied to the hydrogen molecule in greater detail. Equations are given for the Hamiltonian operator and local energy for diatomic molecules in the mixed interelectronic-confocal elliptic coordinate system. Wavefunctions with up to 22 terms and larger numbers of points are considered and it is shown that both lead to values for the dissociation energy that are within ±0.0001 hartrees of the exact value, 0.1744 hartrees.
ESR Study of Ethynyl and Vinyl Free Radicals
Authors: Cochran Edward L. , Adrian Frank J. , Bowers Vernon A.
Published: January 2005

ESR spectra have been observed for ethynyl (C≡CH) and vinyl (HC=CH2) radicals trapped in solid argon at liquid-helium temperatures. Ethynyl radical was obtained by the photolytic decomposition of acetylene. Its ESR spectrum consisted of two narrow lines corresponding to a proton hyperfine splitting of 16.1 Oe. The assignment of this spectrum to ethynyl was confirmed by a study of the photolysis of deuteroacetylene. Hydrogen atoms were not observed in the acetylene—argon photolytic system, suggesting that this photolysis is a second-order process involving two molecules of acetylene. Vinyl radical was obtained by the addition of an H atom, obtained from the photolysis of HI, to acetylene. The ESR spectrum of the vinyl radical consisted of eight broad overlapping lines resulting from the interaction of the unpaired electron with three nonequivalent protons. Addition of an H atom to deuteroacetylene at 4.2°K gave only one of the two possible structural isomers of the 1,2 dideuterovinyl radical. The ESR spectrum of this radical showed that the largest of the proton hyperfine splittings in vinyl is due to a β proton. With the aid of theory the observed hyperfine splittings were assigned to the vinyl protons as follows: Atrans,β=68 Oe, Acis,β=34 Oe, and Aα=16 Oe, where the designations cis and trans refer to the relative positions of the β proton and the unpaired electron orbital. A theoretical treatment of the α proton splitting in vinyl and similar radicals provided a qualitative explanation of the marked difference between the α proton hyperfine splittings in the vinyl and formyl radicals.
On the Magnetic Susceptibility of Xenon Tetrafluoride
Authors: Boudreaux Edward A.
Published: January 2005

The magnetic susceptibility of XeF4 has been treated theoretically in the LCAO—MO approximation with particular emphasis placed on the calculation of the high-frequency elements in the paramagnetic part of the susceptibility. The results are in good agreement with a recently observed susceptibility value and suggests that a previously proposed MO scheme is consistent in accounting for the magnetic properties of the molecule. A small ring current has also been calculated, thus substantiating the delocalized MO description advanced by other investigators.
Paramagnetic Resonance Spectrum of MnCl2 in Molten Alkali Halides
Authors: Yarmus Leonard , Kukk Maret , Sundheim Benson Ross
Published: January 2005

Paramagnetic resonance data is presented for the systems MnCl2 in KCl, in LiCl, and in the LiCl/KCl eutectic over a broad temperature range (25° to 900°C), and a composition range from pure MnCl2 to 0.005M solutions. In the molten state hyperfine structure is observed at dilutions of 0.06M and below, whereas at higher concentrations only a single broad line is seen. The transition concentration (from hyperfine to no hyperfine splitting visible) is almost two orders of magnitude lower than the corresponding transition for aqueous manganese solutions. A preliminary discussion is given in terms of Anderson's theory.
Ion—Molecule Reactions in Methane and in Ethane
Authors: Derwish G. A. W. , Galli A. , Giardini-Guidoni A. , Volpi G. G.
Published: January 2005

Ion—molecule reactions in methane, in methane—methane-d4 mixture, and in ethane have been studied up to a pressure of 0.08 Torr in the ion source of the mass spectrometer.

Ionization-efficiency curves, appearance potentials, and pressure-dependence studies have allowed the parent—daughter ion relationship and the cross sections of the pertinent reactions to be determined.
Electric Conduction in Liquid Hydrocarbons. III. Comparison of Saturated and Unsaturated Hydrocarbons
Authors: Forster E. O.
Published: January 2005

The electric conductance of aliphatic and olefinic type hydrocarbons has been determined between 25° and 65°C. both in the presence and absence of oxygen using electric fields of 50 to 1200 V/cm. Based on the observed potential distribution, the thermal activation energies, and the conductivities, it was concluded that conduction processes of the two types of compounds are distinctly different. The conduction in aliphatic hydrocarbons appears to be attributable to the presence of very low concentrations of polar impurities. Olefinic-type hydrocarbons were found to have higher conductivities as structurally similar aliphatic compounds. Also, their thermal activation energies were consistently higher than those obtained for aliphatic compounds. This difference in behavior has been attributed to the presence of π electrons in the olefinic hydrocarbons. It is suggested that the conduction in unsaturated hydrocarbons involves an electron jumping process which is independent of the presence of trace impurities and is unavailable to saturated substances.
Influence of Atomic Masses on the Coriolis Coupling Coefficients in Some Symmetrical Molecules. I. Tetrahedral XY4-Type Molecules
Authors: Cyvin S. J. , Brunvoll J. , Cyvin B. N. , Kristiansen L. A. , Meisingseth E.
Published: January 2005

Coriolis coupling coefficients (ζ values of tetrahedral XY4 molecules are studied in relation to the same quantities of the Z4 tetrahedron. The existence of upper and lower limits is proved for the ζ values of XY4. In particular, one has |ζ24|→1/2 and ζ44→1/2 as the upper limits with increasing atomic mass ratio mY/mX. The same values, which are independent of the force constants, are found in the Z4 model, where the central atom is absent. Lower limits are also derived for |ζ24| and ζ44, but appear to be functions of the force constants.

Calculated ζ24 and ζ44 values for 36 molecules of the tetrahedral XY4 type are reported, and are studied as function of the atomic mass ratio. The regularities that have been observed are presented graphically.

Carbon tetrahalides, methanes, and silanes are the molecules which have been studied most extensively, and for which the applied force constants are reported.
Ionic Paramagnetic Species Associated with γ-Irradiated Amyl Disulfide
Authors: Truby Frank K.
Published: January 2005

ESR and optical bleaching studies of n-amyl disulfide, γ-irradiated at 77°K in the amorphous state indicate the presence of ionic paramagnetic species in the irradiated material involving unpaired spins localized mainly at the sulfur. A comparison of ESR derivative peak positions from such samples with those arising from an apparent negative ion species produced from amyl disulfide in a tetrahydrofuran matrix indicates that this species may be common to both types of samples. This finding is supported by the fact that the threshold energy for the destruction of the ionic centers by optical bleaching is the same for both types of samples, being 2.1±0.2 eV. If the ESR spectrum of the negative-ion species is substracted from the initial ionic species spectrum of amorphous amyl disulfide an ESR line shape is obtained which is postulated to result from a positive-ion species. The principal g values obtained for this species are 2.003±0.001, 2.035±0.001, and approximately 2.018. Calculated g values based on a model in which the electron hole is localized on a nonbonding 3p sulfur orbital are in qualitative agreement with the observed g values. The The negative-ion species appearing to be common to both types of samples exhibits an axially symmetric g tensor (g‖ = 2.003±0.001, g⊥ = 2.022±0.001). This g tensor symmetry is obtained theoretically using a model in which the unpaired spin is in 3dσ bonding orbitals associated with both sulfurs.
Polyhedral Clathrate Hydrates. VII. Structure of the Monoclinic Form of the Tri-n-Butyl Sulfonium Fluoride Hydrate
Authors: Beurskens P. T. , Jeffrey G. A.
Published: January 2005

The monoclinic form of the clathrate hydrate of (n-C4H9)3S+F— has 23 H2O per guest cation, as determined by a complete three-dimensional crystal-structure analysis.

The water framework consists of sheets of face-sharing pentagonal dodecahedra, separated by layers of hydrogen-bonded water molecules and anions containing large and irregular cavities in which the sulfonium ions are located. These cations are pyramidal in configuration and occupy the large cavities in pairs, with a S+–S+ nearest-neighbor distance of 3.49 Å.
Self-Consistent Field Calculation of the Ground State of Methane
Authors: Woznick Benjamin J.
Published: January 2005

Ground-state wavefunctions for CH4 have been calculated using the self-consistent molecular orbital method of Roothaan. The molecular orbitals have been represented by linear combinations of atomic exponential orbital functions. The size of the basis set has been varied over wide limits; total energies, wave-functions, and one-electron energies are given for these cases.
Collision Cross Sections for Oxygen in the Excitation Energy Range 10 to 80 V
Authors: Silverman S. M. , Lassettre Edwin N.
Published: January 2005

Inelastic, electronic, collision cross section for the scattering of electrons of approximately 500-V kinetic energy have been determined over the excitation energy range 10 to 80 V. Generalized oscillator strengths are calculated from the results and used to test the oscillator sum rule. Extrapolated oscillator strengths are compared with those calculated from ultraviolet absorption coefficients.
Thermally Stimulated Currents and Carrier Trapping in Anthracene Crystals
Authors: Kokado H. , Schneider W. G.
Published: January 2005

Thermally stimulated currents in anthracene single crystals have been investigated. A fairly large current peak observed at a temperature near 0°C, is shown to be characteristic of anthracene and corresponds to a carrier trap level of depth 0.76±0.05 eV. The effects of temperature, applied voltage, and the time of illumination with uv light on trap filling were investigated. Illumination at low temperatures, with or without an applied field, generates charge carriers which are localized in the crystal. Below —60°C the rate of carrier release and/or recombination appears negligibly small, permitting charge storage for indefinitely long periods of time. In addition to thermal detrapping, it was found that carrier detrapping could also be brought about by optical radiation with wavelengths in the visible and near infrared region. The resulting optically stimulated currents depended linearly on the intensity of the long wavelength light. The results suggest that on uv illumination at low temperatures ion pairs are generated at dissociation centers, the electron being deeply trapped by the center. The liberated holes (majority carriers) are partially mobile at low temperatures and are eventually localized in traps. The observed thermally stimulated currents are attributed to thermal release of the majority carriers.
Electrical Properties of the Cerium and Gadolinium Hydrogen Systems
Authors: Heckman Richard C.
Published: January 2005

Conductivities of polycrystalline solid samples of cerium hydride and gadolinium hydride were measured over the composition ranges H/Ce=0–2.5 and H/Gd=0–2.13 at room temperature and at elevated temperatures (400°—750°C). Conduction is metallic and the results for the two systems are very similar. The conductivity in the variable composition dihydride phase of each system decreases with increasing hydrogen content and is explained assuming that the hydrogen is anionic, taking its extra electron from the system's conduction band. Measurements of absolute Seebeck coefficients (CeH2.37, —17 μV/°C; GdH2.12, —6 μV/°C) support this model. The measured conductivity curves extrapolate to zero at CeH2.7 and GdH2.3. For the dihydride phases the composition dependencies of the conductivities are used to calculate carrier mobilities. The values obtained are in the range 1 to 10 cm2/V-sec. The conductivities of compositions H/M=0 to 2 show that the dihydrides can exist with hydrogen-to-metal ratios much less than 2.0. Ionic conduction has been found not to be important to the conduction mechanism from the results of a concentration cell measurement.
ESR Studies of Irradiated Alkali Borate Glasses with High Alkali Oxide Content
Authors: Lee Sook , Bray P. J.
Published: January 2005

Electron spin resonance (ESR) studies have been made of γ-ray irradiated alkali borate glasses containing more than approximately 25 molar % alkali oxide. The alkali borate glasses (Li2O—, Na2O—, K2O—, Rb2O—, and Cs2O–B2O3) exposed to a γ-ray dose of 1×108 R display ESR spectra which are partially resolved into four major absorption lines at both X- and K- band microwave frequencies. Details of this four-line resonance have been found to depend on the particular alkali oxide used in making the glass. When the glass sample was enriched with the 10B isotope, the observed spectrum exhibited a seven-line resonance instead of four absorption lines. It is concluded that the four- and seven-line structures arise from an isotropic hyperfine interaction of a hole with the 11B and 10B nuclei, respectively. The atom containing the 11B or 10B nucleus is believed to be in a tetrahedral BO4 configuration in the glass structure.
Viscosity of Argon—Ammonia Mixtures
Authors: Iwasaki H. , Kestin J. , Nagashima A.
Published: January 2005

The paper reports a series of measurements of the viscosity of argon—ammonia mixtures at 20° and 30°C over a pressure range from atmospheric to 25 atm. The method used was an absolute one, based on the oscillating-disk principle. The precision of the measurement varied from 0.2% for argon-rich to 1.5% for ammonia-rich mixtures, the largest source of error being that of the determination of composition. In spite of the fact that one component is polar, the viscosity defect is small, the mixture behaving nearly perfectly with respect to viscosity. However, the density effect on the viscosity of ammonia and ammonia-rich mixtures has turned out to be negative.
Nuclear Magnetic Resonance Spectrum of 11B and B–Si Order in Danburite, CaB2Si2O8
Authors: Brun E. , Ghose Subrata
Published: January 2005

The nuclear magnetic resonance spectrum of 11B in danburite, CaB2Si2O8, structurally closely related to the feldspars, has been investigated. Boron occupies a single crystallographically unique site. Thermal experiments indicate that B–Si order persists up to the decomposition temperature (∼1000°C). The quadrupole coupling constant and the asymmetry parameter of the electric field gradient tensor are: eQVzz/h412±4 kc/secη0.45.The orientation of the principal axes of the electric field gradient tensor has also been determined.
Anomalously High Specific Rates of Diffusion-Controlled Reactions: Luminescence Quenching in Liquid Systems
Authors: Mullin C. R. , Dillon M. A. , Burton Milton
Published: January 2005

Quenching constants (γs′) and specific rates of quenching (kq) of uv- and high-energy sensitized luminescence by carbon tetrachloride in de-aerated solutions of p-terphenyl in benzene and in cyclohexane are given. Values for kq in benzene ranging as high as 3.6×1010M—1 sec—1 appear, in first approximation, to be quantitatively explicable on the basis of current theoretical treatment. However, the cyclohexane results (kq>3×1011M—1 sec—1) are clearly anomalously high and are not suggested by current theory; some speculation as to the cause of such results is included.
Calculation of Heat Capacities and Compressibilities of Liquids from a Rigid Sphere Equation of State
Authors: Yosim S. J.
Published: January 2005

Equations for heat capacities and compressibilities of liquids were calculated by differentiation of the expression for the entropy of a fluid of rigid spheres. The resulting equations contain no adjustable parameters. The information required in addition to the heat capacity and compressibility of the gas, is the diameter of the molecule, the liquid density and its variation with temperature. The equations were applied to the rare gases and to diatomic and polyatomic molecules at their boiling points. Agreement between the calculated and observed values was with few exceptions very good. Further, the calculated temperature dependence showed good agreement with experimental values.
Nuclear Free Precession in Very Low Magnetic Fields
Authors: Thompson Don D. , Brown Robert J. S. , Bloom Myer
Published: January 2005

Nuclear free-precession signals from two isotropically coupled, spin-½ nuclei are calculated for very weak fields. The density matrix is used to calculate signal frequencies and voltages and the results are compared to experiments using HPO(OH)2. Signals were observed in fields as low as 8×10—3 G. Perpendicular transitions in fields |Hf|≪J/γI may be used to measure field strength accurately. The parallel transition was found to have no first-order magnetic field dependence as predicted and was observed in near zero field. Possible laboratory applications are discussed briefly.
Vibrational Frequency Sum Rules for Distorted Complexes
Authors: Englman Robert
Published: January 2005

The calculation of thermodynamic quantities that involve the change of frequencies due to distortion of octahedral complexes can be effectively simplified by calculating the mean frequency change within a vibrational type, rather than the change in each component individually. On the average each stretching mode frequency changes by the same amount, each bending mode frequency changes by the same amount, while the mixed mode frequencies change by amounts that depend on the percentages of stretching and bending motions in the mode.
Resolution Enhancement for Spectra of Chemical and Physical Interest
Authors: Allen Leland C. , Gladney H. M. , Glarum S. H.
Published: January 2005

When a spectrum is composed of a superposition of lines with known shape and uniform width, the signal output of a spectrometer may be transformed into a spectrum whose effective resolution is significantly improved. If the line shapes are not precisely known or the linewidths not exactly uniform, it is still possible to achieve a worthwhile resolution enhancement. Decomposition and analysis of complex spectra is often aided by this transformation. The theory of filters which produce the desired transformation is developed. Digital and analog implementation for these filters is given as well as several examples.
Theory of Adsorption of the Isotopic Hydrogen Molecules at Low Temperatures
Authors: Katorski A. , White David
Published: January 2005

A theory of adsorption of the isotopic hydrogen molecules is developed where the potential of interaction of the adsorbed molecule with the plane surface is a function of two parameters. The Schrödinger equation is solved for the rotation—vibrational energy levels of the diatomic molecules in the adsorbed state. From these energy levels, isotopic and ortho—para separation factors and heats of adsorption are calculated by statistical thermodynamics. There is a reasonable correspondence between experimental separation factors and heats of adsorption derived from chromatographic experiments, and those computed from the theory for selected values of the potential parameters. The sequence of relative volatilities of the hydrogen isotopes and ortho—para species found experimentally is in accord with that predicted from the theory. Both the separation factors relative to para hydrogen and the heats of adsorption increase in the order; o-H2, HD, HT, o-D2, p-D2, DT, p-T2, and o-T2.
Radial Distribution Functions from a Linear Integral Equation
Authors: Porter Richard A.
Published: January 2005

A linear integral equation derived by Mayer for the radial distribution function of fluids has been investigated numerically. To compare with other recent investigations of integral equations, a Lennard-Jones 6–12 potential was used and the 55°C isotherm of argon investigated. Results for the pressure and the radial distribution function are less satisfactory than are obtained with other integral equations. An estimate of the validity of Kirkwood's superposition approximation in the range of the calculation was also made.
Dielectric Polarizability of Fluid Para-Hydrogen
Authors: Stewart John W.
Published: January 2005

The dielectric constant of liquid and gaseous para-hydrogen has been measured by the capacitance ratio method between 24°—100°K and 2–326 atm. This encompasses the density range 0.002–0.080 g/cm3. These data have been combined with recently available PVT results in order to calculate the Clausius—Mossotti (CM) function to 0.05% precision. In the range considered, the CM function, or polarizability, instead of being constant, initially rises with density to a maximum 0.2% above the low density value of 1.00427 cm3/g, and then falls. The data in this range can be represented within experimental error by a quadratic function of density. The deviation from constancy is too small for detailed correlation with existing theories of polarizability to be feasible. The results are presented in tabular form. Also the dielectric constant at any desired density can easily be calculated to an accuracy better than 0.1% in ε—1 from the function fitting the polarizability.
Mobile Bond Orders of Some Polyphenyls from SCF—LCAO—MO Theory
Authors: Kwun Sook-Il , Ree Taikyue , Eyring Henry
Published: January 2005

For the present calculation of the mobile bond orders of para-quaterphenyl and meta-terphenyl molecules, Pople's simplified SCF—LCAO—MO theory for unsaturated hydrocarbon molecules in their ground states is utilized. The symmetry orbitals for these molecules are formulated in order to simplify the calculations by the use of group theory. The symmetry properties of these molecules and the pairing properties of the molecular orbitals are discussed. Planar configurations of both molecules are assumed as a first approximation. The unreasonable mobile bond orders calculated from the Hückel MO theory are improved in the present calculations. The results are discussed in connection with the recent experimental values of the bond lengths of biphenyl.
Space Charge in Growing Oxide Films. IV. Rate Effects Deduced by an Averaging Technique
Authors: Fromhold A. T.
Published: January 2005

An analysis of nondiffusing and diffusing space-charge effects in growing oxide films using simple models provides justification for the equation L(t)2=L∞2[1−exp(−t/τ)] as a first approximation for describing film growth, where L(t) is the film thickness and t is the time of oxidation. The limiting film thickness squared L∞2 and the pseudo rise-time τ are functions of the space-charge concentration and are temperature-dependent, increasing linearly with temperature for most cases. Space-charge effects for a given defect concentration are predicted to be more important at low temperatures; growth tends to become parabolic at higher temperatures.
Theory of the Dependence of Nuclear Magnetic Relaxation on the Absolute Sign of Spin—Spin Coupling Constant
Authors: Shimizu Hiroshi
Published: January 2005

It is theoretically shown that the nuclear relaxation times and the saturation parameter of each component line of two-spin spectrum depend on the sign of the spin—spin coupling constant J. Then it is suggested that the absolute sign of J can be determined through measurement of the relaxation times or saturation parameters. The experimental conditions are discussed taking two-spin systems of 13C–1H, 13C–19F, 1H–19F, and 1H–31P as examples.
Microwave Spectrum of NO2: Fine Structure and Magnetic Coupling
Authors: Bird George R. , Baird James C. , Jache Albert W. , Hodgeson Jimmie A. , Curl R. F. , Kunkle Albert C. , Bransford James W. , Rastrup-Andersen John , Rosenthal Jack
Published: January 2005

Some 69 microwave absorption lines from three isotopic modifications of NO2 have been observed and identified. This spectrum has been completely analyzed in terms of moments of inertia, magnetic fine structure, and centrifugal distortion. The early stages of analysis were complicated by the existence of many mathematical solutions satisfying all of the data then available, but special methods have been developed for treating limited data and selecting the one solution giving the true molecular parameters.

The results obtained for 14N16O2 are: Rotational constantsA=239 868.7±11 Mc/secB= 13 000.12±0.6 Mc/secC= 12 303.45±0.6 Mc/secOdd electron expectation values with respect to〈(3r̂a2−1)/2r3〉=−1.73×1024cm−3N−nucleus〈(r̂b−ir̂c)2/r3〉=+3.34×1024cm−3|ψ(0)|2=+3.065×1024cm−3Reduced spin−rotation coupling constantsεaa/A=+0.022563εbb/B=+0.000608εcc/C=−0.007764Force constants from combined microwave−infrared datafd=11.043±0.05  mydn/Åfα= 1.109±0.01fdd=0.481±0.014fdα=2.140±0.05.The magnetic coupling constants are discussed in terms of a simplified electronic structure. The agreement between this structure and the experimental parameters is incomplete, but surprisingly good.

Approximate values for the 14N quadrupole coupling constants are obtained.
Van der Waals Forces between Quartz and n-Heptane
Authors: Wade W. H. , Slutsky L. J.
Published: January 2005

The room temperature adsorption isotherm of n-heptane on an AT-cut quartz crystal has been measured in the region of very high coverages (six to 15 monolayers). The isotherm in this region may be represented by the equation lnP=C+Δψ/kTd3, where Δψ/d3, is interpreted as the difference between the potential energy of a heptane molecule at a distance d from a quartz surface and that of a heptane molecule at the same distance from a liquid heptane surface. A value of Δψ/kT of 725 Å3 is obtained.
Variational Calculation of the Optical Activity of 3-Methylcyclopentanone (One-Electron Theory)
Authors: Watanabe Tadashi , Eyring Henry
Published: January 2005

The variational principle is applied to the one-electron theory of optical rotation of 3-methylcyclopentanone. The numerical results are compared with the results obtained by Kauzmann, Walter, and Eyring. The variational method is better than the perturbation theory for the visible, where many excited states make appreciable contributions, since suitable eigenfunctions for excited states are hard to come by. The procedures employed should be widely applicable.
Electronic Energy Levels of the Lighter Actinides: U3+, Np3+, Pu3+, Am3+, and Cm3+
Authors: Carnall W. T. , Wybourne B. G.
Published: January 2005

The results of a systematic theoretical and experimental study of the energy levels of the lighter actinides, U3+ through to Cm3+, in various solution media is reported. Calculations of the ``free-ion'' levels have been made for all these ions and compared with the observed absorption bands. A clear correspondence is found for most of the lower levels. The actinides have been found to show very large departures from Russell—Saunders coupling with spin—orbit constants approximately twice those of the corresponding lanthanides. A pronounced tendency towards jj coupling is noted and its consequences discussed.
Stark Effects on the Nuclear Quadrupole Coupling of 35Cl in Sodium Chlorate
Authors: Collins F. A. , Bloembergen N.
Published: January 2005

The changes in the electric-field-gradient tensor q induced by an applied electric field E and stress δ are described by the relation e(Δq)ij=RkijσEk+Tijlmσlm. The magnitudes and absolute signs of the five independent components of Rσ for 35Cl in NaClO3 were measured at 77°K and related to the absolute atomic configuration of the crystal. The numerical values are in units of 109 cm—1, R111σ = —0.42, R222σ = —2.43, R333σ = —2.22, R113σ = —1.53, and R123σ = +3.53, with respect to the following coordinate system at a Cl site. The positive x3 axis points from Na+ to ClO3—, i.e., towards the [111] direction that develops a positive piezoelectric charge for a tension σ33. The positive x1 axis passes through an oxygen site and x2 completes the right-handed set in the plane of the oxygen triangle. The electric field effects at constant stress and at constant strain are nearly equal. They are attributed to variations in the electron orbitals of the chlorate group and to changes in the ionic lattice sums outside this group.
Molecular Motion in Solid 1,2-Dichloroethane
Authors: Ragle J. L. , Caron A. P.
Published: January 2005

35Cl pure quadrupole spin—lattice relaxation has been studied in solid 1,2-dichloroethane over the presently accessible temperature range below 90°K. T1 for 35Cl changes by about three orders of magnitude between 53° and 82°K, and shows the onset of a thermally activated rate process above 63°K. The activation energy for this motion is found to be 3.93 kcal/mole. The temperature dependence of the proton T1 was also examined. At values of H0 for which relaxation is not complicated by the temperature dependent cross relaxation with the chlorine spin system, the activation energy obtained from proton T1 data agrees with that from the pure quadrupole measurements.

An anisotropic least-squares refinement was made using the 133°K. X-ray data of Reed and Lipscomb and amplitudes were assigned to chlorine atom motions. The physical picture that emerges from the combination of these data is that the amplitude of over-all motion is small below the heat capacity anomaly, relaxation being effected by a reorientation between two (or several) close minima 30° to 40° apart and separated by the above barrier. Near the heat capacity anomaly this precursor motion goes over into a large scale motion, still about the Cl–Cl axis, which has been previously described.
Theory of Subexcitation Electron Scattering by Molecules. II. Excitation and De-Excitation of Molecular Vibration
Authors: Chen Joseph C. Y.
Published: January 2005

The proposed mechanism for the excitation and de-excitation of molecular vibration by slow electron impact involving compound negative-ion states as intermediates is studied in some detail in light of the theory presented in Paper I of this series. The absolute orders of magnitude of the cross sections for such collisional processes are calculated for the (N2, e) system, where detailed measurements have recently been made for the excitation of the ground N2 molecules to various excited vibrational states. The observed multipeak structures for the excitation functions are accounted for. The energy dependence of the cross sections for the excitation and de-excitation of a vibrationally excited N2 molecule exhibits similar multipeak structures in the same energy region. An interpretation of such multipeak structures is offered.
Many-Center Wavefunctions for the Hydrogen Molecule and the Hydrogen Molecular Ion
Authors: Hoyland James R.
Published: January 2005

Many-center wavefunctions for the hydrogen molecule and the hydrogen molecular ion are constructed using basis sets composed of either 1s orbitals or spherical Gaussians. Emphasis is placed on minimization of the total molecular energy with respect to all available nonlinear parameters. In the case of the s-orbital basis, all the many-center integrals are computed without resort to approximation techniques. It is concluded that the basis set of spherical Gaussians is superior to that of 1s orbitals and that further work with these functions may prove fruitful.