bluuebunny/crossref_metadata_2025 huggingface dataset:
Potential Energy as a Function of Internal Rotation in CFClBr–CFClBr by NMR Measurements
Authors: Thompson Douglas S. , Newmark Richard A. , Sederholm Charles H.
Published: January 2005

The NMR spectrum of CFClBr–CFClBr is reported as a function of temperature from 177° to 300°K. The high-temperature spectrum is analyzed in terms of a superposition of the spectra of the meso and dl isomers, each in rapid rotation about the C–C bond; the low-temperature spectrum on the basis of a superposition of the spectra of the three rotamers of each of the two isomers. The gauche coupling constant between fluorine atoms in this compound is 21.5±0.5 cps. Chemical shifts for the fluorine atoms were different for the three rotamers. Fluorine atoms gauche to one fluorine and one chlorine atom are at the highest field, and fluorine atoms gauche to one fluorine and one bromine atom are at the lowest field.

By observing the relative areas of peaks at low temperature, relative energies of the three potential minima for each isomer are calculated. High-temperature areas determined the relative amounts of the two isomers. Using, in addition, chemical shift data from the low-temperature spectra, spectra of this mixture of isomers have been calculated as a function of temperature assigning various potential barriers to internal rotation. By comparing the calculated spectra with those observed at various temperatures, several of the potential barriers to internal rotation have been assigned. In each isomer, the three potential minima vary by at most 450 cal/mole. The potential maxima which can be measured are all approximately 10.0±0.5 kcal/mole above the potential minima.
Frequency Distribution of Hexamethylenetetramine Crystals
Authors: Becka L. N.
Published: January 2005

The energy distribution of neutrons inelastically scattered from hexamethylenetetramine powder at 80° and 300°K is given. Features of the scattering curve are described and interpreted in the light of a simple model of the lattice vibration spectrum.
Double Resonance and Proton Relaxation in Asphalt Solutions
Authors: Poindexter Edward H.
Published: January 2005

Dynamic polarization and proton relaxation in asphalt solutions have been studied as a function of solute concentration, temperature, and oxygen concentration. The observed results are consistent with the Korringa—Seevers—Torrey theory of spin pumping in diluted paramagnetic systems. The reciprocal signal enhancement is proportional to reciprocal asphalt concentration. The signal enhancement is directly proportional to the fraction of proton relaxation arising from the electron. The electron dominates the proton relaxation in the surface regions around the free radical. The observed data indicate a small radical molecule in asphalt. The electron—proton correlation frequency in the surface layer around the asphaltene radical is found to be about 10 Mc.
Small Angle X-Ray Scattering from Montmorillonite Clay Suspensions. II
Authors: Hight R. , Higdon W. T. , Darley H. C. H. , Schmidt P. W.
Published: January 2005

Small angle x-ray scattering has been used to study the interactions between clay platelets in a number of samples. Sodium montmorillonite clays have been studied in concentrations ranging from 5% to 85% by weight. The scattering from the samples with concentrations from 10% to 40% was analyzed by Fourier transformation to obtain the distribution functions for the platelet spacing. For the higher concentrations, the scattering curves were interpreted by fitting the data with theoretical curves for aggregates of platelets. The most probable platelet spacing ranged from 116 Å for the 10% concentration to 13 Å for the 85% concentration. If one plots platelet spacing as a function of grams of H2O per gram of clay for this series of samples, a reasonably linear relation is obtained. The effect of adding NaCl, CaCl2, and AlCl3 to 2% sodium montmorillonite suspensions was studied. Until the salt concentration is raised to a critical value, the scattering curve is identical to the curve obtained for dilute Na montmorillonite suspensions with no salt added. The latter scattering curve has been previously interpreted [R. Hight, Jr., W. T. Higdon, and P. W. Schmidt, J. Chem. Phys. 33, 1656 (1960)] as being due to independent montmorillonite layers 10 Å thick. The critical concentration decreased as the valence of the added salt was increased. Above the critical concentration, the scattering data show that aggregation takes place, with the aggregates consisting of about 6 to 8 platelets and with a platelet spacing of 19 to 21 Å. Calcium montmorillonite suspensions show essentially identical behavior. Fresh hydrogen montmorillonite samples show no aggregation, but in samples aged about four months, the scattering curves indicate the presence of aggregates with a platelet spacing of 22–24 Å and with 2 or 3 platelets per aggregate.
Microwave Spectrum of Methyldifluoroarsine
Authors: Nugent Leonard J. , Cornwell C. D.
Published: January 2005

The spectrum of CH3AsF2 was investigated over the range 10–33 kMc/sec. Three Q branches (Kc=5→4, 6→5, 7→6) and two R transitions (J=2→3, Kc=2→3; J=3→4, Kc=3→4) were fitted by a Hamiltonian which included terms for over-all rotation, internal rotation, nuclear quadrupole coupling, and centrifugal distortion. The internal rotation perturbation calculations were carried in some cases to the fifth order. The reciprocal moments of inertia are A=5414.49±0.15 Mc/sec, B=5381.28±0.15 Mc/sec, and C=3871.88±0.15 Mc/sec. The b axis is perpendicular to the plane of symmetry. The height of the internal rotation barrier (assumed to be sinusoidal) is 463±6 cm−1. The quadrupole coupling constants for As75 are eQqcc=−220±4 Mc/sec and η0=(qbb—qaa)/qcc = −1.20±0.05. The structure, barrier height, and quadrupole coupling constants are discussed briefly.
Kinetics of the Reaction between Acetyl Iodide and HI and the Heat of Formation of the Acetyl Radical
Authors: O'Neal H. Edward , Benson Sidney W.
Published: January 2005

The kinetics of the gas-phase reactionCH3COI+HI⇄CH3CHO+I2has been studied in the temperature range 222°—268°C and the pressure region of about 80 mm Hg. The rate data are consistent with an I-atom, catalyzed path similar to that found for the reaction of alkyl iodides with HI. Specific rate constants and Arrhenius parameters of all the individual reaction steps are evaluated. The bond-dissociation energy of the C–I bond in AcI is found to be D (Ac–I) = 50.6 kcal and the standard heat of formation of the acetyl radical ΔHf0 (Ac) = −6.3 kcal, in excellent agreement with independent work.
Spectra and Photoconduction of Phthalocyanine Complexes (I)
Authors: Day P. , Williams R. J. P.
Published: January 2005

Reflection spectra of Co, Ni, Cu, Zn, and metal-free phthalocyanines have been measured. The Davydov splitting of the main absorption peak in the metal compounds correlates with the relative tendencies of the metals to out-of-plane bonding. Photoconduction response curves have been measured between 1500 and 300 mμ for single crystals of these compounds. Besides a high response following the crystal absorption, metal-free Ni and Cu phthalocyanines also had considerable photosensitivity in the near infrared, peaking at 900–1100 mμ. The effect on the short-wavelength photoconduction of measuring in vacuo instead of in air also correlates with the ability of the metals to bond out-of-plane groups.
Kinetics of Disappearance of the CN Radical Formed from C2N2
Authors: Paul D. E. , Dalby F. W.
Published: January 2005

The flash photolysis technique has been extended to measurement of absolute concentrations and kinetics of small molecules having fine-lined absorption spectra. The rates of disappearance of CN radicals in cyanogen, cyanogen chloride, hydrogen, and hydrocarbons have been determined. The disappearance of CN in cyanogen was found to obey the expression d(CN)/dt=—k(CN)(C2N2), where k = 7.3×107 e−2100/RT liters/mole sec over the temperature range 301° to 447°K.
Madelung Constants for the Calcium Carbide and Pyrite Crystal Structures
Authors: Wood Robert
Published: January 2005

The Madelung constants for the calcium carbide and pyrite crystal structures have been calculated assuming that the anion can be represented by two spherically symmetric charge distributions. The results indicate that the assumption that the anion is spherically symmetric can lead to small errors in the case of the pyrite structure and large errors in the case of the calcium carbide structure.
Electric Resonance Spectrum and Dipole Moment of BaO
Authors: Wharton L. , Kaufman M. , Klemperer W.
Published: January 2005

The dipole moment of BaO in several vibrational states has been determined to be μ0 = 7.955 D, μ1 = .997 D, μ2 = 8.039 D, μ3 = 8.079 D with an error of ±0.003 D by the molecular-beam electric-resonance technique. The change of the dipole moment of BaO with vibrational state agrees with the change predicted by the Rittner model of classically polarizable ions. Measurement of relative intensities of vibrational lines yields a value of 680±100 cm−1 for the vibrational frequency of the molecule and fourth-order Stark effect yields a value of 0.304±0.007 cm−1 for the rotation constant, in agreement with the more accurate spectroscopic determinations. The Ramsey method of separated oscillatory electric fields was used successfully in electric resonance, with the expected narrowing of linewidth. Because BaO is composed of spinless nuclei, it is proposed as the basis of a voltage or electric field standard that could have a precision of 1 part in 108. A table of fourth-order Stark coefficients is appended.
Nuclear Spin Relaxation in Ellipsoids Undergoing Rotational Brownian Motion
Authors: Woessner D. E.
Published: January 2005

The nuclear spin relaxation times T1 and T2 have been calculated for two identical nuclei of spin I = ½ fixed in an ellipsoid undergoing rotational Brownian motion. The ellipsoid is subject to small random changes in orientation in which the rotation probabilities about its three major axes are different. This anisotropic motion yields five nuclear correlation times; isotropic motion yields only one correlation time. The results are applicable provided that the static dipolar coupling is effectively averaged to small values by the rotational motion. For nonviscous liquids, T1 = T2. When the rotation probabilities about two axes are equal, the relaxation-time expressions simplify a great deal, but they retain the essential relaxation features of anisotropic rotational motion; the number of nuclear correlation times is reduced to three; the relaxation times for rapid motion have been calculated as a function of the ratio of the two rotation probabilities for this case. The relaxation rates in ellipsoids of revolution obeying the Stokes approximation for motion in a continuous medium have been compared to those for spheres having the same volume. The rates for very nonspherical particles are large compared to those for the spheres. An example of internal motion of the internuclear vector within the ellipsoid is calculated.
Raman Spectral Studies of Molten Potassium Bisulfate and Vibrational Frequencies of S2O7 Groups
Authors: Walrafen G. E. , Irish D. E. , Young T. F.
Published: January 2005

Raman intensities and frequencies of molten potassium bisulfate, obtained in the temperature range of about 300° to 700°C, provide evidence for the reactions 2HSO4−→S2O72−+H2O and S2O72−→SO42−+SO3. Between 300° and 620°C the HSO4− concentration, inferred from Raman intensities, decreases rapidly. Simultaneously, the S2O72− concentration increases and becomes maximal at 500°C. Above 500°C the S2O72− concentration decreases, and Raman lines of SO42− appear. Analyses of gaseous and solidified products indicate that the production of SO42− is accompanied by the evolution of SO3.

Raman frequencies and polarizations of HSO4− ion obtained at temperatures ranging from the melting point to 620°C have been compared with the corresponding quantities obtained from studies of aqueous solutions. Differences observed are discussed in terms of hydrogen bonding. Raman spectra of molten potassium bisulfate obtained at ∼620°C provide vibrational frequencies of S2O72−. The number of Raman frequencies observed, polarizations of the Raman bands, and comparisons of the Raman frequencies with infrared frequencies of the corresponding solid exclude structures of the dihedral point groups and favor a structure of C2 symmetry (a slightly distorted C2v structure). Vibrational assignments for frequencies of S2O72− were made, and a comparison of those frequencies with frequencies of the related species HS2O7− and H2S2O7 indicates many close correspondences.
Mass Spectral Studies of Kinetics behind Shock Waves. I. Thermal Dissociation of Chlorine
Authors: Diesen R. W. , Felmlee W. J.
Published: January 2005

The coupling of a shock tube to a time-of-flight mass spectrometer for the determination of kinetic data is described whereby analysis is performed every 25 μsec. The rate of dissociation of Cl2 has been measured over the temperature range 1700°—3200°K under essentially isothermal and isobaric conditions with the observed rate constants in fair agreement with those obtained by the spectroscopic technique. The observed temperature dependence is less than predicted by simple collision theory with an apparent activation energy of 41±5 kcal/mole.
Spectrum of Nd3+ in LaCl3
Authors: Eisenstein J. C.
Published: January 2005

The energy levels of the Nd3+ ion in LaCl3 are calculated by finding the eigenvalues of the matrices for the combined Coulomb, spin—orbit, and crystal-field interactions within the f3 configuration. By judicious choice of the three Slater integrals and the spin—orbit coupling constant, the standard deviation between the calculated and the experimental positions of 22 terms can be reduced to 87.5 cm−1. Crystal-field parameters can be chosen which yield a standard deviation of 0.91 cm−1 between the calculated and the measured splittings of 31 levels in seven terms. The calculated Zeeman splitting factors in the direction parallel to the crystal axis are in good agreement with the measured values.
Antiferromagnetic Spherical Ising Model and Some Properties of the Associated Lattice Gas
Authors: Mazo Robert M.
Published: January 2005

The spherical model of Berlin and Kac is applied to an antiferromagnetic interaction. The critical-field curve, magnetization-field curves, specific heats, and long-range order are calculated. The problem is translated into lattice-gas language, to afford a possible model for the solid—gas transition. Very unphysical behavior is found, and a probable reason is discussed. This is ascribed to a ``borrowing'' of spin from one sublattice by the other.
Effective Depth of Formation of X-Ray Line Radiation
Authors: Salem Sema'an I. , Watts John C.
Published: January 2005

The mechanism of production of line radiation in a thick target differs from that of bremsstrahlung radiation. As a result the effective depths of formation of the two types of radiation, under identical conditions, are not the same. With relatively low voltage across the x-ray tube, the average change in the depth of production with voltage was found to be 300 A/kV for the continuum while the line data gave a value of 440 A/kV, in anode material having an atomic number of about 30. The dependence of the two quantities on the takeoff angle has also been investigated.
Copolymerization as a Markov Chain
Authors: Frensdorff H. Karl , Pariser Rudolph
Published: January 2005

The concept of Markov chains has been employed to derive the degree-of-polymerization distribution, the over-all composition, and the compositional distribution for copolymers containing any number of different monomers. The results are then used to obtain explicit expressions for systems of two monomers. It is shown that this method, because of its conciseness and ease of generalization, is particularly well adapted for problems in copolymerization statistics.
Studies on the Alternant Molecular Orbital Method. V. A Many-Parameter Energy Expression for States with Different Multiplicities; Application to Benzene
Authors: de Heer J. , Pauncz R.
Published: January 2005

Within the framework of the refined alternant molecular orbital method, a general energy expression is derived for the lowest state of any desired multiplicity of an arbitrary system with closed-shell structure. A numerical analysis of the lowest singlet, triplet, and quintet state of the pi-electron sextet in benzene reveals that the many-parameter alternant molecular orbital wavefunction does, in each case, account for better than 90% of the energy improvement obtained in a full configuration interaction treatment. A detailed comparison of the AMO and CI wavefunctions for both triplet and quintet state is presented. Both methods yield a singlet—triplet separation that is too low, which suggests a basic deficiency in the customary approach to the quantum chemistry of conjugated hydrocarbons.
Electron-Spin Density in Irradiated Oriented Polyethylene
Authors: Higuchi Jiro
Published: January 2005

Electron spin distribution in free radicals in irradiated polyethylene was calculated from the observed anisotropic hyperfine splittings currently available in electron spin resonance data. The spin density of β-carbon appears to be negative.
Stationary Expression for Effective Range
Authors: Ohmura Takashi
Published: January 2005

A variation principle is presented for the effective range of s wave scattering. This principle applies both to the bound state and to the scattering state. It is proved that some of the stationary expressions for the effective range has the minimum value for the exact solution, thus the calculated value by using an approximate wave function gives an upper bound for the effective range.

A modified method is also proposed which may simplify the calculation in an actual application. The stationary expression gives, however, neither an upper bound nor a lower bound.
Integration in Functional Spaces and its Applications in Quantum Physics
Authors: Gel'fand I. M. , Yaglom A. M.
Published: January 2005

This translation of the survey article by I. M. Gel'fand and A. M. Yaglom on the theory and applications of integration in functional spaces in problems of quantum physics was prepared because it was felt that such a review would be of interest and of use to mathematical physicists working in several different fields.

The article begins with a discussion of Wiener measure, after which the extension is made to the complex measure introduced by Feynman in his formulation of quantum mechanics, and examples are given of the use of these methods in quantum mechanics, quantum field theory, and quantum statistical physics. A comprehensive bibliography of works devoted to the theory and applications of functional integration methods is included.
Rigorous Derivation of the Phase Shift Formula for the Hilbert Space Scattering Operator of a Single Particle
Authors: Green T. A. , Lanford O. E.
Published: January 2005

For a single nonrelativistic particle moving in a spherically symmetric potential, the existence of the Hilbert space wave operators and S operator is proved and phase shift formulas for these operators are deduced. The probability, P(Ω), for scattering into the solid angle Ω is obtained from the time dependent theory. The relation between P(Ω) and the R matrix of the standard plane wave formulation of scattering theory is established. For collimated incoming packets, it is shown that P(Ω) can be expressed as an energy average of the differential cross section.
Method to Obtain the Character Tables of Nonsymmorphic Space Groups
Authors: Zak J.
Published: January 2005

A method is developed to obtain the character tables of nonsymmorphic space groups. The method is based on the possibility of obtaining all the irreducible representations of a group, if one knows all the irreducible representations of its invariant subgroup of index 2 or 3. It turns out that all the space groups have an invariant subgroup of index 2 or 3.
Problem of Rainich for Two-Component Spinors
Authors: Bergmann Otto
Published: January 2005

Some general relations for two-component spinors in general relativity are derived in an attempt to solve the problem of Rainich for this case. A set of algebraic equations allows us in principle to express the current vector in terms of the energy-momentum tensor, and thus in terms of the Einstein tensor, but we have not succeeded in solving these equations except in a special frame of reference. Weyl's equations are expressed in terms of the current vector, its derivatives, and the energy-momentum tensor. In the last chapter, the determination of the spinor variables themselves is studied.
Combinatorial Aspects of the Ising Model for Ferromagnetism. I. A Conjecture of Feynman on Paths and Graphs
Authors: Sherman S.
Published: January 2005

An identity on paths in planar graphs conjectured by Feynman [H] is rigorously established. This permits a complete analysis of the combinatorial approach to the two-dimensional Ising model with nearest neighbor interaction and 0 external magnetic field previously heuristically discussed by Kac and Ward [KW] and Potts and Ward [PW]. Relevant identities are established for the two-dimensional Ising model with next nearest neighbor interactions and 0 external magnetic field, for the two-dimensional Ising model with nearest neighbor interactions and positive external magnetic field, and for the three-dimensional Ising model with nearest neighbor interactions and 0 external field. For the case of a square net with an odd number of spin locations with nearest neighbor interactions and external field equal to iπ/2, it is shown that the partition function is identically zero for both plane and torus imbedding contrary to a result announced by Lee and Yang [LY; Eq. (48)], which turns out to be correct only for an even number of spin locations.
Proof of Carathéodory's Local Theorem and Its Global Application to Thermostatics
Authors: Bernstein B.
Published: January 2005

It is pointed out that Carathéodory's proof of his theorem on pfaffian forms, which was used in his axiomatic development of thermostatics, is not complete and does not make clear whether this result is valid locally or globally. This theorem is replaced by a more precise statement of a local nature, for which a proof is given. By tracing through Carathéodory's use of the concept of thermal equilibrium with respect to simple systems, it is shown how the existence of a global entropy and absolute temperature may be deduced from this local result.
Numerical Integration of the Transport Equation with No Angular Truncation
Authors: Wilf Herbert S.
Published: January 2005

For any given azimuth-independent scattering law, it is shown that the neutron transport equation with external source is rigorously equivalent to a coupled system of Fredholm integral equations. These are derived both for vacuum and periodic boundary conditions. A numerical integration scheme is given for solving these integral equations with no angular truncation error, thereby permitting the solution of the Boltzmann equation numerically, with no error but that in the spatial integration. All cross sections are permitted to be arbitrarily given functions of position, if desired.
Some Remarks Concerning the Real and Imaginary Parts of the Characteristic Roots of a Finite Matrix
Authors: Lewis Daniel C. , Taussky Olga
Published: January 2005

Some theorems are obtained on the existence of certain determinantal equations whose roots are separately the real or imaginary parts of the characteristic roots of a given matrix with simple elementary divisors. When the elementary divisors are not simple, similar, but somewhat less precise, results are obtained.
Analytic Properties of Radial Wave Functions
Authors: Newton Roger G.
Published: January 2005

This is a review article about the properties of radial wave functions and other quantities relevant to the partial wave analysis of scattering theory, as functions of the energy or wave number. The treatment is restricted to the nonrelativistic Schrödinger equation for two particles with a local potential. In addition to regular and irregular solutions of the radial differential equations, the Jost function, S matrix, and Green's functions are analyzed and completeness is proved. The examples investigated in detail include the Bargmann potentials and their generalizations.
Differential-Operator Approximations to the Linear Boltzmann Equation
Authors: Siegel Armand
Published: January 2005

A measure of deviation from equilibrium of an ensemble of particles is proposed, which is physically appropriate and of especially simple form when expressed in terms of the expansion coefficients of the ensemble distribution function with respect to the system of orthogonal polynomials obtained by using the equilibrium distribution function as weight function. The linear Boltzmann operator can then be expanded in a series of terms which, under certain circumstances, may be regarded as of successively diminishing magnitude in their effect on the rate of approach to equilibrium. This expansion of the operator is different from the expansion due to Kramers (later discussed by Moyal) in derivate moments, commonly used in approximate stochastic treatments of irreversible processes. With the aid of a theorem on definite operators, it is possible to break off the series at any point and thereby obtain a correspondingly accurate approximation to the linear Boltzmann operator, whose temporal solutions tend to the correct equilibrium distribution function. The first approximation is the Fokker-Planck operator, exactly. The next approximation would be the appropriate operator to use when the stochastic variable begins to deviate appreciably from a linear dissipation law, etc. The method is applied to the ``Rayleigh process'' (ensemble of particles in a rarefied gas medium, the medium itself being in internal equilibrium), and the second approximation to the linear Boltzmann operator for this case is explicitly derived. A possible form for the second approximation in more general processes, suggested by this, is also given.
Topological Derivation of the Mayer Density Series for the Pressure of an Imperfect Gas
Authors: Green Melville S.
Published: January 2005

A new derivation of Mayer's classical density expansion for the pressure of an imperfect gas based on a classification of cluster graphs according to topological criteria is presented. The classification is a generalization of the classification of simple trees into trees with centers and trees with bicenters.
Singularities and Discontinuities of Feynman Amplitudes
Authors: Cutkosky R. E.
Published: January 2005

The Landau singularities of the amplitude calculated from an arbitrary Feynman graph are considered. It is shown that the discontinuity across a branch cut starting from any Landau singularity is obtained by replacing Feynman propagators by delta functions for those lines which appear in the Landau diagram. The general formula is a simple generalization of the unitarity condition. The discontinuity is then considered as an analytic function of the momenta and masses; it is shown that its singularities are a subclass of the singularities of the original amplitude which corresponds to Landau diagrams with additional lines. The general results are illustrated by application to some single loop graphs. In particular, the general formula gives an immediate calculation of the Mandelstam spectral function for fourth-order scattering. Singularities not of the Landau type are discussed and illustrated by the third-order vertex part.
Spacetime of the Elementary Particles
Authors: Finkelstein R.
Published: January 2005

The possibility is examined that physical space is characterized by a torsion, or an asymmetric connection, which is determined by the matter field. There exists a space with uniform torsion with the same metrical properties as conventional microspace; it is isotropic and homogeneous with a very large radius of curvature (R≅1028 cm). The momentum operators form a group and for practical purposes commute. The torsion defines at every point two kinds of parallel transfer or two screw motions of opposite helicity. There are, consequently, two kinds of spinor field associated with the space; they are distinguished by opposite coupling to the torsion. Viewed from within the Lorentz group the torsion produces an axial vector interaction. To interpret the given mathematical model, it is suggested that there exists a universal axial vector coupling between fermions represented by the spinor fields and bosons associated with the torsion; and that this interaction manifests itself macroscopically as a torsion of space, in the same general way that gravitational interactions correspond to a curvature of space. This general assumption leads to cosmological models characterized by relations connecting the average density of matter and the strength of the assumed interaction. For the observed average density of matter in the known universe (∼10−30 g/cm3) the proposed axial vector coupling turns out, for a space of uniform torsion, to be of the order of the strong interactions.
Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field Theory
Authors: Araki H.
Published: January 2005

Cyclic representations of the canonical commutation relations and their connection with the Hamiltonian formalism are studied. The vacuum expectation functional E(f)=(Ψ0,ei[open phi](f)Ψ0) turns out to be a very convenient tool for the discussion. The uniqueness of a translationally invariant state (vacuum) is proved under the assumption of the cluster decomposition property for E(f). The existence and near uniqueness of the Hamiltonian in cyclic representations of the canonical commutation relations are established. The conditions for the relativistic invariance of the theory are stated in terms of vacuum expectation values at a fixed time. It is shown that E(f) is the Fourier transform of a quasi-invariant nonnegative measure on the space of all linear functionals of the test functions.
Approximate Solutions of the Bethe-Salpeter Equation
Authors: Vosko S. H.
Published: January 2005

A modified representation of the Bethe-Salpeter wave function for scalar particles interacting via a massless scalar field is presented and related to Salpeter's approximate wave function. A procedure for obtaining approximate solutions of the Bethe-Salpeter equation for arbitrary interactions is introduced. The method is based on a variational principle and is capable of high accuracy when used with the trial functions developed here. The choice of trial function is suggested by the important features of the exact solutions for the special case described above. The method is applied to a finite range potential which corresponds to the lowest order approximation to a simple field theory. The results of the calculation suggest that the effect of retardation is large when an interaction is transmitted by a field with mass.
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
Authors: Girardeau M.
Published: January 2005

A rigorous one-one correspondence is established between one-dimensional systems of bosons and of spinless fermions. This correspondence holds irrespective of the nature of the interparticle interactions, subject only to the restriction that the interaction have an impenetrable core. It is shown that the Bose and Fermi eigenfunctions are related by ψB=ψFA, where A(x1 … xn) is +1 or −1 according as the order pq … r, when the particle coordinates xj are arranged in the order xp<xq< … <xr, is an even or an odd permutation of 1 … n. The energy spectra of the two systems are identical, as are all configurational probability distributions, but the momentum distributions are quite different. The general theory is illustrated by application to the special case of impenetrable point particles; the one-one correspondence between bosons with this particular interaction and completely noninteracting fermions leads to a rigorous solution of this many-boson problem.
Generalization of the ``Edge-of-the-Wedge'' Theorem
Authors: Epstein H.
Published: January 2005

It is proved that two analytic functions of several complex variables, having the same boundary values when the imaginary parts of the variables tend to zero inside two arbitrary, but fixed, open cones, possess a common analytic continuation in a certain open set. This is a generalization of the ``edge-of-the-wedge'' theorem, a proof of which is obtained in passing.
Computation of Order Parameters in an Ising Lattice by the Monte Carlo Method
Authors: Ehrman J. R. , Fosdick L. D. , Handscomb D. C.
Published: January 2005

The long-range and short-range order parameters are computed for the Ising lattice using a Monte Carlo sampling scheme. The square lattice, the simple cubic lattice, and the body-centered cubic lattice are considered. In the three-dimensional calculations both the antiferromagnetic and ferromagnetic cases are considered as well as the coupling to an external magnetic field of various strengths. Good agreement is found where the results can be compared with the exact two-dimensional results, and in the three-dimensional case the results agree well with those obtained from series approximations in the regions where the series approximations are valid. The present method appears to give good results for the short-range order even very close to the critical temperature, but in this neighborhood the long-range order estimate is crude. The computations were performed on the high-speed computer ILLIAC, located at the University of Illinois.
Lorentz Invariance and the Gravitational Field
Authors: Kibble T. W. B.
Published: January 2005

An argument leading from the Lorentz invariance of the Lagrangian to the introduction of the gravitational field is presented. Utiyama's discussion is extended by considering the 10-parameter group of inhomogeneous Lorentz transformations, involving variation of the coordinates as well as the field variables. It is then unnecessary to introduce a priori curvilinear coordinates or a Riemannian metric, and the new field variables introduced as a consequence of the argument include the vierbein components hkμ as well as the ``local affine connection'' Aijμ. The extended transformations for which the 10 parameters become arbitrary functions of position may be interpreted as general coordinate transformations and rotations of the vierbein system. The free Lagrangian for the new fields is shown to be a function of two covariant quantities analogous to Fμν for the electromagnetic field, and the simplest possible form is just the usual curvature scalar density expressed in terms of hkμ and Aijμ. This Lagrangian is of first order in the derivatives, and is the analog for the vierbein formalism of Palatini's Lagrangian. In the absence of matter, it yields the familiar equations Rμν=0 for empty space, but when matter is present there is a difference from the usual theory (first pointed out by Weyl) which arises from the fact that Aijμ appears in the matter field Lagrangian, so that the equation of motion relating Aijμ to hkμ is changed. In particular, this means that, although the covariant derivative of the metric vanishes, the affine connection Γλμν is nonsymmetric. The theory may be reexpressed in terms of the Christoffel connection, and in that case additional terms quadratic in the ``spin density'' Skij appear in the Lagrangian. These terms are almost certainly too small to make any experimentally detectable difference to the predictions of the usual metric theory.
Solution of the Equations of Statistical Mechanics
Authors: Lewis Robert M.
Published: January 2005

The solution of the initial value problem for Bogoliubov's functional differential equation of nonequilibrium statistical mechanics is obtained. This solution is then expanded in an infinite power series in the density which has the advantage that the calculation of the leading terms requires the solution of s-body problems only for small values of s. A derivation of the equilibrium equations by reduction from the nonequilibrium equation is included. These results are applied to obtain a simple derivation of the Boltzmann equation.
Determination of Thermodynamic Green's Functions
Authors: Baym Gordon , Mermin N. David
Published: January 2005

In the study of thermodynamic correlation functions or Green's functions, one is naturally led to a calculation of values of the Fourier transform of the Green's function on a discrete set of points in the complex energy plane. It is shown that even though these points do not in general possess a limit point within the region of analyticity, one may still uniquely determine the Fourier transform of the Green's function directly from its values at these points.
Lower Bounds and Isoperimetric Inequalities for Eigenvalues of the Schrödinger Equation
Authors: Keller Joseph B.
Published: January 2005

The potential which minimizes the lowest eigenvalue of the one-dimensional Schrödinger equation is determined among all potentials V for which the integral of Vn has the prescribed value k. For each value of n and k this potential is found to be a special case of the Epstein-Eckart potentials which were originally introduced because the Schrödinger equation for them could be solved explicitly. The minimum eigenvalue is determined and it provides a lower bound on the lowest eigenvalue of any potential for which ∫Vndx=k. The expression of this fact as an inequality yields an isoperimetric inequality. For an arbitrary potential, each value of n provides one lower bound on the lowest eigenvalue, the largest of which is the best. This best bound is determined for the square well, the exponential, and the inverse power potentials. In the case of the square well, it is compared with the exact value. In the limiting case n = 1 our result reduces to that previously obtained by Larry Spruch, who showed that the delta function has the minimum lowest eigenvalue among all potentials of given ``area.''
On the Connection of Spin and Commutation Relations between Different Fields
Authors: Araki Huzihiro
Published: January 2005

The connection of spin and commutation relations for different fields is studied. The normal locality is defined as the property that two Boson fields as well as a Boson field and a Fermion field commute, while two Fermion fields anticommute with each other at a spacelike distance. A regular locality is defined as any combination of commutativity and anticommutativity between various pairs of fields at spacelike distance, where the kinematically related fields are assumed to obey the same type of commutation relations. The normal and regular weak locality is defined in a corresponding way. It is proved on the basis of the Lorentz invariance and spectrum conditions that any regular locality is equivalent to the normal locality plus a set of even-oddness conservation laws. It is further shown, under the assumption of the normal weak locality between pairs of the same field, that any regular weak locality is equivalent to the normal weak locality plus a set of even-oddness conservation laws.
Null Electromagnetic Fields
Authors: Robinson Ivor
Published: January 2005

It is shown that a field of null rays is geodetic and shear-free if and only if the associated family of null bivectors includes a solution to Maxwell's equations for charge-free space.
Some Properties of Empty Space-Time
Authors: Newman E.
Published: January 2005

In close analogy to the ``vierbein'' technique of representing world vectors as linear combinations of four fixed vectors, we have constructed from six linearly independent bivectors a (complete) set, or basis, of ten tensors of rank 4 that possess all the algebraic properties of the empty-space Riemann-Christoffel tensor (i.e., Weyl's tensor). Any actual Weyl tensor must be a linear combination of these ten; the expansion coefficients with respect to a given basis are uniquely determined. We have examined Petrov's classification scheme in terms of this formalism and have developed a further division into subclasses. Finally, we shall present in this paper, as an application of our technique, the derivation of plane-fronted waves.
Some Applications of the Infinitesimal-Holonomy Group to the Petrov Classification of Einstein Spaces
Authors: Goldberg J. N. , Kerr R. P.
Published: January 2005

The classifications of Einstein spaces by Schell and Petrov are combined and certain nonlocal results are obtained. In particular, we show that an Einstein space cannot be type I with a rank four Riemann tensor in a four-dimensional region. On using the notion of a perfect or imperfect infinitesimal-holonomy group, we establish the conditions under which an Einstein space possesses a two-, four-, or six-parameter group. We find that two- and four-parameter groups are associated with special cases of type II null and type III, respectively.
Einstein Spaces With Four-Parameter Holonomy Groups
Authors: Kerr R. P. , Goldberg J. N.
Published: January 2005

The metric tensor is constructed for Einstein spaces which are Petrov type III and whose holonomy group is four parametric. Together with the previously known plane fronted wave solutions, this completes the study of all metrics whose holonomy groups are less than six parameter. The Killing vector equations are studied and it is found that the space cannot admit more than two independent motions.
Nonequilibrium Processes in Isotopically Disordered Crystals. Dependence on Degree of Order
Authors: Zwanzig Robert
Published: January 2005

A previous paper [A. A. Maradudin, G. H. Weiss, and D. H. Jepsen, J. Math. Phys. 2, 349 (1961)] has shown that approximate normal modes of isotopically disordered crystals decay irreversibly when the arrangement of isotopes is completely random. These results are generalized to crystals with an arbitrary degree of order. In particular, it is shown irreversible behavior occurs whenever the spatial correlation between isotopic species extends over a fixed finite range, as the size of the crystal tends to infinity.
Equipartition of Energy for Nonlinear Systems
Authors: Ford Joseph
Published: January 2005

A system of harmonic oscillators weakly coupled by nonlinear forces will not achieve equipartition of energy as long as the uncoupled frequencies ωk are linearly independent on the integers, i.e., as long as there is no collection of integers {nk} for which Σnkωk=0 other than all nk=0. This result is shown to follow from the general form of the Kryloff and Bogoliuboff series solution to the equations of motion. Physically, the linear independence of the uncoupled frequencies means that none of the interacting oscillators drives another at its resonant frequency, and this lack of internal resonance precludes appreciable energy sharing in the limit as the coupling tends to zero. It is shown that the lack of equipartition of energy observed by Ulam, Fermi, and Pasta for certain nonlinear systems may be explained in terms of the preceding remarks. Moreover, a Kryloff and Bogoliuboff series solution to the appropriate equations of motion is shown to yield qualitative agreement with the Ulam, Fermi, and Pasta computer solution. Finally, a particular system of linear differential equations is solved which illustrates a mechanism whereby oscillator systems may achieve equipartition of energy.
Brownian Motion of a Quantum Oscillator
Authors: Schwinger Julian
Published: January 2005

An action principle technique for the direct computation of expectation values is described and illustrated in detail by a special physical example, the effect on an oscillator of another physical system. This simple problem has the advantage of combining immediate physical applicability (e.g., resistive damping or maser amplification of a single electromagnetic cavity mode) with a significant idealization of the complex problems encountered in many-particle and relativistic field theory. Successive sections contain discussions of the oscillator subjected to external forces, the oscillator loosely coupled to the external system, an improved treatment of this problem and, finally, there is a brief account of a general formulation.
Transition Matrix for Nucleon-Nucleon Scattering
Authors: Kowalski K. L. , Feldman D.
Published: January 2005

As part of a study of the influence of off-the-energy-shell effects on the optical potential for nucleon-nucleus scattering, a method is presented for the calculation, via the reactance matrix, of the nucleon-nucleon transition matrix in terms of an internucleon potential and the scattering amplitude. The singular integral equations for the partial-wave amplitudes of the reactance matrix are reduced to a Fredholm form which contains the scattering amplitude parametrically. The iteration solution of these Fredholm equations is shown to be generally unreliable; however, the zeroth-order iteration approximates the exact solution quite well near the energy shell. The replacement of the kernels of these integral equations by separable functions is discussed; the validity of such an approximation is illustrated by a simple example. The requirement that the solutions of the (exact) Fredholm equations be consistent with the original singular integral equations yields a solution for the scattering amplitude in terms of the resolvent kernels of the Fredholm equations. The entire formalism is so constructed as to include the possibility of a hard core being present in the nucleon-nucleon interaction.
Exact Solution of a Critical Problem for a Slab
Authors: Żelazny Roman
Published: January 2005

By using the Case method of expansion of the angular neutron distribution into series with respect to eigenfunctions of the plane Boltzmann equation, the critical problem of a slab has been formulated. By means of symmetry considerations, the problem of boundary condition has been reduced to one singular integral equation, which has been treated by classical methods. This treatment has given an integral equation for expansion coefficients, which by means of a simple transformation can be reduced to a Fredholm type with a regular kernel, and an additional equation, which plays the role of an exact critical condition. The methods and results of numerical calculations will be published soon.
Exact Calculation of the Fluctuation Spectrum for a Nonlinear Model System
Authors: Van Kampen N. G.
Published: January 2005

Fluctuations in a circuit consisting of a diode and a condenser have been treated by means of approximate methods [C. T. J. Alkemade, Physica 24, 1029 (1958); N. G. van Kampen, ibid. 26, 585 (1960)]. In the present paper, exact eigenfunctions and eigenvalues of the master equation for this system are obtained, and the spectral density of the equilibrium fluctuations is calculated. The most striking result is that the spectrum of the eigenvalues (which are reciprocal relaxation times) has an accumulation point, corresponding to the average time interval between two successive electron transitions.
Exact Wave Functions in Superconductivity
Authors: Mattis Daniel , Lieb Elliott
Published: January 2005

The ground-state wave function and some of the excited states of the BCS reduced Hamiltonian are found. In the limit of large volume, the boundary and continuity conditions on the exact wave function lead directly to the equations which Bardeen, Cooper, and Schrieffer found by a variational technique. It is also shown in what sense the BCS trial wave function may be considered asymptotically exact in this limit. Finite-volume corrections are included in an appendix, and explicit calculations are carried out for a one-step model of the kinetic energy which has possible applications to the problem of the finite nucleus.