bluuebunny/crossref_metadata_2025 huggingface dataset:
Radiation of a Point Charge Moving Uniformly over an Infinite Array of Conducting Half-Planes
Authors: Lam John
Published: January 2005

The excitation of an infinite array of parallel semi-infinite metallic plates by a uniformly moving point charge is studied by the Wiener-Hopf method. The problem is treated as a boundary-value problem for the potential of the induced electromagnetic field, and is formulated in terms of a dual integral equation for the current density induced on the plates. The solution of the dual integral equation gives exact expressions for the induced current density and the induced field in the form of Fourier integrals. The Poynting vector is calculated, and the radiation shows that the array of plates behaves both like a diffraction grating and a series of parallel-plate waveguides.
Three-Dimensional Formulation of Gravitational Null Fields. II
Authors: Misra R. M. , Singh R. A.
Published: January 2005

In the previous paper of this series, it was shown that three types of gravitational null fields may be characterized on the analogy of the electromagnetic field. The first two types were discussed in the previous paper. This paper discusses the remaining third type (C) of gravitational null field. The necessary and sufficient condition that the gravitational field be of type C is obtained. The formalism is also extended to include nonempty gravitational fields. It is shown that the nonempty space-time may also admit three types of gravitational null fields under certain circumstances. A typical case is discussed as an example.
Realizations of Lie Algebras in Classical Mechanics
Authors: Mukunda N.
Published: January 2005

Classical Poisson bracket realizations of semisimple Lie algebras are considered. An attempt is made to determine the minimum number of canonical degrees of freedom needed to find a realization of a given Lie algebra. Under the restriction to the symmetric traceless tensor representations of the orthogonal groups, and the symmetric tensor representations of the unimodular unitary groups, it is shown that with n pairs of canonical variables one can find realizations of the Lie algebras of O(n + 2) and SU(n + 1), but no higher groups.
New Approach to Unified Field Theory
Authors: Blackman Jerome
Published: January 2005

A new approach to a unified field theory combining Einstein's gravitational equations and the Maxwell equations is developed using a geometry in which GL(4, C) replaces GL(4, R) as the group of the principal bundle. The resulting equations are the same as Einstein's in the case of empty space but differ from those he proposed for the combined gravitational and electromagnetic fields. Charge is shown to appear only at singularities, and a symmetric solution corresponding to the classical Schwarzschild metric is presented.
Fresnel's Equation in General Relativity
Authors: Kremer Hugo F.
Published: January 2005

The Fresnel equation is derived in general relativity using the classical method applied by Levi-Civita in the study of a nonrelativistic theory of electromagnetic induction. For the description of the anisotropic medium the theory proposed by Quan is adopted. The study of the Cauchy problem is also presented and the convergence of results assures us that the equation proposed is the good one.
Mathematical Methods for Evaluating Second-Order Three-Body Interactions between Atoms or Ions with Gaussian Wavefunctions
Authors: Zimering Shimshon
Published: January 2005

It is shown that the integrals occurring in the expression for the interaction energy between three atoms or ions in second-order perturbation theory with Gaussian wavefunctions can be reduced to single integrals of three different types. The first two types are erf x and erf ix functions, whereas the third type is a single integral of the error function which is easily evaluated by electronic computation.
Probability Distribution of the Radius of Gyration of a Flexible Polymer
Authors: Coriell S. R. , Jackson J. L.
Published: January 2005

Various aspects of the mathematics of the probability distribution PN(Sx) of one component of the square of the radius of gyration of an ideal Brownian chain with N units are presented. A rigorous expression for PN(Sx) in the form of a contour integral is obtained. The resulting integral is written in terms of Tchebichef polynomials. Several rigorous and approximate results are obtained for both the limiting distribution (N infinite) and for finite N.
Approach to Gravitational Radiation Scattering
Authors: Torrence R. J. , Janis A. I.
Published: January 2005

A method is presented for studying asymptotically flat spaces possessing both incoming and outgoing gravitational radiation at infinity. The method uses multipole expansions and the invariance of general relativity under time reversal; calculations are facilitated by a small-parameter perturbation approach. Some calculations are carried out to second order to show the practicability of the method.
Canonical Form Factors and Current Commutation Relations
Authors: Chakrabarti A.
Published: January 2005

Starting with the vector (or axial vector) currents jμ and the momentum operators Pν, we define the canonical operator j̃, such that instead of the four covariantly transforming components of j, we have a scalar j̃0 and three other components j̃ undergoing Wigner rotations under Lorentz transformations. We first give a construction of j̃ explicitly in terms of j and P. But, since the transformation properties are not quite the most convenient ones, a subsequent generalized definition, leading to a convenient canonical parametrization of the matrix elements of j̃, is introduced. We then study the physical significances of the canonical form factors thus obtained. For vector currents j̃v the transformation properties correspond to a separation of the physical charge (j̃0) and magnetic (j̃) form factors in any frame (and not only in Breit frame as for j). For nonconserved axial currents we relate the matrix elements of j̃0A with mass-difference effects and express the partial conservation condition in terms of the canonical form factors. We then study in detail the application of our formalism to the limiting case of infinite momentum and small momentum-exchange, as often introduced in the study of current algebras. Next we give explicitly the canonical form factors for photoproduction processes. In the last section we study the possibility of constructing a canonical spin operator directly in terms of the vector and axial vector charges and the consequences for the ``inner orbital'' contribution to be added to obtain the total spin of a composite particle. Some useful formulas are collected in Appendixes A and B.
Upper Bounds to Eigenvalues of the One-Dimensional Sturm-Liouville Equation
Authors: Nordtvedt K.
Published: January 2005

This work develops a straightforward technique for giving an upper bound to any eigenvalue of the one dimensional Sturm-Liouville problem. It is shown that any trial function that fulfills the proper boundary condition of the problem and possesses the same number of nodes as an exact eigenfunction of the problem can provide an upper bound to that eigenfunction's eigenvalue. Application of the above technique is made to provide a one-sided bound to quantum mechanical scattering phase shifts.
Relation Between ``Outer'' and ``Inner'' Multiplicity for SU(2) and SU(3)
Authors: Gruber B.
Published: January 2005

The Clebsch-Gordan series for SU(3) is given in terms of irreducible representations of SU(3) such that the ``outer'' multiplicity of the Clebsch-Gordan series is related to the ``inner'' multiplicity of irreducible representations.
Unitary Representations of the Lorentz Group and Particle Dynamics
Authors: Rafanelli Kenneth
Published: January 2005

We examine the quantum dynamics of particles with arbitrary spin implied by explicit use of the infinite dimensional unitary representation of the Lorentz group, introduced by Majorana. Comparison with the classical theory of spinning particles shows that this unitary representation leads to a quantum mechanical analog of the relativistic pure gyroscope.
Electromagnetic Behavior of Superconductors with Impurity Scattering
Authors: Wong M. K. F.
Published: January 2005

A general equation for the electromagnetic current J of a superconductor responding to a frequency-dependent external electromagnetic field and under the influence of impurity scattering and temperature has been derived in momentum space using the Green's function method. This general equation can be regarded in two ways. (a) It is the Fourier transform, from coordinate space to momentum space, of the equation of Mattis and Bardeen [D. C. Mattis and J. Bardeen, Phys. Rev. 111, 412 (1958), Eq. (3.3)]. (b) It summarizes, in one equation, the previous works of Abrikosov et al. on the electromagnetic behavior of superconductors. In addition to these general properties, this equation also shows, in particular, that for a superconducting alloy with a few percent of impurity concentration, the kernel for the current is the same as that of a Pippard pure superconductor, with 316vk, where v is the Fermi velocity and k is the momentum exchange during collision replaced by τtr, the transport collision time, valid for all temperatures up to Tc, the transition temperature. Expressions of the current in closed form for both superconducting alloys and normal metal with impurity are also given for vk ∼ 1/τ.
Particlelike Solutions of a Class of Nonlinear Field Equations
Authors: Darewych G. W. , Schiff H.
Published: January 2005

A procedure for generating integral relations satisfied by particlelike solutions of the class of nonlinear field equations Δφ = F1(φ) is proposed and used to develop the first few such relations. The relations are used to reduce the expression for the ``energy'' associated with the system; as an example, the case F1(φ) = φ − φ3 is treated. It is shown generally that the variational bound to any of the possible energy values will approach the exact value from above if the trial functions are chosen to satisfy one of the integral relations, which is satisfied identically by the exact solutions.
Characteristic Hypersurfaces in General Relativity. I
Authors: Daŭtcourt G.
Published: January 2005

Lightlike (null) hypersurfaces are treated by means of an intrinsic Ricci rotation coefficient technique. This provides an effective way of dealing with the various types of geometry on a null hypersurface. The formalism is used to examine inner affinities, differential invariants, local features such as asymptotic and shear directions and geodesic lines, and to give a short description of null hypersurfaces in flat space-time. Applications to gravitational radiation theory and cosmology are briefly mentioned.
Associative Algebra in the Problem of Mass Formulas
Authors: Böhm Arno
Published: January 2005

An associative algebra of continuous operators in a rigged Hilbert space, which contains the enveloping algebra of the Poincaré group and gives rise to a discrete mass spectrum, is studied. In Appendix B some general results on the representation of Lie algebras in a rigged Hilbert space are derived.
Connection between Complex Angular Momenta and the Inverse Scattering Problem at Fixed Energy
Authors: Newton R. G.
Published: January 2005

The paper contains a number of remarks occasioned by Sabatier's enlargement of the class of solutions to the inverse scattering problem at fixed energy found previously by the author. The implications of the large class of scattering-equivalent potentials for the angular momentum interpolation problem are discussed. The additional angular momenta that appear in the expansion of the potential are directly related to the singularities of its Mellin transform. It is shown that the expansion coefficients must not converge too rapidly to zero unless the first moment of the potential vanishes. Finally we analyze the information contained in an ``angular momentum dispersion relation'' obeyed by the Jost function which is found as a by-product.
Description of Extended Bodies by Multipole Moments in Special Relativity
Authors: Dixon W. G.
Published: January 2005

The description of an extended charged body in a given electromagnetic field in flat space-time is considered, and it is shown that such a body may be completely specified by a certain set of multipole moments of the energy-momentum tensor Tαβ and the charge-current vector Jα. These moments include the momentum vector, spin tensor, and total charge of the body, and they completely determine Tαβ and Jα. It is shown that the only relations between the moments due to the ``generalized conservation equations'' ∂βTαβ = −FαβJβ and ∂αJα = 0 are the constancy of the total charge and equations of motion for the momentum vector and spin tensor, in contrast to previous descriptions by moments, such as that of Mathisson, which have an infinite number of such relations. The equations of motion are given exactly, as infinite series in the moments, without assuming the applied electromagnetic field to be analytic, and an approximation procedure is developed, based on the smallness of the body compared with a typical length scale for the external field.
Convergence of the Bremmer Series for the Spatially Inhomogeneous Helmholtz Equation
Authors: Berk H. L. , Book D. L. , Pfirsch D.
Published: January 2005

The convergence of the Bremmer series expansion for the solution of the one-dimensional Helmholtz equation with varying wave number is investigated. It is proved that the series converges provided the quantity εσ is sufficiently small, where ε measures the relative rate of change 1/k2(dk/dx) and σ the relative total change of the wave number k. An exactly soluble example is discussed in order to show that convergence fails if the above criterion is significantly relaxed. It is shown that if the Bremmer method is applied to the calculation of the time-dependent response to an externally imposed signal, the series is convergent at any finite time after the signal is turned on.
Green's Functions and Double-Time Distribution Functions in Classical Statistical Mechanics
Authors: Herzel John C.
Published: January 2005

This paper rederives the Bogoliubov/Sadovnikov classical-equilibrium-correlation Green's function hierarchy by using the double-time theory of Rostoker. Thus the traditional variational technique is avoided.
Unitary Representations of U(2, 2) and Massless Fields
Authors: Kursunoǧlu Behram
Published: January 2005

This paper contains a discussion of unitary irreducible representations of the group U(2, 2) in terms of the noncompact algebra of creation and annihilation operators and some applications to massless fields. In particular, the U(2, 2) algebra yields discrete values for p4 (energy), one of its generators. The little group and wave equations of massless fields are also derived from the Lie algebra of U(2, 2).
Canonical Formulation of Relativistic Mechanics
Authors: Hill Robert Nyden
Published: January 2005

Instantaneous action-at-a-distance relativistic mechanics of the type considered by Currie and by Hill is cast into a Hamiltonian form wherein the transformations of the inhomogeneous Lorentz group are canonical. The Currie-Jordan-Sudarshan zero-interaction theorem is circumvented by renouncing the demand that physical positions be canonical; the implications for measurement theory of renouncing this demand are discussed. Examples are given.
Expansions in Spherical Harmonics. IV. Integral Form of the Radial Dependence
Authors: Sack Robert A.
Published: January 2005

A function f(rAB) YLM (θAB, φAB) of a vector rAB = Σri can be expanded in spherical harmonics Ylm (θ, φ) of the directions of the individual vectors. The radial coefficients satisfy simple differential equations which, in three previous papers, were solved in terms of series in ri2/rj2; these were different in various regions, depending on the relative magnitudes of the ri. In this paper the solutions are found as multiple integrals over the product of Legendre polynomials and of a function G(w), where w depends linearly on the ri. The kernel G(w) is independent of the number of constituent vectors, their relative sizes, and the orders of their harmonics; it contains the Heaviside step function H(w) as a factor which takes care of the various regions. The precise form of G can be found from f and L by an integral equation which for L = 0, 1 is solved for arbitrary f, and for L > 1 for sufficiently large positive powers. The expressions of Milleur, Twerdochlib, and Hirschfelder for the bipolar angle average can be obtained simply by repeated integration of G(w) or directly from the differential equations. For the inverse distance between two points, G(w) becomes Dirac's delta function; the number of integrations is thereby reduced by one. Possible applications of the new approach to the evaluation of molecular many-center integrals are outlined. Some corrections are given for the results of the previous papers in the series.
Electric Fields in a Semi-Infinite Medium Whose Conductivity Varies Laterally
Authors: Mann James E.
Published: January 2005

The electric field induced in a semi-infinite medium whose conductivity varies laterally is calculated when the inducing field is chosen to approximate a vertically incident magnetic wave which is polarized in the direction of the conductivity variation. The specific form of the variation of conductivity is σ = σ0 + σ1(y/d)2, where y is a coordinate parallel to the surface. It is shown for several specific cases that the magnitude of the electric field is less than the electric field in a solid whose conductivity is σ0. In addition, the electric field is calculated for several values of σ0/σ1 at y = 0.
Degree of Higher-Order Optical Coherence
Authors: Mehta C. L.
Published: January 2005

In this paper we define the normalized coherence function of arbitrary order (m, n), in a manner which seems to be a natural generalization of that defined for the second-order coherence function. Both classical and quantized optical fields are considered and the results are compared. It is shown that for classical fields and also for quantized optical fields having nonnegative definite diagonal coherent state representations of the density operator, the modulus of these normalized coherence functions is bounded by the values 0 and 1. This definition differs from the one recently given by Glauber for quantized optical fields, where the normalized coherence functions may take arbitrarily large values even for fields having nonnegative definite diagonal representations of the density operator. Conditions for ``complete coherence,'' i.e., those under which the modulus of the normalized coherence function attains the limiting value 1, are discussed. Some consequences of stationarity and quasi-monochromaticity are also discussed.
Energy-Momentum Conservation Implies Translation Invariance: Some Didactic Remarks
Authors: Williams David N.
Published: January 2005

We discuss from a rigorous viewpoint two more-or-less familiar cases where energy-momentum conservation implies invariance under space-time translations. First, if a closed linear operator on a Hilbert space has a domain that is invariant under spectral projections belonging to the four-momentum operators, and if it ``conserves energy-momentum,'' it necessarily commutes with the appropriate representation of the translations. (Bounded operators, such as the S matrix, are a special case.) At least for separable spaces, the domain restriction characterizes the closed operators for which the theorem is true. Second, if a bounded bilinear form between momentum states of m and n particles in a Fock space (or more generally, a bounded multilinear form) conserves energy momentum, the corresponding tempered distribution has a conservation delta function at points where the mass shell is a C∞ manifold; but no derivatives of delta functions can occur. In this connection, we are led to a result that seems to be new: the cluster parameters (``connected amplitudes'') of a family of bounded bilinear forms, labeled by (m, n), are also bounded bilinear forms. The two systems, of course, mutually conserve energy momentum.
Angular Coefficients of Atomic Matrix Elements Involving Interelectronic Coordinates
Authors: Heintz W. H. , Gibbs R. L.
Published: January 2005

A method for determining the angular coefficients of atomic matrix elements is illustrated. The angular coefficients of matrix elements for rija,rijarjkb,rijarjkbrkic,rijarjkbrklc, and rijarjkbrklcrlid are evaluated using single-particle states of definite angular momentum. The use of tensor operators enables a separation into angular and radial parts. The atomic matrix elements are then expressed as sums over products of n-j symbols and radial integrals. These sums are restricted by the values of the single-particle state angular momenta, and in all cases the effects of single-particle couplings disappear. The calculation does not require the use of a particular coordinate system, as is the case for multiple products of spherical harmonics.
Initial-Value Problem for Relativistic Plasma Oscillations
Authors: Lerche Ian
Published: January 2005

The solution of the collisionless, relativistic Vlasov-Maxwell set of equations is given for the case where neither ambient electric nor magnetic fields are present and a smeared-out negative charge background preserves over-all space-charge neutrality with a relativistic proton plasma. The method of solution is based upon the eigenfunction expansion method invented by van Kampen. It is shown that, besides the relativistically modified modes of Case and Zelazny, there exists a new discrete set of modes whose phase velocities are greater than the speed of light in vacuo. The solution also exhibits the coupling of electrostatic and electromagnetic modes and the existence of complex phase velocities. This initial-value problem (or the problem with the electron and proton roles reversed) is of interest because of the existence of cosmic rays, relativistic electrons emitting synchrotron radiation in nonthermal radio sources, solar noise generation, where electron velocities may approach c (Bailey, 1951), and high-energy electrons in laboratory machines (Post, 1960). In these cases the nonrelativistic treatment is clearly inadequate.
Algebraic Calculation of Nonrelativistic Coulomb Phase Shifts
Authors: Zwanziger Daniel
Published: January 2005

It is observed that the in and out states of a particle of energy k2/2m, entering or leaving a Coulomb field along the +z direction, are eigenstates of L3 with eigenvalue 0, and of A3, the third component of the Runge-Lenz vector, with eigenvalues ±α + ik/m, respectively. From this characterization and the commutation relations of the symmetry group, the phase shifts are easily obtained algebraically.
Three-Particle States and Green's Function
Authors: Pasquier Jeanne-Yvonne
Published: January 2005

The six-dimensional spherical harmonics are specified in connection with SO6 and particular subgroups isomorphic to SO3 and SO2; three-particle states are then labeled by the grand-angular momentum n, the usual angular momentum j, its projection on a fixed axis m, an integer μ related to SO2, and a degeneracy number ω. Also, we derive the plane-wave and free Green's function expansions in terms of these spherical harmonics.
Eigenvalue Problem for Lagrangian Systems. II
Authors: Barston E. M.
Published: January 2005

The quadratic Lagrangian eigenvalue problem [ω2I − ωiA − H]ξ = 0 for H and iA, completely continuous Hermitian operators in a Hilbert space E, H ≥ 0, is investigated. The problem is reduced to an equivalent linear eigenvalue problem for a single completely continuous Hermitian operator in the Hilbert space E × E, and existence and convergence theorems for the eigenvectors and variational properties of the eigenvalues for the original quadratic problem are easily obtained from standard theorems. The general solution of the associated time-dependent problem ξ + Aξ + Hξ = 0 is obtained under the further restriction that E be finite dimensional. Necessary and sufficient conditions for stability are given.
Geometrical View of Lagrange Multipliers in Mechanics
Authors: Gaskill J. R. , Arenstein M.
Published: January 2005

A set of constraints on a mechanical system may be viewed as a set of surfaces in the phase space of the problem. To be satisfied simultaneously by the system, these constraints must intersect forming a differentiable manifold. Lagrange multipliers are eigenvalues which adjust the magnitudes of gradient vectors in the manifold's tangent bundle. A Jacobian transformation on the constraints must therefore exist and be nonsingular over the domain of equilibrium.
Decompositions of Discrete Most Degenerate Representations of SO(p, q) when Restricted to Representations of SO(p, q − 1) or SO(p − 1, q)
Authors: Niederle J.
Published: January 2005

The decomposition of any most degenerate unitary irreducible representation (single-valued of discrete principal series) of an arbitrary noncompact rotation group SO0(p, q) (p ≥ q > 1) when restricted to the unitary irreducible representations of its maximal noncompact rotation subgroup SO0(p, q − 1) or SO0(p − 1, q) is derived, and characteristic features of the decomposition are discussed.
The Mechanism of Processes Initiated by Excited Atoms I. The Quenching of Excited Sodium
Authors: Laidler Keith J.
Published: January 2005

The potential-energy surfaces relevant to a number of simple processes involving excited (2P) sodium have been constructed, and the mechanism of the reactions discussed in terms of them and of the theory of absolute reaction rates. It is shown that quenching by atoms is normally a very inefficient process, the effect of additional atoms in a quencher being to stabilize a quenched complex, commonly a polar compound, which finally decomposes to give the deactivated atom and a vibrationally excited product. The activated state may be either at the top of a rotational-energy barrier or at a crossing point to a polar surface, and the theory is shown to be consistent with the experimental values of the quenching cross sections. In the cases examined the quenching is of a physical nature, the energy passing chiefly into vibrational energy, with a certain amount going into translational and rotational degrees of freedom. Saturated hydrocarbons appear to quench like hydrogen except that there is probably a small energy of activation, but the unsaturated ones quench by means of an interaction between the sodium atom and the unsaturated group, and the efficiency is considerably higher.
The Double Minimum Problem Applied to Potassium Hydrogen Fluoride
Authors: Glockler George , Evans George E.
Published: January 2005

The doublet character of the infra-red absorption line at 2.67μ of solid potassium hydrogen fluoride is due to the ``tunnel effect.'' The proton has two potential minima between the fluorine nuclei in the FHF− ion. The distance of a minimum to the center of the ion is 0.26A. The height of the potential hill is 33,400 calories.
Contribution to Statistical Mechanics
Authors: Mayer Joseph E.
Published: January 2005

The method of the grand partition function may be used to calculate distribution functions Fn(z, {n}) proportional to the probability that n molecules in a system of fugacity z, and fixed temperature, occupy the position of their coordinates symbolized by {n}. The method makes use of the distribution functions Fn(0, {n}) at zero fugacity. The distribution functions may be written Fn(z, {n})=exp[−Wn(z, {n})/kT], in which Wn(z, {n}) is the potential of average force of n molecules at the fugacity z, which becomes equal to the ordinary potential energy at zero fugacity. The equations may be generalized to permit the calculation of the distribution functions at any fugacity assuming a knowledge of them at any other fugacity. Using methods previously employed for imperfect gases, the pressure, and also the density in molecules per unit volume, may be developed in a power series of difference of fugacity around any arbitrary fugacity. The coefficients of these developments are calculable at all fugacities by the same equations always employing the potentials of average force at the fugacity around which the development is made. The power series obtained represent functions which are regular on the real positive axis of fugacity except at the points characteristics of the phase transitions in the system.
The Temperature Dependence of Reaction Rates from the Standpoint of the Broensted-Christiansen-Scatchard Equation
Authors: Amis Edward S. , Jaffé George
Published: January 2005

In Section I arguments were presented for the necessity of splitting the log k∞* term in the general kinetic equation into a part which represents the rate constant extrapolated to a standard reference state of temperature, dielectric constant and concentration, and into a part giving the temperature dependence. In Section II the repulsive potential between reactants at close distances was formulated and this potential was then incorporated in the general kinetic equation to give the temperature dependence of the reaction rate constant. In Section III this equation was applied to existing kinetic data and found satisfactory. Also the repulsive forces between reactants calculated from the temperature and dielectric dependence of the reaction rate constants were compared with the intermolecular forces between the molecules of noble gases calculated from the second virial coefficients as evaluated by Fowler.
The Infra-Red Spectrum of Furan
Authors: Pickett Lucy W.
Published: January 2005

The infra-red spectrum of furan vapor has been investigated in the region from 500 to 35,000 cm−1 with a prism spectrograph using potassium bromide, rocksalt, and fluorite prisms. The data have been compared with those of other investigators and the frequency assignments proposed by Lord and Miller for pyrrole were applied to these data.
Infra-Red Spectrum of Polyatomic Molecules XVI. Methyl-d3-Chloride and Methyl-d3-Bromide
Authors: Noether Hermann D.
Published: January 2005

Methyl-d3-chloride and methyl-d3-bromide have been synthesized, their infra-red spectrum in the range from 2.8 to 18μ measured, and a complete assignment of the fundamental frequencies has been given. A modified valence-type potential function including two interaction terms fits the fundamental frequencies of the four molecules CH3Cl, CD3Cl, CH3Br, and CD3Br to within one percent.
The Cadmium (3P1) Photosensitized Reactions of the Lower Olefins
Authors: LeRoy D. J. , Steacie E. W. R.
Published: January 2005

An investigation has been made of the cadmium (3P1) photosensitized reactions of ethylene, propylene, butene-1, and butene-2. The low quantum yields are attributed to the influence of the C=C bond on the actual quenching process and are not inconsistent with the data on C–H bond strengths.
The Heat Capacities of Molecular Lattices III. Some Simple Molecular Solids
Authors: Brucksch W. F. , Ziegler Waldemar T.
Published: January 2005

The experimental heat capacity data for crystalline Cl2, CO2, SO2, SCO, N2O, C2N2, C6H6, C2H4, and CH3Br have been compared with the results of calculations made employing a semitheoretical method suggested by Lord, Ahlberg, and Andrews and amplified by Lord. Good agreement between the calculated and experimental results is obtained.
An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures II. Mixtures of Methane, Ethane, Propane, and n-Butane
Authors: Benedict Manson , Webb George B. , Rubin Louis C.
Published: January 2005

An empirical equation is given for the isothermal variation with density of the work content of hydrocarbon mixtures in the gaseous or liquid state. From this fundamental equation are derived (a) an equation of state, (b) an equation for the fugacity, (c) an equation for the isothermal variation of the enthalpy, and (d) an equation for the isothermal variation of the entropy. These equations summarize P-V-T-x properties of the gaseous or liquid phase, liquid-vapor equilibria, critical properties, latent heats of evaporation, and heats of mixing. The equation is a generalization to mixtures of the equation for pure hydrocarbons given in the first paper of this series. Methods are proposed for determining the parameters in the equation for mixtures from the parameters in the equation for pure hydrocarbons. A comparison is made between observed properties of mixtures and those predicted by the equations. These comparisons show that the equations provide a satisfactory practical summary of the volumetric properties and liquid-vapor equilibria of mixtures of methane, ethane, propane, and n-butane.
Absorption of Polysubstituted Benzene Derivatives
Authors: Sklar A. L.
Published: January 2005

The intensification, by nonchromophoric substitutions, of the forbidden, 1A1g→1B2U, transition in benzene is due, on the one hand, to the unsymmetrical distortion of the ring by the normal vibrations and, on the other hand, to the transition moment produced at the equilibrium position by the migration of charge from the substitution into the ring or vice versa. The latter effect is treated by the method of antisymmetrical molecular orbitals, all calculations being limited to the first order. The rules for combining transition moments due to the various groups in a polysubstituted benzene are calculated. It is shown that, for weak nonchromophoric substitutions, the intensity ratios (except for the less important variation in the normal vibrations) are for C6H5X:oC6H4X2:mC6H4X2:pC6H4X2:1,3,5 C6H3X3:1,2,3 C6H3X3:1,2,4 C6H3X3=1:1:1:4:0:0:3. It is further shown that if one substitutes benzene by a meta-directing group, M, and by an orthopara-directing group, P, of the same intensifying power, the ratios for the mono : ortho : meta : para-derivatives should be 1 : 3 : 3 : 0. These ratios are shown to be in good qualitative agreement with experimental data.
Supersonic Measurement of the Heat Capacity of Propylene
Authors: Telfair D.
Published: January 2005

An apparatus designed for (1) a general study of acoustical dispersion in gases, and (2) measurement of gaseous heat capacities has been used to measure the heat capacity of propylene between 273 and 490°K. The general methods used are outlined and discussed. The measured heat capacity values agree well with those calculated from the frequency assignment as given by Wilson and Wells, and an assumed potential restricting rotation of about 2000 cal./mole, but deviate from the values calculated from Pitzer's frequency assignment and an 800-cal./mole potential. The measurements on propylene also have the value of serving as a test of the usefulness and practicality of the supersonic method of heat capacity determinations.
Vapor Pressures of the Tritium Liquid Hydrogens Dependence of Hydrogen Vapor Pressure on Mass of the Molecule
Authors: Libby W. F. , Barter Cyril A.
Published: January 2005

The Henry's law constants for HT evaporating from approximately 10−9M solutions in normal H2 and for DT from nD2 were determined by distillation and measuring the radioactivities of the distillate gases. On the basis of Lewis' and Hanson's data showing H2 and D2 to form nearly perfect solutions, the Henry's law constants were taken to represent the vapor pressures of the pure HT and DT liquids. A plot of vapor pressures of various kinds of hydrogen at 20.4°K led to 45±10 mm of Hg as the predicted vapor pressure of liquid nT2 at 20.4°K.
The Diffraction of X-Rays by Liquid Benzene-Cyclohexane Mixtures
Authors: Eisenstein A. , Gingrich N. S.
Published: January 2005

The x-ray diffraction pattern of a liquid mixture of benzene and cyclohexane is investigated, using both the photographic method and the Geiger-Mueller tube counter method. The fine structure on the main peak, and a secondary peak as reported by Bell and Davey, cannot be obtained. It is concluded that these features do not exist in this pattern.
The Infra-Red Absorption of Silver Cyanide
Authors: Stallcup W. David , Williams Dudley
Published: January 2005

The spectrum of powdered AgCN has been studied in the region 2500–1800 cm−1. Intense absorption at 2178 cm−1 is attributed to an oscillation involving the CN group. The CN frequency for AgCN is almost 100 cm−1 higher than the CN frequencies of NaCN and KCN.
Second Virial Coefficients and the Forces Between Complex Molecules
Authors: Hirschfelder J. O. , McClure F. T. , Weeks I. F.
Published: January 2005

The second virial coefficients of ethane, propane, n-butane, n-heptane, ammonia, methyl chloride, and the freons are computed from available experimental data. The causes for sizeable errors in second virial coefficients are considered. At temperatures above the critical, the second virial agrees with the theorem of corresponding states. Below the critical temperature, molecules with dipoles have unusually large virials and the values of their reduced dipole moment, μ/(TcVc)½, determine the discrepancy. The data for isomeric hydrocarbons show that the second virial is not sensitive to the shape of the molecule. This makes it impossible to determine the exact laws of intermolecular interaction from the temperature variation of the second virial. The imperfections of a gas are considered to arise from the presence of double molecules which exist for the duration of a collision. The equilibrium constant for the formation of double molecules is related to the second virial and its temperature variation gives the entropy ΔS and the energy ΔE of their formation. These may be interpreted qualitatively in terms of the intermolecular forces. The second virial coefficient for all substances fits the equation: B(T) = ba(1 — c exp (—ΔE/RT)) where ba, c, and ΔE are taken as constants. Here bac=exp (ΔS/R). A corresponding states equation is given for estimating second virials when no experimental data are available.
The Approximate Solution of Schrödinger Equations by a Least Squares Method
Authors: Frost Arthur A.
Published: January 2005

A method of approximation to the solution of a Schrödinger equation has been developed in which variation functions are used but no integrations are involved. The procedure involves the evaluation of the energy for a set of representative points in configuration space. The parameters in the variation function are then chosen by applying the condition that the mean square deviation of the energy from the average should be a minimum.
Energy Relations of the Surface of Solids I. Surface Energy of the Diamond
Authors: Harkins William D.
Published: January 2005

From the known structure of the diamond the total surface energy of the crystal has been calculated in terms of the energy of the carbon-carbon bond, and is found to be: 1.50×10−9EB erg cm−2 for the 111 face, and 2.10×10−9EB erg cm−2 for the 100 face, where EB is the energy in ergs per bond. If the bond energy is assumed to be 90 kcal. mole−1 the values become 5650 erg cm−2 for the 111 face, and 9820 erg cm−2 for the 100 face. The corresponding free surface energies are found to be: 111 face at 25°=5400 erg cm−2 100 face at 25°=9400 erg cm−2. One uncertain feature in the calculation is that involved in the calculation of the decrease in energy caused by the long range binding of the valence bonds in the surfaces. In the 111 face the bonds are 2.517A apart, and are perpendicular to the surface. Thus the bond directions are parallel, while inside the diamond the carbon-carbon distance is only 1.54A, and the bonds meet head on. While in the 111 face there is only one bond per carbon atom, in the 100 face there are two bonds per atom. In the 111 face there are 1.825×1015 bonds per sq. cm−2, with an area of 5.48A2 each, while in the 100 face the corresponding values are 3.158×1015 bonds per cm2 and 3.167A2 per bond. It is concluded that in the 111 face the interaction energy of the type described above is less than one percent and is negligible. Even in the 100 face the interaction should be small. No account was taken of any adjustment of the energy of the unsevered bonds in the surface region. This should cause a greater decrease of energy than the long range binding of the severed bonds. Thus the values of the surface energy calculated in this paper should be considered as maximum values.
On the Strength of Carbon-Hydrogen and Carbon-Carbon Bonds
Authors: Stevenson D. P.
Published: January 2005

Electron impact critical potentials are combined with thermochemical data to obtain values for the heats of the dissociation reactions, CH4=CH3+H, C2H6=C2H5+H, C2H6=2CH3, and nC4H10=2C2H5. The values found are: D(CH3–H)=101 kcal./mole, D(C2H5–H)=96 kcal./mole, D(CH3–CH3)=82.6 kcal./mole and D (C2H5–C2H5)=77.6 kcal./mole. These values are compared with estimates based on kinetic and photochemical data.
The Photolysis of Persulfate
Authors: Heidt Lawrence J.
Published: January 2005

The photochemical efficiency, φ, for the decomposition of persulfate by light of λ254 mμ is determined by comparison with φ for the uranyl oxalate actinometer. The persulfate content was followed by the method of Kurtenacker and Kubina and in representative cases the hydrogen ion produced also was determined. The equation S2O8=+H2O+hv = 2HSO4−+O2/2 accounts quantitatively for the data. Evidence is given to show that the main reaction is not the decomposition of SO4−. Six tenths of a mole of persulfate is decomposed per Einstein absorbed by persulfate in dilute neutral and alkaline solutions when all oxidizable material is absent. Acetic acid increases this yield to unity but non-oxidizable ions have a depressing effect. Many of the observations of Morgan and Crist also are verified. At constant ionic strength, φ remains nearly unchanged in alkali, but drops abruptly to less than 0.01 when solutions are acidified suggesting the formation of a weak acid containing photochemically inert persulfate. Absorption spectra and conductivity measurements, however, give no indication that such a weak acid is formed. The explanation offered for these facts is that the hydrogen ion associates with the thereby stabilizes the persulfate ion after the latter absorbs a photon. The stabilizing effects of other ions, except perhaps bisulfate, is much less than hydrogen which is thought to be related, among other things, to their larger size. Hydrogen peroxide was not found in any of the solutions.
Polarization of Light Scattered by Isotropic Opalescent Media
Authors: Perrin Francis
Published: January 2005

A general study is given of the polarization of light scattered by isotropic media whose elements of heterogeneity are not very small in comparison with the wavelength, (suspensions, colloidal solutions, solutions of large molecules, ...). This includes an extension of a theory by R. S. Krishnan, who, considering certain particular states of polarization of the incident light and applying the law of reciprocity, had proved the equality of two of the four coefficients which are to be considered in these cases. Using Stokes' linear representation of the polarization of light beams, it is shown that the scattering through a given angle and for a given wave-length is characterized by the 16 coefficients of the linear forms which express the four polarization parameters of the scattered beam in terms of the four corresponding parameters of the incident beam and that the law of reciprocity leads to six relations between these sixteen coefficients. For an isotropic asymmetrical medium (having rotatory power), the scattering is thus characterized by ten independent coefficients. In the case of a symmetrical medium, four of these coefficients must be zero, leaving only six scattering coefficients, and if the scattering particles are spherical, there are two additional relations between these coefficients. The comparison with dipolar scattering by very small elements shows that the best test to prove multipolar scattering is the existence of some ellipticity in the scattered light when the incident beam is linearly polarized in a direction oblique to the scattering plane.
The Second Virial Coefficient for Gas Mixtures
Authors: Beattie James A. , Stockmayer Walter H.
Published: January 2005

The second virial coefficients B for methane, normal butane, and three mixtures of these gases were evaluated from the experimental data, and the interaction term B12 computed for methane-n-butane from 150° to 300°C. The results were used to study the methods of combination of constants in an equation of state. Computation of B12 from a Lennard-Jones expression similar to that used for a pure gas with σ and θ evaluated as σ12=½(σ11+σ22) and θ12=θ11½θ22½ where the subscripts 1 and 2 refer to the pure components gave exceptionally good results. This suggested a new method of combination of constants in the equation of state which led to the best results of any method so far used.
A Practical Method for the Solution of Certain Problems in Quantum Mechanics by Successive Removal of Terms from the Hamiltonian by Contact Transformations of the Dynamical Variables Part I. General Theory
Authors: Thomas L. H.
Published: January 2005

Problems in quantum mechanics may be solved by canonical change of the representation in terms of which the dynamical variables are expressed. They may also be solved by contact transformations of the dynamical variables. The usual notation is modified slightly to make it more convenient for developing these two methods. Their parallel development shows their essential equivalence but formal difference.
Entropy of the Monomeric Forms of Formic Acid and Acetic Acid
Authors: Halford J. O.
Published: January 2005

A recent measurement of the entropy of gaseous formic acid at its equilibrium vapor pressure is combined with vapor density data to give 60.0±0.3 as the entropy of the monomer at 25° and one atmosphere. The corresponding dimer entropy is 83.1±0.3 e.u. Pauling's residual entropy of R ln 2 per dimer weight for random orientation of hydrogen bonds in the crystal has been included in the above figures in order to allow a reasonable entropy for the torsional motion of the hydroxyl group in the monomer. The same correction has been applied to a previously published result for the acetic acid monomer to yield 70.1±1.0 as a revised value. It is highly probable that only a single significant potential minimum of undetermined breadth and depth occurs in the rotational cycle of the hydroxyl group.
The Derivation of a General Kinetic Equation for Reaction Between Ions and Dipolar Molecules
Authors: Amis Edward S. , Jaffé George
Published: January 2005

An equation has been derived for the reaction rate constant in the case of ion-dipole reactions. Section II contains the extension of Debye-Hückel's theory of ionic atmospheres to the case of dipoles surrounded by ions, coupling it with Onsager's theory of electric moments of molecules in liquids. Section III applies the potential constructed to the derivation of the rate constant by the kinetic procedure of Christiansen and Scatchard. The result is substantiated by existing data both from concentration and dielectric constant dependence of the rate of reaction between ions and dipoles (Section IV).
Electric Circuit Models for the Vibration Spectrum of Polyatomic Molecules
Authors: Kron Gabriel
Published: January 2005

Electrical circuits are developed to determine the normal frequencies and normal modes of vibration of polyatomic molecules having arbitrary configurations. The networks for each molecule are set up without equations from physical considerations alone and may be solved by an a.c. network analyzer, by numerical methods, or by digital (punch card, etc.) calculating machines. The networks also allow the establishment of the resultant secular equations of the molecule by simple inspection. The potential function considered is either a general quadratic form of the displacements, or it may correspond to the customary ``valence-force'' system employing stretching, bending, and twisting of the valence bonds and valence angles. A companion paper contains network analyzer tests on the CO2, OCS, and ethyl alcohol molecules by the ``valence-force'' model. Both the normal frequencies and normal modes of vibration check satisfactorily with known results within the accuracy of the instruments.