bluuebunny/crossref_metadata_2025 huggingface dataset:
Antisymmetric Functions and Slater Determinants
Authors: Foldy Leslie L.
Published: January 2005

Given a function w completely antisymmetric in n variables, there may exist a set of n functions of one variable such that the given function is a Slater determinant in the latter. The first problem considered is that of obtaining a criterion for this to be the case for a given function. This problem is solved by considering the function w as a mapping of the space of functions in n − 1 variables onto the space of functions of one variable. A necessary and sufficient condition for the initial function to be a Slater determinant is then shown to be that the image space be n dimensional. This criterion is converted into practical algorithms which can be employed for the determination. The application of one of these yields the theorem that an arbitrary linear combination of the n + 1 Slater determinants in n variables formed from n + 1 one-variable functions can always be written as a single Slater determinant. It is further proved that if the image space of the mapping is m(>n) dimensional, the original function can be expressed as a linear combination of m!/(m − n)!n! Slater determinants in n variables formed from m one-variable functions. Playing an important role in the analysis is the product of the mapping described above by its adjoint (the product is simply related to Dirac's density matrix for a quantum mechanical system of identical particles) as well as the eigenvectors and eigenvalues of this Hermitian positive semidefinite mapping. The latter form a basis for a systematic approximation procedure for representing a given function by a single Slater determinant or by sums of Slater determinants formed from a particular number of one-variable functions, which yields results obtained previously by Löwdin. Problems of simultaneous approximation of sets of antisymmetric functions and possible physical applications to many-fermion systems are briefly discussed.
Locally Maxwellian Solutions for a ``Positronium'' Plasma
Authors: Frisch H. L.
Published: January 2005

Exact locally Maxwellian solutions of a neutral ``positronium'' plasma are explicitly presented. They correspond to a flow which is a superposition of a parallel flow, a radial expansion, and a rigidbody rotation.
The Solution of a Transition Problem in a Superconducting Strip
Authors: Liniger Werner
Published: January 2005

The isothermal transition of a strip of superconducting material from the superconducting state to the normal state, under the influence of a supercritical external magnetic field, is studied on the basis of the London theory of superconductivity. The problem can be formulated as a free boundary problem with parabolic differential equations which is solved mainly by numerical methods; an analytical solution in the form of series expansions is given for the early part of the transition.

It is found that, in the beginning, the transition in the strip behaves almost like the transition in a half-space. However, the two differ quite drastically as the transition nears completion. It is pointed out that to predict the total transition time for the strip by extrapolating from the analytical solution for the half-space is incorrect. The results show that such an estimate for the transition time would be much too small.
On Forces and Interactions between Fields
Authors: Pandres Dave
Published: January 2005

After a discussion of certain properties of multivalued functions is given, these functions are used to give a scalar representation of electromagnetic theory. In this representation, the four-vector potential A appears as the four-gradient of a multivalued function φ. The problem of solving the time-dependent Schrödinger equation for a particle of charge e in an electromagnetic field is equivalent to the problem of solving the corresponding field-free equation in a space of multivalued functions ψ̄, which is connected to the space of single-valued functions ψ by the relation ψ̄=Uψ where U = exp (—ieφ). Further, if L0(ψ̄, A) is the Lagrangian for a noninteracting particle field ψ̄ and photon field A, then L0(Uψ, A), regarded as a functional of ψ rather than ψ̄, is the Lagrangian for interacting fields ψ and A. This suggests that other interactions (e.g., strong and weak interactions) should be introduced by using a transformation T which is more general than U.

More fundamental reasons for believing that this is the case arise when one considers multivalued coordinate transformations. It is shown that any curved Riemannian space may be connected with a flat space by a multivalued coordinate transformation. This is possible because the metric transforms like a tensor under these transformations, but the Riemann curvature symbol does not. If one writes the equations of motion of a free, classical, relativistic particle in flat-space coordinates and assumes that the equations transform covariantly under multivalued coordinate transformations (this is a natural generalization of the equivalence principle), one obtains equations of motion in the curved-space coordinates which describe a particle in a gravitational and electromagnetic field. Unfortunately, however, the electromagnetic field at any point of space-time depends on the four-velocity of the test particle at that point. This defect, together with the known existence of essentially quantum-mechanical forces and the fact that the uncertainty principle prevents one from measuring velocity when position is measured exactly, suggests that one should write the Klein-Gordon (or Dirac) equation for a free particle in flat-space coordinates, and then make a change of independent variables into curved-space coordinates. When this is done, it is seen that a corresponding change of dependent variable ψ̄=Tψ is required in order that the curved-space wave function shall be a single-valued function of the curved-space coordinates. The fully transformed equation describes a particle in a gravitational and electromagnetic field as well as certain other fields whose properties are not fully understood.
Quantization of Fields with Infinite-Dimensional Invariance Groups. II. Anticommuting Fields
Authors: DeWitt Bryce S.
Published: January 2005

The Green's function approach to the definition of commutators for fields possessing infinite-dimensional invariance groups is extended to the case of anticommuting fields. The discussion is restricted to fields which provide linear homogeneous or inhomogeneous representations of the group, a restriction which excludes no case of practical interest and facilitates setting up the formalism in a manifestly covariant way. Self-consistency of supplementary conditions, Huygens' principle, and reciprocity relations are established just as for commuting fields. Careful attention must be paid to the ordering of anticommuting factors, particularly in the demonstration of the Poisson-Jacobi identity. The invariance properties of the Poisson bracket are investigated in detail and the notion of conditional invariant is introduced. A special class of conditional invariants called asymptotic invariants, which give a complete physical characterization of initial and final states of the dynamical system, is studied in the final section.
The Spin-Statistics Theorem
Authors: Arnowitt R. , Deser S.
Published: January 2005

A derivation of the connection between spin and statistics is obtained for spin 0, ½, and 1 fields with arbitrary local interactions. The basis used is the Schwinger action principle, whose assumptions are specified; they include neither positive energy spectrum nor TCP invariance. The connection can be obtained without either of these two extra requirements in most cases. The remaining cases are characterized by non-TCP invariant free Lagrangians and nonpositive definite free-particle energies. Commutation relations among different fields are also briefly discussed by means of the action principle.
On Scattering of Waves by Random Distributions. I. Free-Space Scatterer Formalism
Authors: Twersky Victor
Published: January 2005

Approximations are derived for the bulk parameters of the coherent multiple scattered field in a slab region of randomly distributed arbitrary scatterers. (The one-, two-, and three-dimensional cases are treated simultaneously.) The propagation number K, and, e. g., ε and μ, are given explicitly in terms of conventional free-space isolated scattering amplitudes; these results generalize existing special forms for monopoles, dipoles, cylinders, and spheres. Corresponding approximations are obtained for the differential-scattering cross section per unit volume (i.e., the incoherent scattering), such that the total flux (coherent plus incoherent) fulfills the energy principle explicitly. Scattering and reciprocity theorems are derived for a ``multiple scattering amplitude'' of a scatterer within the distribution, and these are used to trace the energy ``losses'' of the coherent field which ``reappear'' as incoherent scattering. Several applications are considered.
Analytic Properties of the Quantum Corrections to the Second Virial Coefficient
Authors: DeWitt Hugh E.
Published: January 2005

The usefulness of the perturbation expansion and the Wigner-Kirkwood expansion of the quantum-mechanical partition function is discussed for various interaction potentials. It is shown that, contrary to what is expected from the Wigner-Kirkwood expansion, quantum-mechanical diffraction corrections at high temperature to the classical partition function may involve nonanalytic forms of ℏ2. This occurs when the second-order perturbation term is finite in the classical limit, and the interaction potential has a cusp or singularity in any derivative. The second-order perturbation term is evaluated exactly for the exponential, screened Coulomb, and square barrier potentials, and the nonanalytic form (ℏ2)½ is found. For potentials more singular than 1/r at the origin, the diffraction corrections are analytic in ℏ2.

A new method of deriving the Wigner-Kirkwood expansion from the perturbation expansion is given. The method allows one to subtract off any order of the perturbation expansion which may be evaluated separately, and is particularly useful for the screened Coulomb potential.

The classical second virial coefficient and the O(ℏ2) and O(ℏ4) diffraction corrections are evaluated for the singular potential, u(r) = (gp/rp)e−r/ro, by using the Mellin transform of e−βu.
Derivation of Generalized Master Equations
Authors: Swenson Robert J.
Published: January 2005

We present a simplified derivation of a generalized master equation for the diagonal part of the occupation probability density. This derivation is valid for systems of arbitrary volume. It does not require the use of perturbation expansions nor the use of a diagonal singularity condition. In addition, a similar derivation is presented of a generalized master equation for the nondiagonal part of the occupation probability density. These equations become identical to the generalized master equations of Van Hove and Janner, respectively, if a perturbation expansion is made, if a diagonal singularity condition is assumed, and if the limit of infinite volume is taken.
On the Number of Electron Levels in a One-Dimensional Random Lattice
Authors: Morrison J. A.
Published: January 2005

Let the potential of a one-dimensional scalar particle be V(x) = V0 Σ∞i=−∞ δ(x — xi), — ∞ < x < ∞, where V0 < 0, and where the sequence (xi) is random, with a Poisson distribution. This paper investigates analytically the number N of electron levels per atom below energy E = —ℏ2κ2/2m, when 0 < n/κ0 « 1 and 0 < κ/κ0 < 2, where n is the expected density of atoms and κ0 = —mV0/ℏ2. The region κ/κ0 ≈ 1, with n/κ0 small, is of considerable interest, and some previous numerical computations have been inaccurate in this region. Explicit bounds on N−1 may be written down which give the asymptotic behavior of N, as κ0/n → ∞, for 0 < κ/κ0 < 1 and 1 < κ/κ0 < (2 — δ), δ > 0.
Symmetry Restrictions on Field Dependent Tensors with Application to Galvanomagnetic Effects
Authors: Grabner Ludwig , Swanson John A.
Published: January 2005

The usual formalism for determining symmetry relations, due to macroscopic space symmetry, among the components of constant tensors, is shown to apply equally well to tensors that are a function of the applied fields. It differs only in two respects from the special case of constant tensors: (a) Only a subgroup, containing, in general, drastically fewer members than the entire group of symmetry operations, yields symmetry relations. (b) This subgroup contains elements other than the identity only for directions of the applied fields that are left invariant by the elements of macroscopic symmetry of the medium. Examples using first- and second-order tensors arising in electrical conductivity, with and without a magnetic field, are given and the even and odd parts of the tensor are separated.
Nonrelativistic S-Matrix Poles for Complex Angular Momenta
Authors: Newton Roger G.
Published: January 2005

Regge's introduction of complex angular momenta is studied in more detail. The shape and number of trajectories of S-matrix poles as functions of the energy is investigated, with particular attention to the way they leave the real axis, and to their ends at E → ± ∞. The conditions are found under which the S matrix is meromorphic even in Re l < −1/2. Some properties of the S matrix in the left half-plane are discussed and so are its symmetry between left and right half-planes, its branch point at E = 0, and the residues at its poles.
Spectral Theory of Dirac's Radial Relativistic Wave Equation
Authors: Roos B. W. , Sangren W. C.
Published: January 2005

The analytical methods developed by Weyl and Titchmarsh for the study of the Sturm-Liouville equation are extended to the investigation of the spectral properties of the Dirac radial wave equation. It is shown how Weyl's limit-point, limit-circle theorem may be generalized to include the singular cases of a system of two first-order differential equations. A transformation is introduced and order properties are established for the solution of the corresponding integral equations. The nature of the spectrum is discussed for specific singular potentials.
Behavior of Asymptotically Flat Empty Spaces
Authors: Newman Ezra T. , Unti Theodore W. J.
Published: January 2005

The asymptotic behavior of the Weyl tensor and metric tensor is investigated for probably all asymptotically flat solutions of the empty space Einstein field equations. The systematic investigation utilizes a set of first order differential equations which are equivalent to the empty space Einstein equations. These are solved asymptotically, subject to a condition imposed on a tetrad component of the Riemann tensor ψ0 which ensures the approach to flatness at spatial infinity of the space-time. If ψ0 is assumed to be an analytic function of a suitably defined radial coordinate, uniqueness of the solutions can be proved. However, this paper makes considerable progress toward establishing a rigorous proof of uniqueness in the nonanalytic case. A brief discussion of the remaining coordinate freedom, with certain topological aspects, is also included.
A Note on the Scattering of Boson Fields
Authors: Shale David
Published: January 2005

A physically operational and mathematically simple definition is given for the convergence of states for a boson field. The relevant formulation of the scattering matrix is discussed. As an example, the scattering of a free Boson Field by a given linear time-independent unquantized source is treated. It is shown that cases usually called ``infrared'' and ``ultraviolet'' catastrophes are actually convergent.
Exact Eigenfunctions of Angular Momentum by Rotational Projection
Authors: Percus J. K. , Rotenberg A.
Published: January 2005

By an appropriate rotational procedure, a projection operator can be constructed to give exact eigenfunctions of angular momentum. Applications to cases involving spin and orbital angular momentum are given and, in particular, all spin multiplets of the alternant molecular structure are obtained. The connection with the group theoretical approach is discussed.
Variational Formulations of Equilibrium Statistical Mechanics
Authors: De Dominicis Cyrano
Published: January 2005

Thermodynamical functions for classical and quantum systems are expressed in terms of the one-particle density n1 and the two-particle correlation matrix C12 (or quantities in direct relation to them). Use is made of topological relations valid for the diagram representations of the grand partition function expansions. The result considered as a functional of n1 and C12 is stationary under independent variations δn1 and δC12. In particular, the entropy functional of a classical system no longer contains any reference to the equilibrium parameters (or to the interactions) and the second functional derivative is a negative definite matrix. The entropy functional of a quantum system conserves traces of the equilibrium parameters in the Lee-Yang formulation; the Green's function formulation does not, but in this case the second functional derivative is no longer a negative definite matrix.
Divergence Conditions and the Gravitational Field Equations
Authors: Pagels Heinz R.
Published: January 2005

It is shown that in addition to the four divergence laws Tαβ|β = 0, stress tensors satisfying the Einstein field equations must also satisfy the additional divergence conditions (Tγα|β−Tγβ|α)|γ=0. Conversely, under quite general assumptions these ten conditions on the source, Tαβ, dictate the metric—matter connection proposed by Einstein.
Parameter Differentiation of Quantum-Mechanical Linear Operators
Authors: Aizu Kêitsiro
Published: January 2005

Quantum-mechanical linear operators have some real-number parameters in them. The differential coefficients of functions, including eigenvalues and eigenvectors, of such an operator with respect to a parameter are calculable from the differential coefficient of the operator with respect to the parameter. The formulas for this purpose are presented together with their proofs.
Reduction of S-Matrix Elements
Authors: Syed A.
Published: January 2005

We have obtained expressions for the commutators of in- and out-fields with the generalized retarded operators of Burgoyne and Ruelle. These are then used to show that the matrix element 〈p1, ··· , pmout/−pm+1, ··· , −pnin〉,where p ≡ (p1, p2, ···, pn) is arbitrary, can be reduced in terms of retarded functions without using the assumption of stability of one-particle states.
Zeros of Hankel Functions and Poles of Scattering Amplitudes
Authors: Keller Joseph B. , Rubinow S. I. , Goldstein Max
Published: January 2005

The complex zeros νn(z), n = 1, 2, ··· of Hν(1)(z), dHν(1)(z)/dz and dHν(1)(z)/dz+iZHν(1)(z) are investigated. These zeros determine the poles in the scattering amplitudes resulting from scattering of various kinds of waves by spheres and cylinders. Formulas for νn(z) are obtained for both large and small values of |z| and for large values of n. In addition, for Hν(1)(z) and dHν(1)(z)/dz, numerical solutions are found for real z in the interval 0.01 ≤ z ≤ 7 and n = 1, 2, 3, 4, 5. The resulting loci of νn(z) in the complex ν plane are presented. These loci are the trajectories of the so-called Regge poles for scattering by spheres and cylinders.
Notes on Resolution in Scattering Measurements
Authors: Kusch P.
Published: January 2005

The instrumental factors that determine the resolution of an atomic beam apparatus in the measurement of total scattering cross sections are discussed. A definition of resolution as the minimum scattering angle for which the efficiency of detection of scattering is 50% is proposed.
Mass-Spectrometric Investigation of the High-Temperature Reaction between Nickel and Chlorine
Authors: McKinley John D.
Published: January 2005

The volatile products of the reaction between a molecular beam of room-temperature chlorine and a polycrystalline nickel surface have been identified; their formation rates have been measured by a mass-spectrometric technique at surface temperatures between 1000° and 1600°K and beam fluxes equivalent to pressures of 10—7 to 10—5 mm Hg. The surface coverage is estimated to be less than 0.1% under these conditions. NiCl and NiCl2 are formed on the nickel surface; the former is observed above 1450°, the latter below 1100°; and both are found at intermediate temperatures. About 70% of the incident chlorine is consumed by the interaction with nickel over the pressure and temperature ranges covered. The removal of chlorine and the production of NiCl and NiCl2 are first order in chlorine pressure. A mechanism which accounts satisfactorily for the results involves dissociative adsorption of chlorine to form two NiCl's on the surface; these either evaporate, or disproportionate to form NiCl2 which evaporates.
Infrared Spectra of SiH3C≡CH and SiD3C≡CH
Authors: Reeves R. B. , Wilde R. E. , Robinson D. W.
Published: January 2005

Low-resolution infrared studies of silylacetylene and silylacetylene-d3 have enabled the fundamental vibrational frequencies to be assigned to normal modes of motion. Also, many of the overtone and combination bands have been tentatively asigned. Argon-matrix spectra at 4.2°K have been helpful in assigning nearly degenerate vibrations, particularly the Si–C stretching motion. Medium-resolution spectra have enabled approximate values to be obtained for the band origins and Coriolis coupling constants of most of the perpendicular-type fundamentals.
Nonsphericalized Free Volumes for Hole Theories of Liquids
Authors: Weissmann Mariana
Published: January 2005

Free-volume integrals for hole theories of liquids were calculated for some special cases by Monte Carlo numerical integration. The dependence of the free volume on the number of nearest neighbors is thus obtained. Only molecules interacting with a Lennard-Jones potential and a temperature near the critical one have been considered. The results differ considerably from those of earlier theories, where spherical symmetry was assumed. However, the introduction of vacant cells (holes) does not improve the thermodynamic functions obtained with the cell theory of Lennard-Jones and Devonshire.
Magnetic Susceptibility of Praseodymium Oxides
Authors: Kern Sanford
Published: January 2005

Magnetic susceptibility measurements have been made on Pr2O3, PrO1.72, PrO1.83, and PrO2 from liquid-helium to room temperatures. The results are interpreted in terms of the crystal fields acting upon the cation for Pr2O3 and PrO2. For these two compounds, D3d symmetry was assumed for the disposition of oxygen ions about the cation, in order to explain the susceptibility results. A total crystal field splitting of 935 cm—1 is obtained for the ground multiplet of PrO2 and 1383 cm—1 for Pr2O3.
High-Resolution Infrared Determination of the Structure of Carbon Suboxide
Authors: Lafferty Walter J. , Maki Arthur G. , Plyler Earle K.
Published: January 2005

High-resolution spectra have been obtained and the vibration—rotation absorption spectrum has been analyzed for a Σu—Σg and a Πg—Πu transition in C3O2 between 3142 and 3195 cm—1. The absorption region studied contains a parallel combination band and a series of associated ``hot bands.'' The successive ``hot bands'' are displaced toward high frequencies in such a manner that the Σ—Σ and Π—Π bands are relatively free of overlapping lines. The analysis shows that the molecule must have D∞h symmetry with B0=0.073206 cm—1. The large number of ``hot bands,'' the variation of intensity of these with temperature, and the large value of the l-doubling constant q all indicate that the lowest frequency bending mode must be of very low energy.
Transference Phenomena in Liquid Electrolytes
Authors: Sundheim Benson Ross
Published: January 2005

Examination of transference number experiments in fused salt systems reveals that there is a nonspecific interaction with the walls of the containing cell. Attention is directed to the boundary layer on one side of which the electrolyte meets laminar boundary conditions and on the other side of which the bulk flow pattern prevails. A formal description of the phenomenon is obtained in terms of partial viscosities of each species. In fused salt systems the dimensions of the transition layer are estimated as being of the order of magnitude of the ionic radius so that the partial viscosities should be viewed as a device for treating the transition layer and not as being vested with hydrodynamic significance. In other electrolytes the boundary layer may be considerably larger.
Photosensitivity of Germanium Electrodes as a Function of Quantum Energy
Authors: Hemilä Simo
Published: January 2005

In this work the relative photosensitivities H = | Δφ/F |i=const of a germanium anode and a germanium cathode were determined as a function of quantum energy (Δφ=electrode potential change caused by light, F = quantum flux, measured in quanta/cm2 sec, and i = current density of electrode). The first increase in the photosensitivity H (Eν) of a n-Ge anode occurs at a quantum energy Eν≈0.93 eV, the second increase at Eν≈1.10 eV, and one relative sensitivity minimum at Eν≈1.27 eV. The sensitivity was approximately constant at larger quantum energies.

According to earlier experimental results, the slow phase in a dissolution reaction of Ge at a Ge anode is the breaking of the bond. The form of the sensitivity spectrum can therefore be explained on this basis. The holes, which have an excess energy for activation, break the bond of a Ge atom to the lattice immediately and lead to a fast excess reaction and to a strong photosensitivity.

The photosensitivity spectrum of a p-Ge cathode is of the same shape as that of a n-Ge anode. One may therefore make a conclusion, that the photoeffect of a Ge cathode is due to the fast dissolution reaction caused by holes with excess energy. The author proposes that this reaction is the dissolution of germanium as germane.
Heat Capacity of α-NiSO4·6H2O between 1 and 20°K. Electronic Energy Levels of the Ni++ Ion
Authors: Stout J. W. , Hadley Wayne B.
Published: January 2005

The heat capacity of α-NiSO4·6H2O has been measured over the temperature range between 1 and 20°K. The heat capacity passes through a rounded maximum of 1.51 cal deg—1 mole—1 at 2.58°K. The magnetic contribution to the heat capacity is well fitted by that calculated for the three spin states associated with the singly degenerate ground orbital level of the Ni++. From the heat-capacity data the energy spacing between the lowest and middle spin states is calculated to be 4.48±0.07 cm—1 and between the lowest and highest spin states 5.05±0.07 cm—1. The magnetic susceptibilities in the directions of the three principal axes of a Ni++ ion are calculated and, by comparison with literature data on the magnetic anisotropy and single-crystal magnetic susceptibilities, the orientations of these axes relative to the crystal axes are deduced. Data of other investigators on the magneto-optical rotation and high field magnetization are interpreted.
Absolute Quantum Yield Measurements of the NO–O Reaction and Its Use as a Standard for Chemiluminescent Reactions
Authors: Fontijn A. , Meyer C. B. , Schiff H. I.
Published: January 2005

The spectral distribution of the chemiluminescent reactions O+NO→NO2+hv has been determined over the wavelength region 3875–14 000 Å. The absolute rate constant was determined by a method of chemical actinometry which required only relative intensity measurements and which is virtually free from geometry errors. The rate constant over this spectral region was found to be 6.4×10—17 cm3 molecule—1 sec—1 within an accuracy of 30%. This reaction can be used as a standard from which the rate constants for other chemiluminescent reactions can be readily obtained without requiring detector calibration or geometry corrections.
Pariser—Parr Calculations and Electro-Optical Effects in Benzene
Authors: Donath Wilm E.
Published: January 2005

Pariser—Parr calculations were done for the singlet states of benzene using singly and doubly excited configurations. Good agreement is obtained with the experimental locations of the 1B2u, 1B1u, and 1E1u states as well as the oscillator strength of the 1A1g→1E1u transition. The 1E2g state is calculated to be 0.5 eV above the 1E1u state and its photodissociation can be deduced from its bond orders. A possible assignment of the 1A1g→1E2g transition is discussed. On the basis of this simple model, electro-optical effects are small, such as the Stark shift for the 1E1u and 1B1u states.
Electric Conductance in Liquid Hydrocarbons. II. Methyl-Substituted Benzenes
Authors: Forster E. O.
Published: January 2005

The electric conductance of methyl-substituted benzenes has been determined between 20° and 65°C both in the presence and in the absence of oxygen over a range of electric fields (50 to 1200 V/cm). Five of the six compounds studied resembled benzene in their electric behavior. Although the conduction level decreased with increasing number of substituent methyl groups, the thermal activation energy, within experimental error, was the same and was similar to that of benzene. The behavior of 1,3,5-trimethylbenzene was found to differ in all respects from the other members of this series. Its temperature dependence and over-all conduction level were, however, closely similar to that of saturated hydrocarbons, such as cyclohexane or n-hexane. The unusual behavior of this compound suggests that the available π electrons cannot participate in the conduction process. The steric arrangement of the methyl groups appears to significantly influence the conduction process. These findings have been interpreted to suggest the existence of an electron transfer mechanism involving sterically favorable molecular collisions.
Shock Front Structure in O2 at High Mach Numbers
Authors: Wray Kurt L. , Freeman Thomas S.
Published: January 2005

Shock structure measurements were made on O2 in a 24-in. diameter shock tube at initial pressures of 15 and 30 μ of Hg from Mach 4 to 21. An ultraviolet absorption technique using 1470-Å radiation was employed to monitor the density of O2 molecules. In order to reduce shock front curvature effects, the knife-edge technique was employed using only a 4-in. optical path between knife edges. The data indicate that translational and rotational degrees of freedom are excited simultaneously. At about Mach 10 vibrational excitation begins to appear in the same zone as translational and rotational excitation; by Mach 14 all these processes occur simultaneously. Around Mach 16 dissociation starts to occur in the same zone. The thickness of the shock front decreases from three ambient mean free paths at Mach 4 to 2 ambient mean free paths at Mach 10 and remains essentially constant at higher Mach numbers.
Gaseous Ion Recombination Rates. II
Authors: Mahan Bruce H. , Person James C.
Published: January 2005

An analysis of the mechanics of three-body ion recombination is given. The relative efficiencies of various gases in promoting ion recombination are calculated and found to be in satisfactory agreement with experiment. The calculations lead to qualitative conclusions about how mass, relative velocity, and the nature of the deactivation criterion affect the magnitude of the recombination rate.
Electron Traps in Colored KCl at —30°C
Authors: Hirai Masamitsu , Scott Allen B.
Published: January 2005

The photoconductive sensitivity of additively colored KCl during bleaching of the F band has been measured at temperatures between —30°C and room temperature. At —30° and —15°C, a pronounced increase in sensitivity occurs during the early stages of bleaching which indicates the presence of traps of large cross section, unstable at higher temperatures. Estimated cross sections, combined with trap concentrations deduced from optical data, are used to account for the general form of the dependence of sensitivity upon exposure.
Spectral Emission of the Helium Afterglow
Authors: Niles Franklin E. , Robertson W. W.
Published: January 2005

The spectral emission from a dc pulsed helium discharge for pressures from 5 to 30 Torr has been investigated during the early afterglow using a spectrometer with gated photomultiplier and from the early afterglow through the late afterglow using interference filters with gated photomultiplier. The afterglow spectrum was predominately that of molecular light which was attributed to the collisional-radiative recombination of molecular ions. The time-decay of molecular light at late times indicated ambipolar diffusion control by an ion with a Dap of 710±10 cm2/sec, which corresponds to a μ0 of 16.4±0.2 cm2/V·sec, in good agreement with values reported for the helium molecular ion employing other techniques.
Average Density Approximation for the Radial Distribution Function of a Fluid
Authors: Lebowitz J. L. , Praestgaard Eigil
Published: January 2005

The radial distribution function of a fluid, g(r), is directly related to the difference between the work W(r, ρ) necessary to introduce an extra particle at a distance r from the known position of a particle, and the work W(ρ) of introducing a particle at an arbitrary point in the fluid. Now a system in which one particle is kept fixed can be thought of as a nonuniform system with density ρg(r). This suggests that W(r, ρ) can be written as W(ρ*) where ρ*(r) is some appropriate effective local density. We have utilized this idea to approximate the radial distribution function using for ρ* the average density ρ̄, of the nonuniform system, with the Mayer f-function as a weighing factor. This leads to an integral equation for g(r) which we have investigated in detail for a fluid of hard spheres. When this equation is solved in a virial expansion it yields reasonably good results for the first few terms. A linearization of this equation leads to an integral equation of the type considered by Kirkwood who was first to consider this type of approximation. We obtain the solution of this linearized equation. A different approximation for ρ*, using the direct correlation function as the weighing factor is obtained by the use of functional Taylor expansion. It leads to an improvement in the virial coefficients and is shown to lead upon appropriate linearizations to either the hypernetted chain or the Percus—Yevick equations for g(r). We also discuss the rigorous form of ρ*(r).
Reactions of Photochemically Produced Hot Hydrogen Atoms. I. Photolysis of HI at 1849 Å
Authors: Martin Richard M. , Willard John E.
Published: January 2005

Spectroscopic evidence as to the primary processes caused by absorption of 1849-Å radiation by HI is evaluated and clarified as a basis for consideration of chemical reactions of the 3.6 and 2.6-eV H atoms which may be formed at this wavelength. The energetics of possible hot H reactions with HI which might raise φH2 above the value of unity observed at 2537 Å are evaluated. Experimental results are presented on the photolysis of HI by 1849-Å radiation at —78° and 25°C, showing that little or no enhancement of the yield by such hot processes occurs. Quantum yields of HI decomposition at 1849 Å of 0.5 or greater are found in HI–I2 systems where 90% of the radiation is absorbed by I2, indicating a high probability of photosensitized decomposition of HI by excited I2 molecules or of absorption of I2 fluorescence radiation by HI, or both.
Heat Capacities of Solid Deuterium (33.1%—87.2% Para) from 1.5°K to the Triple Points. Heats of Fusion and Heat Capacity of Liquid
Authors: Grenier George , White David
Published: January 2005

The heat capacities of a number of deuterium samples enriched in para content have been measured in the temperature range 1.5° to 22°K. The variation of the triple points and heats of fusion as a function of ortho—para composition have also been measured.

All the heat capacities of the solid show anomalies due to the quenching of the molecular rotation of the J = 1 species present in the mixtures. For para compositions above 60% para-D2 a sharp λ transition is observed. A linear dependance of the transition temperature with para content is observed. The high-temperature heat capacities of the solid show a dependence on ortho—para composition, suggesting a structural dependence on composition.

A calculation of the entropy from the data shows that the threefold degeneracy of the J = 1 species is completely removed at the absolute zero. An analysis of the anomalies resulting from the removal of the degeneracy confirm Nakamura's conclusions that the quenching of the molecular rotations is principally a result of quadrupolar interactions. The anomalous heat capacities of the solid, at sufficiently high temperatures, are expressed by the relation CT2/R=αx+βx2just as in the case of hydrogen. The ratio of the experimental β's for the two isotopes is in excellent agreement with the theoretical ratio. This ratio is a measure of quadrupolar interactions in the two isotopic solids.
Fluorescence and Energy Transfer in Y2O3:Eu3+
Authors: Axe J. D. , Weller P. F.
Published: January 2005

Experimental evidence for nonradiative resonant energy transfer between Eu3+ and other trivalent rare-earth ions in Y2O3 is presented and possible interaction mechanisms are examined. It is concluded that coupling via overlap of near zone quadrupolar fields is important. Measurements on the transient behavior of the Eu3+ fluorescence are also discussed.
Quantitative Measurements of Gas Phase O and N Atom Concentrations by ESR
Authors: Westenberg A. A. , de Haas N.
Published: January 2005

The general theory relating the measured integrated intensities of ESR absorption lines to the concentrations of odd electron species in the gas phase is reviewed and discussed in some detail. It is then applied in the form required for determining the absolute concentrations of O, N, and H atoms using O2 as a calibrating gas as first suggested by Krongelb and Strandberg. Experimental data are presented which verify the theoretical predictions of the intensities of various O2 lines. The determination of absolute O and N concentrations by ESR is shown to be a reliable experimental technique by comparison with the independent results of titration with NO2 and NO, respectively. Agreement of the two techniques strongly supports the validity of both. The O–NO2 titration curves enable a value for the rate constant of O+NO+O2→ lim k6NO2+O2to be evaluated at 300°K as 2.9×1016 cm6 mole—2 sec—1 in agreement with other reported values.
ESR Study of a Single Crystal of L-Cystine Dihydrochloride Irradiated at Low Temperature
Authors: Akasaka Kazuyuki , Ohnishi Shun-ichi , Suita Tokuo , Nitta Isamu
Published: January 2005

An electron spin resonance study has been made on free radicals produced in a single crystal of L-cystine dihydrochloride by irradiation at liquid-nitrogen temperature and on the process of their transformation during warming up to room temperature. All the spectra observed showed remarkable anisotropy in g factor, whereas the hyperfine structures were almost isotropic. From the analysis of the spectra the following conclusion has been drawn. The main primary radical produced at liquid-nitrogen temperature is the L-cystine dihydrochloride molecule with its S–S bond ionized probably to minus [R–CH2–S–S–CH2–R]—. At —72°C, the ionized bond is unstable and is ruptured to form the ``semistable'' radical R–CH2–S·* in which the direction of the C–S bond as well as the electronic structure remains almost unchanged from those of the parent radical. At room temperature the radical further transforms into the stable free radical R–CH2–S· in which the CH2–S group has rotated to a stable position accompanied by a change in the electronic state. The electronic structure for each radical is discussed in relation to the g factor analysis.
Influence of Vibrations on Molecular Structure Determinations. III. Inertial Defects
Authors: Herschbach Dudley R. , Laurie Victor W.
Published: January 2005

The relationships between various types of moments of inertia and vibration—rotation corrections are developed from general theory, with emphasis on the qualitative physical features and the quantities which may be calculated without knowledge of anharmonic force constants. The inertial defects of planar triatomic and tetratomic molecules and nonplanar molecules with a plane of symmetry are considered, and it is found that simple approximations, which depend mainly on the one or two modes of lowest frequency, give results within 10%—20% of the experimental values. The application of inertial defect corrections in structure analysis is illustrated for the calculation of HH distances in CH2Cl2, SiH2F2, and CH3CXO molecules (X = H, F, Cl, Br).
Molecular Theory of Dissipative Processes in Gases
Authors: McLaughlin I. L.
Published: January 2005

The velocity distribution function associated with a molecule entering a dilute gas, either in equilibrium or with a temperature gradient, is evaluated by solving a forward Boltzmann equation.

In the equilibrium case, the velocity distribution function associated with the molecules, other than the incoming molecule, is also evaluated and the contributions to the Kubo-type coefficient of thermal conduction from both distribution functions are evaluated for Maxwellian molecules. These contributions give the coefficient of thermal conduction obtained by the Chapman—Enskog method.

The various mean accelerations experienced by a molecule moving in a gas are calculated using the above solutions of the forward equation and also the solutions of a backward Boltzmann equation. These expressions are then used to evaluate the friction coefficients, first introduced by Kirkwood, for both equilibrium and nonequilibrium gases.

An experimental procedure using radioactive particles injected into a gas is also suggested as a method of confirming the obtained results.
Study of First-Order Phase Changes in a Number of Organic Crystals
Authors: Kluth E. L. E. , Clarke H. , Hogg B. G.
Published: January 2005

The change in the long lifetime τ2 for positron annihilation has been measured as a function of temperature for benzene, diphenylamine, cyclohexane, naphthalene, N-phenylbenzylamine, p-bromotoluene, and phenol. In each case, the temperature range covered a first-order phase transition.
Self-Consistent-Field Theory. III. General Treatment for Excited States
Authors: Fraga Serafin , Birss Fraser W.
Published: January 2005

The general coupling operator defined in the first paper of this series is used, in conjunction with the modified variation method due to Weinstein and MacDonald, to formulate a general self-consistent-field scheme. In principle this permits the determination of the eigenfunctions and eigenvalues of any state of an electronic system with no restrictions on orbital occupancy, symmetry, or multiplicity. A tentative generalization of the concept of a Hartree—Fock function is given and the meaning of correlation energy, in the context of the modified variation method, is discussed.
Off-Center Hydrogen Atom Calculations
Authors: Turner Almon G. , Honig Barry H. , Parr Robert G. , Hoyland James R.
Published: January 2005

Studies are carried out of truncated expansions of a hydrogen-atom 1s orbital in spherical harmonics at another center, with Coulson—Barnett and with Slater-orbital radial factors.
Raman Spectral Studies of Water Structure
Authors: Walrafen G. E.
Published: January 2005

Raman frequencies and polarizations and infrared frequencies of water and heavy water have been obtained, and the intermolecular vibrations of water have been related to a five-molecule hydrogen-bonded C2v model consistent with x-ray data. Observed variations of the integrated Raman intensity of the 175-cm—1 hydrogen-bond-stretching vibration, with variations of temperature, have been interpreted in terms of the five-molecule model. That interpretation leads to reasonable values for the enthalpy of hydrogen-bond formation. Effects of electrolyte addition on the intensity of the 175-cm—1 band are also described.
Effects of Pressure on the Resistivity of Some Organic Charge-Transfer Complexes
Authors: Schwarz Meyer , Davies Helen W. , Dobriansky B. J.
Published: January 2005

The effect of pressure on the electrical resistance of samples of several organic charge-transfer complexes was investigated over the range 1 to 15 kbars. The resistances decreased exponentially with increased pressure up to at least 6 kbars. At higher pressures, a different behavior was observed in only two complexes; their resistivities leveled off. These latter compounds had very low resistivities at atmospheric pressure.
Photoionization of Aliphatic Ketones
Authors: Murad Edmond , Inghram Mark G.
Published: January 2005

The photoionization of a series of ketones, acetone, 2-butanone, 2-pentanone, 3-methyl-2-butanone, 2-hexanone, and 4-methyl-2-pentanone was studied using mass spectrometric techniques. Adiabatic ionization potentials were determined. It was found that for the ketones the cross section above threshold is not constant, and a modified method of treatment of the results was developed in order to obtain information about fragmentation processes. The shifts in appearance potentials of fragments with increasing temperature were found to be close to the change in internally stored energy. Bond dissociation energies in ions were calculated. The adiabatic ionization potential of the acetyl radical was calculated to be 7.08 eV, which is considerably lower than reported by authors using electron impact where no effort was made to distinguish between adiabatic and vertical ionization potentials. A lower limit was calculated for the ionization potential of the n-propyl radical leading to a value of the adiabatic ionization potential of 7.2±0.2 eV.
Optical Spectra of Benzamide—Triiodide Ion Complexes : A Model of the Starch—Iodine Complex
Authors: Robin Melvin B.
Published: January 2005

Earlier work has shown that the chromophoric group in the HI3·2C6H5CONH2 complex is an infinite chain of triiodide ions linked end to end, and the close similarity of the spectra of the benzamide—triiodide complexes and the blue starch—iodine complex strongly suggests that such a chain is also the chromophore in the latter. The electronic spectrum of such a one-dimensional chain of triiodide ions is explained by first assigning the transitions in the free triiodide ion and then assuming an excitonlike coupling of these transitions in the chain. The two well known transitions of the free triiodide ion at 28 300 and 34 800 cm—1 are assigned as antibonding pi to antibonding sigma and bonding pi to antibonding sigma, respectively. The high intensity of the pi to sigma bands results from a mixing of pi and sigma orbitals due to the supposed nonlinearity of the free ion. Electrostatic coupling of the strong, long-axis pi to sigma transitions then leads to a semiquantitative understanding of the number of bands in the polymeric triiodide spectrum as well as their polarizations, intensities, and frequencies.
Virial Coefficients and the Classical Theory of Fluids for the Square-Well Potential
Authors: McQuarrie Donald A.
Published: January 2005

The term g2(r) proportional to the square of the density in the expansion of the radial distribution function in powers of the density has been evaluated for a square-well potential for the Born—Green—Yvon integral equation, the Kirkwood integral equation, the Percus—Yevick integral equation, the hyperchain approximation, and an integral equation derived by Meeron. The square-well potential used has a hard-core diameter of σ and attractive diameter of 2σ. Each g2(r) is then used to calculate Dp, the fourth virial co-efficient calculated from the pressure equation, and Dc, that calculated from the compressibility equation, for the above five liquid theories. This allows a comparison over the entire temperature range, rather than at infinite temperature, the only value given by the previously used hard sphere potential. It is shown that the Percus—Yevick equation yields virial coefficients in best agreement with the exact value over a large temperature range. All the results presented are low-order polynomials in f=exp(ε/kT—1), where ε is the depth of the well, and reduce to the hard-sphere results when f goes to zero.