bluuebunny/crossref_metadata_2025_split huggingface dataset:
Molecular Rotation in the Solid State. Theory of Rotation of Trapped Molecules in Rare-Gas Lattices
Authors: Flygare W. H. 
Published: January 2005

A theory is presented to explain the rotational perturbations experienced by a molecule trapped substitutionally in a rare-gas lattice at low temperatures (4°—20°K). The nonbonded repulsive interaction due to the Pauli exclusion principle between the molecule and the host lattice has been ignored in preference to the multipole charge interaction. In the case of an octahedral substitutional trapping site the dominant interacting term is the rotation of a permanent molecular hexadecapolar charge distribution interacting with the fourth gradient of the electric potential at the molecular center of mass due to all of the lattice charges. A general method of computing the fourth gradient of the potential due to the rotational independent induced-dipole—induced-dipole effect is given in the Appendix in terms of the molecular and atomic polarizabilities and ionization constants. Matrix elements are given for linear, spherical-top, symmetric-top, and asymmetric-top molecules.
The theory for a trapped linear molecule is applied to the vibration—rotation data of HCl trapped in an Ar lattice yielding a value of the single molecular hexadecapole moment in HCl of 3.9×10−42 esu cm4. Other effects discussed are: (1) higher-order terms in the potential expansion, (2) isotopic substitution in the molecule, and (3) the rotation of HCl in the other rare-gas lattices.
Pair Distribution Function of a Hard Sphere Bose System Calculated by the Pseudo-Potential Method
Authors: Garcia-Colin Leopoldo S. 
Published: January 2005

The pair distribution function for a hard sphere Bose system has been calculated by using a method in which the hard sphere potential is replaced by the so-called pseudo-potential. The problem is carried through using the quasi-particle formalism of Bogoliubov. In this calculation one considers a system of bosons interacting via the pseudo-potential which can be regarded as a weak interaction when the system is very dilute. The Hamiltonian of the system is diagonalized by means of a canonical transformation which has the effect of separating the energy into two parts, one of which is the ground state energy and the other corresponds to an ideal Bose gas composed of ``elementary excitations'' or ``quasi-particles.'' This formalism is applied to the calculation of the pair distribution function. This quantity is calculated by averaging over a grand canonical ensemble constructed with the total number of elementary excitations. A result which is seen to be valid both for the condensed and gaseous phases of the system and also for any distance r between the particles is obtained.
A discussion of the difference between these results and the ones obtained in a previous calculation and a comparison between both results and the experimental ones is also given.
A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field
Authors: Araki Huzihiro 
Published: January 2005

Von Neumann algebras associated with the normal representation of canonical commutation relations are studied. Corresponding to each subspace of a real Hilbert space (test function space), a von Neumann algebra on another complex Hilbert space (the Fock space) is defined. This correspondence is proved to be an isomorphism between a certain complemented lattice of subspaces and that of the von Neumann algebras. This result has an application to the duality theorem in the theory of a free scalar field, which is to be discussed in a separate paper.
A necessary and sufficient condition on a subspace, in order that the corresponding von Neumann algebra is of type I, is obtained.
The Remainder in Mayer's Fugacity Series
Authors: Penrose Oliver 
Published: January 2005

Upper and lower bounds are obtained for the remainder after a finite number of terms of the expansions in powers of fugacity z for the pressure p, the s-particle distribution functions, the density ρ, and the fugacity coefficient z/ρ, for a system of particles with two-body interactions. The interaction potential must be either nonnegative or else have a hard core and decrease faster than r−3 at large distances. The results hold for all positive z, and apply to lattice gases as well as to fluids.
For nonnegative potentials, the results imply that successive partial sums of each of these fugacity expansions provide alternate upper and lower bounds, valid even if the series diverges, on the physical quantity the expansion represents.
Correlation Functions and the Critical Region of Simple Fluids
Authors: Fisher Michael E. 
Published: January 2005

The ``classical'' (e.g. van der Waals) theories of the gas-liquid critical point are reviewed briefly and the predictions concerning the nature of the singularities of the coexistence curve, the specific heat, and the compressibilities are compared critically with experiment and with the analytical and numerical results for lattice gas models.
The critical singularities are related to the behavior of the pair correlation function G(r) = g(r) − 1 and the Ornstein-Zernike theory of critical scattering is reviewed. Alternative derivations of the theory are discussed and its validity is assessed in relation to experiment and to more detailed theoretical calculations. The nature and magnitude of the expected deviations from the ``classical'' theory are described. The analogies with critical magnetic phenomena are mentioned briefly.
On the Reduction Formula of Feinberg and Pais
Authors: Bollini C. G. , Giambiagi J. J. , Domínguez A. González 
Published: January 2005

Feinberg and Pais have considered a ``reduction'' formula for the Fourier transform of functions which depend only on the hyperbolic distance. They have shown that the formula is valid in particular cases and stated that it should be valid in general.
We show that it is valid for any causal distribution and furthermore that it is actually an extension of the well-known Bochner Theorem on the Fourier transform of radial functions.
S-Matrix Theory and Double Scattering
Authors: Iagolnitzer Daniel 
Published: January 2005

In the double scattering case, we show that the introduction of a pole in the S-matrix elements, is consistent with a description in terms of successive interactions.
We then show that among Olive's class of possible ``propagators'' c(k2 - m2 + iε)−1 - (1 - c) ·(k2 - m2 - iε)−1, only the usual value c = 1 gives a consistent result.
Correlation Functions and the Coexistence of Phases
Authors: Fisher Michael E. 
Published: January 2005

We discuss the existence, continuity and other properties of the canonical and grand canonical many-particle correlation functions ns(r1, … rs) in the thermodynamic limit of classical and quantum mechanical systems.
If the pressure of the system for fixed T is constant in the range of specific volume va to vb, one expects physically to observe the coexistence of two separated phases. In terms of the correlation functions this is expressed by ns(v)=xa(va/v)ns(va)+xb(vb/v)ns(vb),where x and xb are the mole fractions of the phases so that v = xava + xbvb. With the aid of various lemmas on convex functions we prove that such a ``separation of the phases'' follows rigorously from statistical mechanics provided the correlation functions are ``well defined'' in an appropriate sense.
Cluster-Star Inversion by Means of Generating Functionals
Authors: Stell G. 
Published: January 2005

The cluster-star equations are inverted. These equations, Eq. (2.1), define a set of cluster functions Um in terms of star functions Vn for 2 ≤ n ≤ m. The inversion, Eq. (2.2) gives the Vn in terms of the Um; 2 ≤ m ≤ n.
The cluster-star inversion yields the coefficients βn that appear in the number-density expansion of the logarithm of the grand partition function Ξ of a statistical mechanical system in terms of the coefficients bn that appear in its fugacity expansion, even when the system is in the presence of an external field.
In the course of obtaining the inversion, an expression for the work necessary to bring a particle from infinity to a point r inside a classical system at equilibrium is obtained in terms of the Vm and the one-particle distribution function ρ(r), and also in terms of the Um and ρ. The expression in terms of the Vm and ρ has been previously derived by others with restrictions on the form of the potential energy; the alternative expression in terms of the Um seems to be new.
Operators with essentially the same algebraic structure as the Vm appear in a recently considered asymptotic expansion of the distribution functions of a nonequilibrium system. The cluster-star inversion facilitates the determination of these operators in terms of the solution operators of the n-body Liouville equation, n ≥ 2.
Trace Formalism for Quantum Mechanical Expectation Values
Authors: Langerholc John 
Published: January 2005

The trace of a positive bounded operator in a Hilbert space is defined and shown to be independent of the basis used in the definition. The trace of the product WA is defined for bounded A and positive bounded W with unit trace and is also shown to be basis-invariant. An integral representation is derived and used to define Tr(WA) for unbounded A. Linearity, isotony, and continuity with respect to uniform covergence are proved for Tr(WA) as a function of (bounded) A. Several formulas used in statistical mechanics are derived, and it is proved that if A and B are commuting positive operators, then Tr(W(A + B)) = Tr(WA) + Tr(WB). A counter example is given which shows that the commonly used definition of Tr(WA) in terms of an orthonormal basis is not invariant under permutation of the basis vectors even in the case of a very simple unbounded operator A.
An expectation-value function M which associates the expectation value M(A) to the operator A is assumed given and subject to certain restrictions. For bounded operators, these include positivity, normalization, additivity, and a condition which may be considered as a requirement of regularity for the probability function induced by M. Modifications of these requirements are imposed for unbounded operators, and von Neumann's statistical formula is proved: there is a unique bounded positive operator W with unit trace for which M(A) = Tr(WA). The requirements placed on M are weaker than those of von Neumann, and are in fact satisfied by Tr(WA) as a function of A.
Homogeneous Solutions of the Einstein-Maxwell Equations
Authors: Ozsváth István 
Published: January 2005

In this paper the solutions of the Einstein-Maxwell equations are investigated under the assumption that the metric of the space-time and the electromagnetic field are invariant under the transformations of a four-parametric, simply transitive group.
The results can be summarized as follows: In the case of null electromagnetic fields there are two different possibilities; If Λ = 0, all the solutions are Robinson waves; if Λ ≠ 0, there exists only one solution, first given here by (6.26). There exist no other solutions for null electromagnetic fields. In the case of nonnull electromagnetic fields two solutions are found. One metric is known having been first given by Robinson; we give a new solution of type I. The question as to whether there are solutions different from these remains open.
Studies in Perturbation Theory. IX. Connection Between Various Approaches in the Recent Development—Evaluation of Upper Bounds to Energy Eigenvalues in Schrödinger's Perturbation Theory
Authors: Löwdin Per-Olov 
Published: January 2005

The treatment of Schrödinger's perturbation theory based on the use of a series of inhomogeneous differential equations of iterative character is briefly surveyed. As an illustration, the method is used to derive the general expression for the expectation value of the Hamiltonian to any order which provides an upper bound for the ground-state energy. It is indicated how the well-known theory for inhomogeneous equations may be utilized also in this special case.
The solution of the Schrödinger equation by means of the partitioning technique and the concept of reduced resolvents is then treated. It is shown that the expressions obtained are most conveniently interpreted in terms of inhomogeneous differential equations. A study of the connection with the first approach reveals that the two methods are essentially equivalent, but also that the use of reduced resolvents and inverse operators may give an alternative insight in the mathematical structure of perturbation theory, particularly with respect to the ``bracketing theorem'' and the use of power series expansions with a remainder. In conclusion, it is emphasized that the combined use of the two methods provides a simpler and more powerful tool than any one of them taken separately.
Far-Ultraviolet Spectrum of Ethylene and Ethylene-d4
Authors: McDiarmid Ruth , Charney Elliot 
Published: January 2005

The ultraviolet absorptions of the V←N transitions of C2H4 and C2D4 have been reinvestigated. The strongest observed bands are found to fit the empirical expressions: C2H4, ν̄ (cm−1)=46 697+807ν; C2D4, ν̄ (cm−1)=46 948+547ν. From the ratio 807/547 of the corresponding term differences of the two isotopic species, geometric considerations and group theoretical arguments, the frequencies 807 (C2H4) and 547 (C2D4) cm−1 are concluded to be the torsional frequencies in the V state. In the V state the two CH2 groups are consequently deduced to be skewed. Another frequency, 150 cm−1 in C2D4 has been observed but not interpreted.
An analysis of the torsional progression shows the torsional potential of the V state to be parabolic. If a parabolic potential is also assumed for the ground state, the experimental and theoretical energy-level diagrams are shown to be in reasonable agreement.
Mössbauer Resonance Studies of Ferrous Ions in Ice
Authors: Nozik Arthur J. , Kaplan Morton 
Published: January 2005

Mössbauer resonance experiments have been carried out over a wide temperature range on frozen aqueous solutions of ferrous chloride and ferrous sulfate. Well-resolved spectra were obtained which show the two-line absorption pattern characteristic of a nuclear quadrupole hyperfine interaction in 57Fe. Measurements of quadrupole splitting, resonance linewidths, and anisotropic intensities were made as a function of temperature and for samples with different temperature histories. Upon quenching from the liquid state to −196°C, hexaquo ferrous ions are trapped in the ice lattice and induce the formation of cubic ice, rather than the stable hexagonal form. Warming of the quenched sample to −80°C causes a nonreversible transformation to hexagonal ice and associated pronounced changes in the Mössbauer spectrum. Analysis of the experimental data, and comparison with results obtained for the crystal FeSiF6·6H2O which contains hexaquo ferrous ions, has permitted a detailed description of the symmetry properties of ferrous ion in ice. In hexagonal ice, the ferrous ion is located at the center of an axially ``squashed'' octahedron of water molecules, the ground state wavefunction being the orbital singlet | xy 〉. The temperature dependence of the quadrupole splitting in hexagonal ice is consistent with a crystal-field axial splitting δ∼700 cm−1. In cubic ice, the symmetry contains a rhombohedral field component which can be fitted with splitting parameters Δ1∼450 cm−1 and Δ2∼950 cm−1. A model is suggested for the structure of ferrous ion in cubic and hexagonal ice. The model satisfies the necessary symmetry requirements and is consistent with the observed anisotropic Mössbauer intensities in hexagonal ice and isotropic intensities in cubic ice.
Several interesting phase changes in the ice—salt systems have been observed. In ferrous chloride frozen solutions, the sharp disappearance of the Mössbauer effect above −40°C is associated with eutectic formation. Also, by careful temperature treatment, the hydrate FeCl2·6H2O has been produced (it is unstable above −10°C) and its Mössbauer spectrum in ice was obtained. In the ferrous sulfate experiments, complex precipitation phenomena were observed and are not well understood.
Note on the Algebraic Aspect of the Integration of a System of Ordinary Linear Differential Equations
Authors: Wichmann Eyvind H. 
Published: January 2005

In this note the Lie algebra generated by the coefficient matrix of a system of ordinary, linear, first-order differential equations is considered. A systematic discussion, based on some well-known results in the theory of Lie albegras, is given for the reduction of the problem of integration of such a system. For the purposes of this note the integration of a system of equations for which the coefficient matrix does not depend on the independent variable is regarded as ``elementary.'' It will be shown that the problem of integrating any system of linear ordinary differential equations can be reduced to the problem of integrating a set of such systems, each one of which has the property that the corresponding Lie algebra is simple, and in such a way that the sum of the dimensionalities of the Lie algebras of the reduced systems in the set does not exceed the dimensionality of the Lie algebra of the original system.
The application of the reduction principle to the equations of motion in classical mechanics and in quantum mechanics is considered. It is shown that the principle in question applies to a class of Hamiltonian equations of motion not customarily regarded as describing linear systems.
Simple Realizations of the Infinitesimal Generators of the Proper Orthochronous Inhomogeneous Lorentz Group for Mass Zero
Authors: Lomont J. S. , Moses H. E. 
Published: January 2005

A realization of the infinitesimal generators for the mass-zero case of the proper orthochronous inhomogeneous Lorentz group is given explicitly for both continuous and discrete spin cases in terms of a uniform notation. The realization for the discrete spin case is unitarily equivalent to that given by Shirokov.
For the sake of completeness the infinitesimal generators for the case of nonzero mass, derived by Foldy, are also given. Hence the present paper contains realizations for all irreducible unitary representations of the inhomogeneous Lorentz group of physical interest.
Since the irreducible representations of the two-dimensional Euclidean group play an important role in the massless case, simple realizations of the irreducible representations of the generators of this group are also given.
Studies in Nonequilibrium Rate Processes. V. The Relaxation of Moments Derived from a Master Equation
Authors: Shuler Kurt E. , Weiss George H. , Andersen Knud 
Published: January 2005

A study has been made of the relaxation of the moments of probability distributions whose time evolution are governed by a master equation. The necessary and sufficient condition for the first moment, M1(t), to undergo a simple exponential relaxation is found to be ∑ n=0∞nAnm=βm+γ,where Anm is the transition probability per unit time for transitions from state m to n, and where β and γ are constants. The necessary and sufficient condition under which the first k moments, M1(t), M2(t), ···, Mk(t), satisfy a closed system of linear equations is found to be ∑ n=0∞nrAnm= ∑ i=0kβrimi.Near equilibrium, i.e., as t → ∞, all the moments Mr(t) obey, to a good approximation, a simple exponential relaxation law irrespective of the form of the Anm.
For systems described by the Fokker-Planck equation ∂P(x, t)∂t=−∂∂x [b1(x)P(x, t)]+12∂2∂x2 [b2(x)P(x, t)],the necessary and sufficient condition that the first moment M1(t) undergo a simple exponential relaxation is found to be b1(x) = βx + γ and the necessary and sufficient condition for the 2nd moment, M2(t) to have a simple exponential relaxation is 2xb1(x)+b2=β22x2+γ2. It is shown that these conditions are equivalent to the conditions on the Anm stated above.
Asymptotic Properties of the Wave Function for a Bound Nonrelativistic Three-Body System
Authors: Slaggie E. Leo , Wichmann Eyvind H. 
Published: January 2005

The asymptotic properties of a Schrödinger wave function which represents the bound ground state of a system of three interacting particles are examined. It is assumed that the interaction can be described by a static potential which is the sum of three two-body potentials and one three-body potential, where the potentials have the property that if any one of the particles is separated from the other two by a distance which tends to infinity, then the part of the potential energy which depends on the position of that particle tends to zero. The problem is treated nonrelativistically. Decreasing exponential bounds on the ground-state three-body wave function are established in configuration space. It is shown that these bounds depend only on the masses of the three particles, on the ground-state energy of the three-body system, and on the lower bounds on the spectra of the Hamiltonians for the three two-body systems arising when one of the three particles is removed and the remaining two interact through the corresponding two-body potential.
It is furthermore shown that the three-body wave function in momentum space admits of analytic continuation into a tube-region in complex momentum space, which tube-region is the product of real momentum space and a convex bounded region in imaginary momentum space. The tube-region is explicitly determined.
The implications of the results for the theory of the vertex function in quantum field theory are discussed. The relevancy of the results obtained in this paper to the variational computation of energy levels and wave functions of three-body systems is also briefly discussed.
In the course of the derivation some generalizations are pointed out; in particular, the final results remain valid for a class of more general interactions, which cannot be described by static potentials. Likewise, the results remain valid for a class of spin-dependent interactions.
Ion—Molecule Reactions in Methane and in Ethane
Authors: Derwish G. A. W. , Galli A. , Giardini-Guidoni A. , Volpi G. G. 
Published: January 2005

Ion—molecule reactions in methane, in methane—methane-d4 mixture, and in ethane have been studied up to a pressure of 0.08 Torr in the ion source of the mass spectrometer.
Ionization-efficiency curves, appearance potentials, and pressure-dependence studies have allowed the parent—daughter ion relationship and the cross sections of the pertinent reactions to be determined.
Influence of Atomic Masses on the Coriolis Coupling Coefficients in Some Symmetrical Molecules. I. Tetrahedral XY4-Type Molecules
Authors: Cyvin S. J. , Brunvoll J. , Cyvin B. N. , Kristiansen L. A. , Meisingseth E. 
Published: January 2005

Coriolis coupling coefficients (ζ values of tetrahedral XY4 molecules are studied in relation to the same quantities of the Z4 tetrahedron. The existence of upper and lower limits is proved for the ζ values of XY4. In particular, one has |ζ24|→1/2 and ζ44→1/2 as the upper limits with increasing atomic mass ratio mY/mX. The same values, which are independent of the force constants, are found in the Z4 model, where the central atom is absent. Lower limits are also derived for |ζ24| and ζ44, but appear to be functions of the force constants.
Calculated ζ24 and ζ44 values for 36 molecules of the tetrahedral XY4 type are reported, and are studied as function of the atomic mass ratio. The regularities that have been observed are presented graphically.
Carbon tetrahalides, methanes, and silanes are the molecules which have been studied most extensively, and for which the applied force constants are reported.