bluuebunny/crossref_metadata_2025_split huggingface dataset:
Low-Energy Expansion of Scattering Phase Shifts for Long-Range Potentials
Authors: Levy Bertram R. , Keller Joseph B. 
Published: January 2005

Phase shifts can be used to describe the quantum mechanical scattering of a particle by a spherically symmetric potential. They are odd functions of the wave number k, which is proportional to the square root of the energy of the incident particle. For short-range potentials, they are analytic at k = 0 and can be expanded in odd powers of k. However for long-range potentials they are not analytic at k = 0 so they cannot be expanded in powers of k. Since electron-atom, atom-atom, proton-neutron, and multipole-multipole potentials are of long range, it is important to consider such potentials. A method is presented for determining the appropriate expansions around k = 0. The method is applied to potentials which are O(r−v) as r → ∞, and the phase shifts for any angular momentum are obtained up to and including the first nonanalytic term. For L = 0 and 3 &lt; v &lt; 4 the next term is also obtained. The nonanalytic terms involve ln k and fractional powers of k. The results for v = 4 and the k dependence for v = 2L + 3 agree with those obtained in a different way by O'Malley, Spruch, and Rosenberg.
The method involves a function η(r) whose asymptotic value η(∞) is the desired phase shift. A nonlinear first-order ordinary differential equation is derived for η(r). This equation is solved by expansion and iteration methods. To expand the solution around k = 0, two simple theorems are proved concerning the asymptotic forms of certain integrals containing a parameter.
Lattice Statistics-A Review and an Exact Isotherm for a Plane Lattice Gas
Authors: Fisher Michael E. 
Published: January 2005

Progress in the theory of lattice statistics is reviewed with emphasis on the use of series expansions to study the critical behavior and on the exact results obtained by transformation theory. Recent work is reported which indicates that the magnetization of the three-dimensional Ising model vanishes as (Tc − T)β with β≃516, while the low-temperature susceptibility diverges as (Tc − T)−γ with γ=54(γ=74 in two dimensions). An Appendix is devoted to a detailed tabulation of the exact numerical values and best estimates for the critical temperatures, energies, specific heats, entropies, magnetizations, and the ferro- and antiferromagnetic susceptibilities of four plane lattices and the simple, body-centered, and face-centered cubic lattices.
A square lattice gas with infinite nearest-neighbor repulsions and weak second-neighbor attractions (across alternate squares) is solved exactly for one particular temperature by transformation. The gas undergoes a transition at a density ρt=142, the corresponding form of the isotherm being p−ptkT=α(ρt−ρ)ln α |ρt−ρ|,where α=π(1+342), so that the isothermal compressibility becomes logarithmically infinite.
Stationary Entropy Principle and Renormalization in Normal and Superfluid Systems. II. Diagrammatic Formulation
Authors: De Dominicis Cyrano , Martin Paul C. 
Published: January 2005

Quantum statistical mechanics is renormalized, that is, the thermodynamical functions and the ``bare'' ν-body potentials vν occurring in the Hamiltonian are expressed as functionals of the ν-body distribution functions Gν (the expectation values of 2ν field operators). The field operators are considered as having two components (creation and annihilation), and Gν thus has (2)2ν components. The renormalization is carried out for superfluid Bose systems for which it is necessary to consider the expectation values of 2ν = 1, 2, 3, 4 operators. Superfluid Fermi systems and normal systems appear as particular cases, described by expectation values of 2ν = 2, 4 operators.
This problem, dealt with by algebraic methods in part I, is attacked here by diagrammatic methods. These methods are more dependent on convergence properties but the resulting functionals are obtained explicitly as power series of the Gν′s, the general term being represented by a class of diagrams characterized by their topological structure.
In the final result, the entropy is exhibited as an explicit functional of the distribution functions Gν, (2ν = 1, 2, 3, 4), or more precisely, of functions directly related to them. This functional no longer involves the potentials (nor the equilibrium parameters). It is stationary under independent variations of the Gν′s, subject to the constraints of constant energy and particle number. The four equations of stationarity exhibit each function vν as a functional of the Gν′s, self-consistently defining these distribution functions.
Some Exact Radial Integrals for Dirac-Coulomb Functions
Authors: Reynolds J. T. , Onley D. S. , Biedenharn L. C. 
Published: January 2005

The zero energy loss Dirac-Coulomb integrals are evaluated using the technique of contour integration. The expressions obtained have a closed analytic form, showing that these integrals are formally similar to the corresponding classical and nonrelativistic quantum mechanical, zero energy loss integrals which also have exact elementary solutions.
Application of the zero energy loss Dirac-Coulomb integrals occurs in inelastic electron scattering and similar problems. The investigation of the finite energy loss Dirac-Coulomb integrals requires a study of the zero energy loss integrals as a preliminary.
Diffraction by a Smooth Transparent Object
Authors: Chen Yung Ming 
Published: January 2005

In previous investigations the so-called geometrical theory of diffraction was established. Its application has been limited to problems of diffraction of waves by smooth opaque objects.
In the present paper, the geometrical theory of diffraction is extended and applied to problems of diffraction by a smooth transparent object of any shape. For simplicity only scalar fields and two-dimensional problems are considered. However, this method can be modified easily to apply to vector fields and three-dimensional problems.
In Part I, the fields associated with the geometric rays and the diffracted rays are constructed in detail for the case of a circular cylinder. Afterwards a general method for treating diffraction by a smooth transparent cylinder of arbitrary shape is given. In order to determine the coefficients, the exact solution for the case of a circular cylinder is found and evaluated asymptotically for large ka in Part II. Then it is compared with the solution obtained from geometrical theory in Part I.
Two-Photon Ionization of Atomic Hydrogen. II
Authors: Zernik W. , Klopfenstein R. W. 
Published: January 2005

This paper contains a generalization of results described in previous work. A general formula is given for the total cross section for two-photon ionization of a hydrogenic state. An implicit method for evaluating the second-order radial matrix elements that occur in this expression is described in detail. Numerical results were obtained for the states with principal quantum numbers n = 1 through 5. It is concluded that, when both one-photon and two-photon ionization are energetically possible, the effect of the latter may be expressed as an intensity-dependent correction to the Gaunt factor which may therefore be written as G = g1 + ζIλ3g2. Here g1 is the usual Gaunt factor, I is the intensity of the light in W cm−2, λ is the wavelength in cm, g2 is a dimensionless factor of order unity, and ζ is a constant given by ζ = 0.1504 W−1 cm−1. Graphs of g2 are given as a function of electron energy.
These results do not include the effect of three-photon processes, which can also contribute to the first-order intensity-dependent correction to the Gaunt factor as a result of interference between the first- and third-order amplitudes.
Formalization of the Lagrangian, the Hamiltonian, and Related Concepts
Authors: Pease M. C. 
Published: January 2005

We consider linear system of finite dimensionality in which the system matrix is a well-behaved function of the independent variable—z or t. The system is assumed to obey a conservation law with zero signature, but is otherwise unrestricted. Using what we call the ``vectorial derivative,'' it is shown that we can obtain Lagrangian and Hamiltonian functions in terms of which the system behavior is described in the usual way. Thus, the methods of classical physics are made available for the study of such systems, without the physical connotations usually carried by such functions.
In carrying out this formalization, we define a functional—e.g., the Hamiltonian—and, at the same time, define the operator that generates the function. It is shown that the interrelation of two functionals involves the appropriate commutator of the operators involved. For example, the Poisson bracket of a functional, F, and the Hamiltonian, H, is the functional obtained from the operator Γ[ΓH, ΓF], where Γ=(O I−I O)and F and H are the operators involved in F and H. The analogy to quantum mechanics is striking.
Finally, it is shown that the contact transformations that preserve the Hamiltonian operator form a rotational system in the Lie algebra, L, in which ΓH is embedded. That is, they obey equations of the form M = [ΓH, M]. It follows, then, that all H-preserving transformations can be split into components in the intersection of the Γ-unitary group and either L or a subspace derived from L.
Null Fields in Einstein-Maxwell Field Theory
Authors: Wyman M. , Trollope R. 
Published: January 2005

The role of the electromagnetic null field, within the framework of classical relativistic electrodynamics, has never fully established. The object of this paper is to present a large class of exact solutions to the Einstein-Maxwell null field equations with the hope that the physical implications of these solutions may lead to a more thorough understanding of these fields.
In the present analysis, it appears that the nature of the solutions depends on the form of the propagation vector. In the cases for which the divergence of this vector vanishes, an extensive class of solutions is obtained and particular examples are considered. The analysis of the case when the divergence is nonzero is far from complete and only a particular solution is given.
Transformation from a Linear Momentum to an Angular Momentum Basis for Relativistic Particles of Nonzero Mass and Any Spin
Authors: Moses H. E. 
Published: January 2005

The infinitesimal generators of the inhomogeneous Lorentz group have been given in a basis in which the components of the linear-momentum operators are diagonal and in another basis in which the square of the angular momentum is diagonal for all unitary irreducible ray representations of the group. In a previous paper we showed how the two bases were related for representations corresponding to zero mass and any finite spin. In the present paper we show how the two bases are related for representations corresponding to nonzero mass and any spin. Thus this paper and the preceding one enable us to expand relativistic plane waves into relativistic spherical waves and vice-versa for particles of any spin and any mass.
In the previous paper we used the relation between the linear- and angular-momentum bases to integrate the infinitesimal generators in the angular-momentum basis and thereby obtain closed expressions which show how the angular momentum of particles of zero mass and any finite spin transform under changes of frame of reference. Similar use could be made of the transformation of the present paper. Results of such use will be given in a later paper.
General Operator Potential for the Two-Nucleon System
Authors: Tharrats J. , Cerceau O. , Rojo O. 
Published: January 2005

The interaction between two nucleons is assumed to be described by a general Hermitian operator having certain symmetry and invariance properties.
It is shown that the usual phenomenological potentials employed in dealing with the two-nucleon system, i.e., nonlocal, velocity-dependent and hard-core, are related by means of unitary transformations of the interaction operator. In addition it is shown that another such transformation of the total Hamiltonian operator leads to the effective mass formalism. Some numerical results on phase shifts are compared with most accepted values.
The Stability of Many-Particle Systems
Authors: Fisher Michael E. , Ruelle David 
Published: January 2005

It is shown that a quantal or classical system of N particles of distinct species α,β = 1, 2, … μ interacting through pair potentials φαβ(r) are stable, in the sense that the total energy is always bounded below by −NB, provided φαβ(r) exceeds some φαβ(2)(r) whose Fourier transform φ̂αβ(p) corresponds to a positive semidefinite μ × μ matrix for all p.
This result is applied to discuss ``charged'' systems and stability is proved for Coulomb interactions if the charges are somewhat smeared rather than concentrated at points. For a large class of potentials it is shown that classical instability implies quantum instability in the case of bosons and, in three or more dimensions, also of fermions. Quantum systems with Coulomb interactions (point charges) are discussed and it is shown in particular that their stability cannot depend on the ratios between the masses of the particles.
Model of an Oscillating Cosmos which Rejuvenates during Contraction
Authors: Schmidt Helmut 
Published: January 2005

For an oscillating cosmos we assume time-symmetric initial conditions, invariant under t→ —t and t→ T + t, where t = 0, ±T, … are the times of maximal cosmos contraction. In particular we specify the same value U0 for the cosmos' ``internal energy'' U at all these times. The expectation value of an Heisenberg operator becomes now 〈Q(t)〉 = Tr {Q(t) D}, with D=[A(T),A(0)]+/2 Tr {A(T)A(0)}. Here A(0) is the projector into the space of the eigenvectors of U with eigenvalue U0, and A(t) has the time dependence of an Heisenberg operator.
The time symmetry implies that the cosmos' oscillations are periodic and that expansions and contractions occur (except for local statistical fluctuations) time-symmetrically to each other: If the entropy increases during expansion then it must decrease during contraction.
The general theory is applied to a highly simplified cosmos model in which no star condensation occurs. Assuming here that the initial state contains equal numbers of particles and antiparticles, the theory predicts a slightly inhomogeneous distribution of these particles such that during the cosmos' expansion not all particles annihilate, but a realistic density of particles and antiparticles (in different space regions) survives the expansion.
Covariant Conservation Laws for General Relativistic Exploding Matter
Authors: Droz-Vincent Philippe H. 
Published: January 2005

In this paper we attempt a general relativistic extension of some simple notions, e.g., total angular momentum, so far correctly defined only in the frame of special relativity. The mathematical aspect of the problem leads us to ask, given a tensor of vanishing divergence, how to construct an integral object, conserved in time and covariant.
A formalism based upon bitensors ensures the covariance, while the assumption of an exploding (or imploding) schema of matter seems to be the only available means to preserve conservation when the space-time is curved. This can be formulated in a general theorem then applied to different physical situations. The total linear momentum occurs as a vector fixed at the point of explosion (or implosion). Its length turns out (at least when a pure matter schema is concerned) to be superior to the total mass of the fluid. The excess appears as the energy carried by the explosion. The case of a so called ``uncompressible'' holonomic fluid gives a quite analogous result. In order to find a nontrivial angular momentum we also consider, in the last section, the case of a fluid possessing an intrinsic spin density. Both linear and angular momenta are conserved and covariantly defined. Moreover, they reduce to the conventional ones when the curvature vanishes.
Solution of very Singular N/D Equations—An Approach to Nonrenormalizable Field Theory
Authors: Halpern Martin B. 
Published: January 2005

In this paper, we find closed form solutions to unsubtracted and once-subtracted N/D equations, both nonrelativistic and relativistic, with pathological left-hand absorptive parts that increase at large ν like α(−ν) ∼ −λνm, m not necessarily integral. The solutions allow dispersive, unitary and regulator-free calculation in nonrenormalizable field theory. For example, N/D equations with exchange of a higher spin particle (spin 32 etc.) can be solved. In general, the technique allows the use of a large class of divergent graphs as input, that is, those whose left-hand absorptive parts are finite, although asymptotically ill behaved. For example, in the W theory of leptonic weak interactions, one of the possible inputs is any number of ladder graphs cut so that all the bosons are on the mass shell. Many nonplanar graphs can be included as well. In much the same way, we can also calculate in the Fermi theory, (multiple exchanges in) theories of higher spin in general, and theories with derivative coupling.
There are an infinite number of solutions to these singular integral equations, each of which is characterized by a branch point at g2 = 0, and a branch point of oscillatory nature at infinite |ν|. Out of these, we pick the solution which sums the iterative expansion of the equations as most meaningful. It is seen explicitly that the unitary requirement generates its own regulation in the form of rapid oscillations at large unphysical energies, thus eliminating the need for any regulator limiting process. The oscillations are associated with an infinite number of ghosts, but these stay very far from the physical region. In addition, the solutions violate unitarity in the cross channels, so we expect the program to be useful at most in and near the physical region. As shorter range forces are systematically included, there is some indication that the program may converge rapidly for small physical energies.
Spectrum of the Scattering Integral Operator in the Physical Energy Sheet
Authors: Meetz K. 
Published: January 2005

The kernel of the integral equation for the nonrelativistic scattering of a spinless particle by a potential —λV can easily be symmetrized, if V has a definite sign. Under suitable conditions for the potential the symmetrized kernel is square integrable and generates a completely continuous transformation of the space L2 that has a pure point spectrum.
The scattering kernel is a two-valued function of the energy s. For negative real values of s in the first Riemann sheet it is symmetric (Hermitian) and can be spectral decomposed in the usual way. Eigenvalues and eigenelements can be analytically continued, at least into the first s sheet and even into the finite second s sheet, if the potential decreases faster than any exponential function for r → ∞. Eigenelements at two complex conjugate points s, s* form a complete biorthogonal system of L2. The original and the resolvent kernel can be expressed in terms of that system and the eigenvalues, for s in the first and eventually finite second sheet.
If the potential is indefinite, the scattering kernel is of polar type for negative real s and can be represented in terms of polar eigenvalues and eigenelements. These may be continued in the same way as for a definite potential.
The distribution of eigenvalues in the λ plane is studied for arbitrary complex s and related to the occurrence of bound states and resonances. It is shown that Born expansions for resolvent quantities do converge, if and only if neither λV nor —λV create bound states.
Energy Transfer in Charge-Transfer Complexes. III. Intersystem Crossing
Authors: Christodouleas N. , McGlynn S. P. 
Published: January 2005

The quantum yield ratio of phosphorescence to fluorescence, φp/φf, of the donor component has been investigated for charge-transfer complexes of naphthalene, phenanthrene, and acenaphthene with the acceptors sym-trinitrobenzene, 2,4,7-trinitrofluorenone, tetrachlorophthalic anhydride, tetrabromophthalic anhydride, and tetra-iodophthalic anhydride. It is shown that φp/φf increases for fixed donor concentration as the concentration of the acceptor increases, and that the value of φp/φfΞy″ of the complexed emitter may be deduced from the observed rate of increase of φp/φf. By this means it is shown that complexing with sym-trinitrobenzene increases the quantum yield ratios of naphthalene and acenaphthene by factors of approximately 30 and 75, respectively. An increase of approximately 103 is observed upon complexation with the tetrahalophthalic anhydrides, and a heavy-atom effect is distinctly manifested within the anhydride series. It is possible to bracket values of the intersystem rate constant, ki, whence it is shown that in charge-transfer complexes the increase in the intersystem crossing probability makes it an important fluorescence quenching mode. It is also shown that the intersystem crossing process is significantly more sensitive to complexation and heavy-atom effects than the phosphorescence emission or quenching processes. The observed effects are briefly discussed in terms of conventional theories.
Charge-transfer fluorescence of some crystalline complexes at room temperature is described, and the mirror-image relationship to the charge-transfer absorption shown by Czekalla et al. is verified. Finally, some thermodynamic data for the investigated complexes are presented, and from the behavior of extinction coefficient and stability of the complexes as a function of λmax of the charge-transfer bands it is inferred that the charge-transfer band borrows much of its intensity from transitions proper to the donor.
Ultrasonic Dispersion Observed by Optical Diffraction. I. Nitrous Oxide
Authors: Martinez J. V. , Strauch J. G. , Decius J. C. 
Published: January 2005

Ultrasonic wavelengths in gases can be measured with a precision of about 1 in 103 by photographing the diffraction due to the traveling ultrasonic waves acting as a grating. The fundamental problems involved in the optical technique are discussed. An apparatus utilizing an objective lens of focal length 1.5 m and of aperture f/20 was constructed, and employed at an ultrasonic frequency close to one megacycle sec—1 to photograph the first order diffraction of the Hg 5461 Å line due to argon and nitrous oxide at pressures ranging from ¼ to 10 atm with exposures between 0.02 and 60 sec.
Using argon as a nondispersive gas for a standard, the ultrasonic velocities were calculated for N2O; a well-defined dispersion curve for N2O was obtained, from which a relaxation time at one atmosphere and 300°K of τ=0.99 μsec. was obtained, in excellent agreement with the results of other workers who have employed ultrasonic absorption or interferometry.
The use of an optical system of the type employed in the Lyot Coronagraph is discussed as a means of increasing the utility of the optical method.
Heats of Mixing in Binary-Liquid—Alkali-Metal Mixtures
Authors: Yokokawa T. , Kleppa O. J. 
Published: January 2005

The enthalpies of mixing in all the binary-liquid alloys formed among the alkali metals sodium, potassium, rubidium, and cesium have been measured by reaction calorimetry at 111°±2°C. All systems except rubidium—cesium show positive enthalpies of mixing. There is a tendency for the mixing enthalpies to become more positive and also more unsymmetrical as the two metals become more separated in the periodic table.
A comparison of the new enthalpy data with reported phase-diagram information indicates that the three liquid alloys which contain sodium all exhibit nearly ideal entropies of mixing. For potassium—rubidium, potassium—cesium, and rubidium—cesium, the new heat data, combined with the available phase diagrams, permit estimates to be made of the excess free energies of mixing in the solid solutions.