Showing papers on "Energy (signal processing) published in 1979"

Unified nuclear potential for heavy-ion elastic scattering, fusion, fission, and ground-state masses and deformations

Abstract: We develop a unified nuclear potential for the description of large-scale nuclear collective motion and find that it satisfactorily reproduces experimental data for heavy-ion elastic scattering, fusion, fission, and ground-state masses. Obtained by generalizing the modified liquid-drop model so that two semi-infinite slabs of constant-density nuclear matter have minimum energy at zero separation, this potential is given in terms of a double volume integral of a Yukawa-plus-exponential folding function. For heavy nuclear systems the resulting heavy-ion interaction potential is similar to the proximity potential of Swiatecki and co-workers. However, for light nuclear systems our potential lies slightly below the proximity potential at all nuclear separations. For heavy nuclei fission barriers calculated with our Yukawa-plus-exponential model are similar to those calculated with the liquid-drop model. However, for light nuclei the finite range of the nuclear force and the diffuse nuclear surface lower the fission barriers relative to those calculated with the liquid-drop model. Use of a Wigner term proportional to $\frac{|N\ensuremath{-}Z|}{A}$ in the nuclear mass formula resolves the major part of the anomaly between nuclear radii derived from elastic electron scattering on the one hand and from ground-state masses and fission-barrier heights on the other.NUCLEAR REACTIONS $^{4}\mathrm{He}$+$^{12}\mathrm{C}$, $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$, $^{84}\mathrm{Kr}$+$^{208}\mathrm{Pb}$; calculated heavy-ion interaction potential. $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$, $E=37.7, 81.0, 215.2$ MeV; calculated elastic-scattering angular distribution. $^{32}\mathrm{S}$+$^{27}\mathrm{Al}$, $^{35}\mathrm{Cl}$+$^{62}\mathrm{Ni}$, $^{16}\mathrm{O}$+$^{208}\mathrm{Pb}$; calculated compound-nucleus cross section. Calculated fission-barrier heights and ground-state masses for nuclei throughout Periodic Table. Nuclear potential energy of deformation, liquid-drop model, droplet model, modified liquid-drop model, Yukawa-plus-exponential model, proximity potential, Woods-Saxon potential, double-folding potential, optical model, ingoing-wave boundary condition, single-particle corrections, Strutinsky's method.

Variations on a theme of nuclear matter

Abstract: The authors review new techniques developed to apply the variational method to the nuclear matter problem. The variational wave function is taken to be ($S{\ensuremath{\Pi}}_{ilj}{\mathrm{F}}_{\mathrm{ij}}$) $\ensuremath{\Phi}$; the correlation operators ${\mathrm{F}}_{\mathrm{ij}}$ can in principle induce central, backflow, spin isospin, tensor, etc. correlations, and $\ensuremath{\Phi}$ is the ideal Fermi gas wave function. The application of diagrammatic cluster expansion and chain summation techniques to calculate expectation values with such wave functions is discussed in detail. The authors also give a brief overview of various other approaches to the calculation of the binding energies of quantum fluids, and a comparison of results for simple systems such ad helium liquids. Results obtained by various methods for simplified models of nuclear matter, which include central, spin, isospin, and tensor forces, have converged significantly in recent months. Results obtained with more realistic models which include the spin-orbit potentials are also discussed. The potential models considered so far either give too little binding or too high equilibrium density.

Quantum limits on resonant mass gravitational radiation detectors

Abstract: The methods of quantum detection theory are applied to a resonant-mass gravitational-radiation antenna. Quantum sensitivity limits are found which depend strongly on the quantum state in which the antenna is prepared. Optimum decision strategies and their corresponding sensitivities are derived for some important initial states. The linear detection limit (${E}_{min}\ensuremath{\sim}\ensuremath{\hbar}\ensuremath{\omega}$) is shown to apply when the antenna is prepared in a coherent state. Preparation of the antenna in an excited energy eigenstate or in a state highly localized in position or momentum space leads to increased sensitivity. A set of minimum-uncertainty states for phase-sensitive detection is introduced.

Electron emission from clean metal surfaces induced by low-energy light ions

Abstract: We have measured the electron emission yields of clean Li, Al, Cr, Cu, Ag, and Au surfaces under bombardment with ${\mathrm{H}}^{+}$, ${\mathrm{H}}_{2}^{+}$, ${\mathrm{D}}^{+}$, ${\mathrm{D}}_{2}^{+}$, and ${\mathrm{He}}^{+}$ ions in the energy range 2-50 keV. The clean surfaces were produced by in-situ evaporation of high-purity metals under ultrahigh-vacuum conditions. It is found that the ${Z}_{2}$ dependence of the yields for hydrogen and helium projectiles are very similar, that the yields for ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ show the same energy dependence as that of the electronic stopping powers, that molecular ions give lower yields per atom than atomic ions, and that isotope effects are negligible in our energy range. It is proposed that kinetic-electron emission under low-energy-light-ion bombardment results mainly from the escape of excited electrons produced by direct binary collisions between the projectile and the valence electrons of the target.

Pion decay constant, electromagnetic form factor, and quark electromagnetic self-energy in quantum chromodynamics

Abstract: We examine dynamical chiral symmetry breaking in quantum chromodynamics (QCD). To lowest order in a double perturbation expansion in $g$, the gauge coupling, and $\ensuremath{\lambda}=\mathrm{exp}(\ensuremath{-}\frac{1}{b{g}^{2}})$ we obtain exact representations for the pion decay constant ${f}_{\ensuremath{\pi}}$ and electromagnetic form factor ${F}_{\ensuremath{\pi}}({q}^{2})$. Using the experimental values for ${f}_{\ensuremath{\pi}}$ and ${F}_{\ensuremath{\pi}}({q}^{2})$, we estimate the dynamically generated quark mass to be 270-300 MeV, in good agreement with a value obtained from ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data. We also calculate the finite electromagnetic self-energy of a quark in QCD and discuss the implications.

Variance of the distributions of energy levels and of the transition arrays in atomic spectra

Abstract: Formulas are derived for the mean values and variances of the energy distributions of the levels of an atomic configuration and of the radiative transitions between the levels of two configurations (in intermediate coupling). The variance ${\ensuremath{\sigma}}^{2}$ of the distribution of the eigenstate energies belonging to a given configuration is considered first: ${\ensuremath{\sigma}}^{2}$ is expressed as a linear combination of squares and cross products of the usual Slater electrostatic and spin-orbit radial integrals. It is shown how this expression can be used to check the numerical matrices of energy-integral coefficients. Then expressions are derived for the mean value and for the variance of the weighted distribution of the transition energies between two configurations (the weight of each transition being its strength) in the $n{l}^{N+1}\ensuremath{-}n{l}^{N}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ and $n{l}^{N}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}\ensuremath{-}n{l}^{N}{n}^{\ensuremath{'}\ensuremath{'}}{l}^{\ensuremath{'}\ensuremath{'}}$ cases. This derivation is based on the second-quantization formalism. An extension is made to the case of complementary configurations. For transitions $n{l}^{N+1}\ensuremath{-}n{l}^{N}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$, an explicit formula is obtained for the shift between the mean energy of the transition array and the difference of the mean energies of the configurations. Numerical tables of the angular coefficients appearing in ${\ensuremath{\sigma}}^{2}$ are given for most cases where $l$, ${l}^{\ensuremath{'}}$, ${l}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\le}3$. The main application presented here concerns highly ionized spectra of molybdenum, with transitions between $3{d}^{N+1}$ and $3{d}^{N}4p$, $3{d}^{N}4f$, $3{d}^{N}5p$, and $3{d}^{N}5f$. The agreement between experimental and theoretical (ab initio) mean wave numbers and variances is good. A discussion of the physical conditions of applicability of the results to experimental situations is given.

Interaction energy of superconducting vortices

Abstract: By means of a constrained variational calculation we determine the interaction energy of two-vortex configurations in the Ginzburg-Landau theory or, equivalently, in the Abelian Higgs model. The energy is evaluated as a function of the separation between vortices and of the parameter $\ensuremath{\lambda}$, which measures the relative strength of the matter self-coupling and the electromagnetic coupling. Our results provide a precise determination of the inter-vortex potential, attractive for $\ensuremath{\lambda}l1$ and repulsive for $\ensuremath{\lambda}g1$. They also show that for $\ensuremath{\lambda}=1$ the lower bound on the energy which can be then derived is actually reached at all separations and, therefore, that in this case vortices do not interact.

Connection between quark-model eigenstates and low-energy scattering

Abstract: We propose a new method of analyzing low-energy hadron-hadron scattering designed to reveal internal quark-gluon eigenstates. Our method is a modification of the Wigner-Eisenbud formalism suited to the case of confining boundary conditions. We have identified a matrix function of the energy (which we call $P$) whose poles and residues correspond to the masses and channel projections of quark-gluon eigenstates calculated with spherical bag boundary conditions. To illustrate the formalism we apply it to the low-energy $S$-wave scattering of pseudoscalar mesons. We find from the data clear evidence of internal states corresponding to quark-model predictions of ${Q}^{2}{\overline{Q}}^{2}$ states at 0.69 and 1.04 GeV in the $I=0$ channel, at 0.96 GeV in the $I=\frac{1}{2}$ channel, at 1.19 GeV in the $I=\frac{3}{2}$ channel, and at 1.04 GeV in the $I=2$ channel. We believe the $I=\frac{3}{2} \mathrm{and} 2$ internal states to be the low-energy exotics long predicted by quark models.

Spatial excitation patterns induced by swift ions in condensed matter

Abstract: It is shown that a charged particle moving with velocity $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$ in a medium of resonance frequency ${\ensuremath{\Omega}}_{0}$ may set up two types of electron-density fluctuations. Collective fluctuations trail the particle, composing a conical pattern in a relatively extended periodic wake of wavelength $\ensuremath{\sim}\frac{2\ensuremath{\pi}v}{{\ensuremath{\Omega}}_{0}}$. They constitute a mode of energy transport from the particle track leading eventually to particle-hole excitations. Single-particle interactions give rise to bow waves ahead of the particles of wavelength $\frac{2\ensuremath{\pi}\ensuremath{\hbar}}{\mathrm{mv}}$. The gradient along $\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}$, at the site of the ion, of the wake potential set up by density fluctuations, multiplied by the ionic charge, yields an expression for the retarding force of the medium on the projectile in exact agreement with the Bethe stopping-power formula appropriate to the medium. The wake of a dicluster causes forces between the constituent ions which account quantitatively for measurements of the breakup behavior of swift molecular ions in thin foils. The increase in the energy straggling of a test charge, when moving in the wake of a leading ion, is shown to be small compared with the straggling induced by its own wake under normal conditions.

Vortex patterns and energies in a rotating superfluid

Abstract: The two-dimensional vortex patterns that occur in a rotating cylinder of superfluid $^{4}\mathrm{He}$ are systematically ordered for numbers of vortices $N=1,2,\dots{},30,37,50$ using a prescription for their free energy that is independent of angular velocity and is based upon the justified omission of images. Barrier energies between patterns of the same $N$ and of neighboring $N$ are discussed. A new derivation of the vortex free energy for perfect square and triangular lattices gives the result in terms of $\ensuremath{\Gamma}(x)$. Patterns that are expected to display high triangular symmetry are studied up to $N=217$, but circular distortion strongly reduces the region of triangular symmetry even in an unbounded fluid, as shown by the scattering structure factor. According to calculations on arrays containing over one million vortices, the destabilizing velocity at the vortex position $R$ in a finite circular region of a perfect triangular lattice is proportional to ${(\frac{R}{{R}_{0}})}^{5}$ where ${R}_{0}$ is the radius of the circular region.

Energy correlations in electron-positron annihilation in quantum chromodynamics: Asymptotically free perturbation theory

Abstract: In the absence of infrared mass singularities, the asymptotic behavior of cross sections for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation in quantum chromodynamics can be expressed entirely in terms of the energy dependence of the renormalization-group running coupling constant. Since the theory is asymptotically free, the running coupling vanishes at high energy, and such infrared-finite cross sections can be calculated perturbatively. We extend previous work by calculating, through second order, the energy-weighted angular correlations of the hadrons produced in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. This involves the computation of quark-antiquark-gluon production and the correction to the lowest-order quark-antiquark production from virtual gluon exchange. A dimensional-continuation scheme is employed to establish that these correlations, taken in a distribution-theory sense, are indeed free of mass singularities. The correlations exhibit interesting features which vanish slowly ($\ensuremath{\propto}\frac{1}{\mathrm{ln}W}$) as the energy $W$ increases. We estimate that the nonperturbative, confinement contributions to these features vanish much more rapidly ($\ensuremath{\propto}\frac{1}{{W}^{2}}$). Thus, effects characteristic of quantum chromodynamics should be quite evident at high energies.

A Comparison of Noise and Dose in Conventional and Energy Selective Computed Tomography

Abstract: We compare the noise properties of conventional and energy selective X-ray computed tomography. The images produced by the systems are not directly comparable so we discuss their relationship and show that the conventional image is a subset of the energy selective data. We describe how to form a conventional image from the energy selective images and demonstrate that, if this is done at the optimal display energy, the resulting conventional image will have the same noise as that produced by a conventional system with the same dose. But the energy selective system also extracts all the energy dependent information so it produces more information for the same dose than a conventional system.

Energy levels and line intensities of Pr 3 + in LiY F 4

Abstract: High-resolution polarized absorption and fluorescence spectra of ${\mathrm{Pr}}^{3+}$ in LiY${\mathrm{F}}_{4}$ were measured at temperatures between 10 and 300\ifmmode^\circ\else\textdegree\fi{}K. Energy-level assignments were made assuming electric-dipole transition selection rules for ${S}_{4}$ site symmetry. Forty-six energy levels of the $4{f}^{2}$ ground configuration were established, including 44 in the lowest nine multiplets. Crystal-field parameters were determined that gave a rms deviation of 15.8 ${\mathrm{cm}}^{\ensuremath{-}1}$ between 41 of the experimental energy levels and calculated values. The parameters were ${B}_{20}=488.9$, ${B}_{40}=\ensuremath{-}1043$, ${B}_{44}=1242$, ${B}_{60}=\ensuremath{-}42$, Re ${B}_{64}=1213$, and Im ${B}_{64}=22.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$. These parameters were used to obtain the remaining energy levels, yielding a complete energy-level scheme for the $4{f}^{2}$ configuration of ${\mathrm{Pr}}^{3+}$. The crystal-field parameters for ${\mathrm{Pr}}^{3+}$ in LiY${\mathrm{F}}_{4}$ were compared to those for other ions in this host. A theoretical calculation of line intensities was performed in which the odd-fold crystal-field parameters were obtained from a lattice sum. Line intensities were measured and compared with theory.

Processing Depth, Elaboration of Encoding, Memory Stores, and Expended Processing Capacity.

Abstract: The divided attention technique introduced by W. A. Johnston was used to assess the effects of several factors on expended processing capacity, which was indexed by the slowing of simple reaction time during the concurrent processing of other information. Expended processing capacity was greater when information was retrieved from secondary memory than from primary memory; when processing was of a deep, semantic nature than when it was shallow and physical; and it was greater when processing was more elaborate. The evidence thus suggests that expended processing capacity accurately reflects important aspects of memorial functioning. The relevance of these findings to limited capacity theories is discussed. The experiments reported in this article are concerned with the effects of several variables (memory store, depth of processing, and elaboration of processing) on expended processing capacity. There are valid theoretical reasons for investigating these issues: If people have limited processing capacity, then it is obviously of importance to establish the relative demands on that processing capacity imposed by different processing activities. To obviate semantic confusion, some of the key concepts referred to in this article will be defined at this point. We follow Johnston and Heinz (1978) in defining processing capacity as "the limited pool of energy, resources, or fuel by which some cognitive operations or processes are mobilized and maintained" (p. 422). We assume that tasks differ in terms of the demands they make on this processing capac

Systematics of carbon- and oxygen-induced fusion on nuclei with 12 ≤ A ≤ 19

Abstract: Measurements of the total fusion cross sections for $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, $^{14}\mathrm{N}$, $^{15}\mathrm{N}$, $^{16}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{19}\mathrm{F}$ and $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$ have been performed over the energy range from 1.5 to 3 times the Coulomb barrier energy. Fusion barrier parameters were extracted for each system. Three systems, $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $^{12}\mathrm{C}$ + $^{16}\mathrm{O}$, and $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, show rather pronounced oscillatory structure in the energy dependence of the fusion cross sections. The maximum fusion cross sections for the systems studied vary by as much as 10-20%, depending on the particular entrance channel. The specific structure of the interacting nuclei clearly does have an effect; the fusion process is not entirely dominated by the macroscopic features of the ion-ion interaction.NUCLEAR REACTIONS, fusion, measured ${\ensuremath{\sigma}}_{\mathrm{fusion}}(E)$; $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $7.4l~{E}_{\mathrm{c}.\mathrm{m}.}l~31.2$ MeV; $^{12}\mathrm{C}$ + $^{13}\mathrm{C}$, $7.6l~{E}_{\mathrm{c}.\mathrm{m}.}l~24.9$ MeV; $^{12}\mathrm{C}$ + $^{14}\mathrm{N}$, $15.1l~{E}_{\mathrm{c}.\mathrm{m}.}l~24.0$ MeV; $^{12}\mathrm{C}$ + $^{15}\mathrm{N}$, $8.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~26.7$ MeV; $^{12}\mathrm{C}$ + $^{16}\mathrm{O}$, $12.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~27.0$ MeV; $^{12}\mathrm{C}$ + $^{18}\mathrm{O}$, $11.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~28.0$ MeV; $^{12}\mathrm{C}$ + $^{19}\mathrm{F}$, $11.6l~{E}_{\mathrm{c}.\mathrm{m}.}l~27.1$ MeV; $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, $14.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~36.0$ MeV; deduced fusion barrier parameters.

Measurement of fast-electron energy spectra and preheating in laser-irradiated targets

Abstract: Fast electrons produced by the irradiation of plane-layered targets with 20-J, 100-ps, ${10}^{15}$-W.${\mathrm{cm}}^{\ensuremath{-}2}$, neodymium-laser pulses have been diagnosed by the $K\ensuremath{\alpha}$ emission which they cause at various depths in the targets. The fast-electron energy spectrum and absolute energy deposition (target preheat) are measured.

Investigation of competitive recombination processes in rare-earth activated garnet phosphors

Abstract: Spectral, kinetic, and relative quantum intensity measurements are reported for a series of ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ (YAlG) crystals, both nominally undoped and activated by ${\mathrm{Ce}}^{3+}$ and ${\mathrm{Tb}}^{3+}$. The undoped crystal shows a complex emission band in the near uv with fast- and slow-decaying components, analogous to the alkali halides. The band shape appears to involve emission from an unrelaxed and a relaxed defect state of the lattice. In the doped crystals these defect states compete with the activator ions as recombination pathways. The essential properties of the rare-earth activated crystals are described by a simple kinetic model, and initial estimates of the relative magnitudes of the rate constants are made. Temperature-dependence measurements for the cathodoluminescence of the YAlG: Ce (0.01%) crystal show that energy trapped at the defect centers can be thermally released, leading to an interaction between the defects and the activator ions. The effective activation energy for release is approximately 1900 ${\mathrm{cm}}^{\ensuremath{-}1}$ and an initial estimate for the thermalization time constant based on the kinetic model is approximately 160 nsec at room temperature. At low concentration the time constant for the initial defect trapping state is slower than this value because of multiple capture effects, $\ensuremath{\tau}(D)\ensuremath{\sim}200$ nsec. The rise and decay curves for ${\mathrm{Ce}}^{3+}$ luminescence reflect this slow time constant, but annealing the crystals in an oxidizing atmosphere introduces an additional shunt path which reduces the luminescence efficiency but decreases the activator time constant to the intrinsic ${\mathrm{Ce}}^{3+}$ value $\ensuremath{\tau}(\mathrm{Ce})\ensuremath{\sim}60$ nsec. The significance of the results for phosphor action in these oxides is discussed.

Hard X-ray time profiles and acceleration processes in large solar flares

Abstract: The hard X-ray time profiles of the (1972) August 4 and 7 flares are investigated, taking into account a comparison of the time profiles of different energy channels. It is shown that for these flares the temporal features of the intensity profiles of higher energy channels are delayed with respect to those of channel 1. The delay time gradually increases to approximately 5 sec as the channel number increases from 1 to 5, and it jumps to approximately 15 sec for channels 6 and 7. A description is presented of a model in which the delay and other characteristics of the observed time profiles in channels 1-5 are self-consistently explained by the increase of the electron energy loss time with electron energy.

Energy absorbed by elastic waves during plastic impact

Abstract: During the normal impact of a hard particle on a metal surface, some of the kinetic energy of the particle is radiated into the target as elastic waves. The amount of energy involved is calculated for impacts where the metal is deformed plastically, and is found to be typically only a few per cent of the initial kinetic energy.

Energy gaps of the A − 15 superconductors Nb 3 Sn, V 3 Si, and Nb 3 Ge measured by tunneling

Abstract: Tunnel junctions with good quasiparticle (Giaever) and pair (Josephson) tunneling characteristics have been made on electron-beam coevaporated thin films of some important high-temperature superconductors which have the $A\ensuremath{-}15$ crystalline structure. Using the thermally grown oxide of niobium tin to make Nb-Sn---oxide---Pb junctions we estimate the gap, ${\ensuremath{\Delta}}_{\mathrm{N}\mathrm{b}\ensuremath{-}\mathrm{S}\mathrm{n}}$, as a function of composition from the current-voltage characteristics. Stoichiometric ${\mathrm{Nb}}_{3}$Sn is strong coupling with $\frac{2\ensuremath{\Delta}}{{k}_{B}{T}_{c}}=4.2\ensuremath{-}4.4$ whereas with less tin Nb-Sn has a low ${T}_{c}$ and becomes weak coupling. On vanadium silicon we could only make good junctions by evaporating a thin silicon layer, with thickness in the range 1.6-16 nm, on the fresh $A\ensuremath{-}15$ film before junction fabrication. V-Si is essentially weak coupling for all compositions with $\frac{2\ensuremath{\Delta}}{{k}_{B}{T}_{c}}=3.5\ifmmode\pm\else\textpm\fi{}0.2$. The characteristics of tunnel junctions on high-${T}_{c}$ niobium-germanium films always show evidence for multiple gaps and the data on this interesting material are more difficult to interpret.

Quantum-statistical mechanics of extended objects. I. Kinks in the one-dimensional sine-Gordon system

Abstract: Making use of thermal-Green's-function technique, we study the quantum-statistical mechanics of a sine-Gordon system in 1 + 1 dimensions. In the weak-coupling limit, the temperature dependences of the soliton energy, ${E}_{s}$, the soliton inertial mass, and the soliton density are determined. At high temperatures ($Tgm$, where $m$ is the mass of the fundamental field), ${E}_{s}$ decreases monotonically as the temperature increases, and ${E}_{s}$ jumps to zero around $T={T}_{\mathrm{cr}}$ ($\ensuremath{\equiv}{e}^{\ensuremath{-}1}{{E}_{s}}^{0}$), where ${{E}_{s}}^{0}$ is the soliton energy at $T=0$ K. The soliton density agrees with the classical statistical-mechanics results for ${T}_{\mathrm{cr}}gT\ensuremath{\gg}m$, if ${E}_{s}$ in the classical theory is replaced by the temperature-dependent one of the present theory.

Energy producing system

Abstract: In an energy producing system, a movable device is mounted at least partially within a housing which, in turn, is mounted in the ground at the surface of a road or the like. The movable device at least partially extends through an opening in the housing and is positioned transversely within the path of travel of vehicles moving along the road for engaging the vehicles seriatim to be set into motion thereby. A coupling device connects drivingly the movable device and a generating device for transmitting drivingly the motion of the movable device to the generating device, such as an electrical generator. A flywheel is journaled for rotation about its axis for storing the energy in response to the movable device to provide a more continuous production of energy from the generating device.

XY model and the superfluid density in two dimensions

Abstract: By computing the incremental free energy of the two-dimensional $\mathrm{XY}$ model in a state with a long-wavelength twist of the local short-range order, we evaluate for all $Tl{T}_{c}$ the superfluid density ${\ensuremath{\rho}}_{s}$ for superfluid systems. Spin-wave excitations in the $\mathrm{XY}$ model imply a substantial (nonuniversal) depletion of ${\ensuremath{\rho}}_{s}$ at low temperatures. We find that these contributions do not affect the asymptotic universality; as $T\ensuremath{\rightarrow}{T}_{{c}^{\ensuremath{-}}}$, $\frac{{\ensuremath{\rho}}_{s}}{T}$ becomes universal and we recover the previous results of Nelson and Kosterlitz. In the Appendix we derive the Kosterlitz recursion relations by transforming to a sine-Gordon system and using conventional momentum shell integration techniques.

Hypervirial theorems applied to the perturbation theory for screened Coulomb potentials

Abstract: By applying the hypervirial relations with the Hellman-Feynman theorem to screened Coulomb potentials, the authors derive the energy levels of atoms correct to the sixth order of the perturbation parameter $\ensuremath{\lambda}$ explicitly without any calculation of perturbed wave functions. The energies of atoms up to the twentieth order of $\ensuremath{\lambda}$ are also calculated by computer. In the case of the Yukawa potential, the authors demonstrate by explicit calculation that the $K$-shell energy converges, at least for $Z\ensuremath{\ge}5$, with the value of ${\ensuremath{\lambda}}_{0}=0.85$, and that the $L$-shell energy converges, at least for $Z\ensuremath{\ge}24$, with ${\ensuremath{\lambda}}_{0}=0.70$.

Energy-modified adiabatic approximation for scattering theory

Abstract: The adiabatic approximation in scattering theory is modified by allowing for the splitting and shifts of perturbed target-state energy levels. This energy-modified adiabatic approximation, derived from operator equations formally equivalent to close-coupling equations in the basis of perturbed target states, is shown to be qualitatively correct for threshold and resonance structures, for which the usual adiabatic theory is inadequate. In the case of electron-molecule vibrational excitation, it is shown that electronic threshold scattering structures should be associated with each vibrational threshold. A single electronic resonance becomes a manifold of multichannel vibrational excitation resonances. Vibrational excitation structures in ${e}^{\ensuremath{-}}\ensuremath{-}{N}_{2}$ scattering are computed as an example of the method.

Limitation on the density-equation approach to many-electron problems

Abstract: The density equation proposed by Nakatsuji assumes a matrix form when a basis set is introduced The matrix equation is shown to have highly degenerate solutions for almost any value of the energy, and thus to provide little useful information in the absence of $N$-representability constraints The imposition of such constraints is also considered, and approximate constraints are predicted to be of little value

Plasma Confinement Studies in the ISX-A Tokamak

Abstract: Gross-energy-confinement times (${\ensuremath{\tau}}_{E}$) in the ISX-$A$ (Impurity Study Experiment) tokamak exceeded predictions of the usual empirical scaling relations. We attribute this performance to reductions of impurity radiation and magnetohydrodynamically driven loss channels. The value of ${\ensuremath{\tau}}_{E}$ reached a limit as a function of plasma density. We suggest that this limit is due to a transition from electron- to ion-dominated loss regimes. Maximum attainable values of ${\ensuremath{\tau}}_{E}$ increased with discharge current, in agreement with this interpretation.

Stark Effect in Hydrogen: Dispersion Relation, Asymptotic Formulas, and Calculation of the Ionization Rate via High-Order Perturbation Theory

Abstract: By a generalization of the Herbst-Simon dispersion relation for hydrogen in an electric field, an expansion asymptotic in $N$ for the perturbed energy coefficient ${{E}_{{n}_{1}{n}_{2}m}}^{(N)}$ is obtained from the formal asymptotic expansion (in the field strength $F$) for the ionization rate. Perturbation-theory calculations of ${{E}_{{n}_{1}{n}_{2}m}}^{(N)}$ to $N\ensuremath{\sim}150$ confirm the formula. Via reverse use of the dispersion relation, perturbation-theory values of ${{E}_{{n}_{1}{n}_{2}m}}^{(N)}$ yield numerical values for constants in the ionization-rate expansion that are tediuous to obtain directly. Ionization rates so calculated compare favorably with values obtained by others.

Dynamical chiral symmetry breaking in quantum chromodynamics

Abstract: We examine both dynamical chiral symmetry breaking and explicit breaking due to current quark masses in quantum chromodynamics (QCD). The renormalized current and constituent quark mass are defined. The quark self-energy $\ensuremath{\Sigma}(p)={\ensuremath{\Sigma}}_{D}(p)+{\ensuremath{\Sigma}}_{E}(p)$ has unique contributions from dynamical and explicit symmetry breaking. We determine the asymptotic behavior of ${\ensuremath{\Sigma}}_{D}(p)$ and ${\ensuremath{\Sigma}}_{E}(p)$ as $\ensuremath{-}{p}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$. Although the explicit symmetry breaking dominates in the region controlled by perturbation theory, the dynamical term, which receives contributions from instantons, dominates in the subasymptotic region. The dynamical term is often ignored in the calculations. We also discuss the possibility of a phase transition in QCD for massive quark systems. The structure of the chiral perturbation expansion for light quarks is found to have not only an essential singularity in the gauge-field coupling constant for ${g}^{2}\ensuremath{\le}0$ but also a cut for ${g}^{2}\ensuremath{\le}0$ in amplitudes for which the essential singularity is absent. We also calculate the second-order axial-vector renormalization for a quark with the result ${g}_{A}=1\ensuremath{-}\frac{{g}^{2}}{6{\ensuremath{\pi}}^{2}}$.

What is a Magnetospheric Substorm

Abstract: It is suggested that if the solar wind-magnetosphere energy coupling, represented in first approximation by the coupling function \( {\rm{\varepsilon ( = V}}{{\rm{B}}^{\rm{2}}}{\rm{ si}}{{\rm{n}}^{\rm{4}}}{\rm{ }}\frac{{\rm{\theta }}}{2}{\rm{ }}{\ell _{\rm{o}}}^2) \), increases above about ~ 1018 erg/sec, the magnetosphere suddenly develops a more efficient energy dissipation process than that operating during periods of e < 1018 erg/sec. It appears that the magnetosphere achieves this enhanced energy dissipation by interrupting the cross-tail current in the magnetotail and diverting it into the ionosphere, causing an enhanced Joule heat production in the ionosphere. The good correlation between e and the total energy dissipated in the magnetosphere suggests that the substorm is more like a process directly driven by the solar wind, rather than an unloading process of energy accumulated prior to the onset.