Showing papers in "Physica Scripta in 1986"
TL;DR: In this paper, it is shown that the theory of effective Hamiltonians allows the determination of Pauli-like Hamiltonians that are regular enough to be used in variational calculations.
Abstract: The standard Pauli Hamiltonian is highly singular for Coulomb potentials near the nuclei of the atoms. It is shown that the theory of effective Hamiltonians allows the determination of Pauli-like Hamiltonians that are regular enough to be used in variational calculations. A numerical illustration is given for hydrogenic atoms with atomic number varying from Z = 1 to Z = 86. These calculations yield relativistic correction potentials which are used for studying the series of neutral rare gas atoms. Our approach opens the way for accurate two-component calculations for molecules.
615 citations
TL;DR: The general properties of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed in this paper.
Abstract: The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem.
360 citations
TL;DR: In this article, the main mechanisms for the observed large optical nonlinearities in semiconductors are briefly discussed and illustrated for the example of the exciton ionization by plasma screening.
Abstract: The main mechanisms for the observed large optical nonlinearities in semiconductors are briefly discussed and illustrated for the example of the exciton ionization by plasma screening. These nonlinearities cause various types of optical bistability, either of intrinsic nature or evoked by an additional resonator feedback. Under certain operation conditions also higher instabilities such as oscillations and chaos can be obtained. As an example, the self-pulsing of an induced absorber in a ring cavity is treated. The resulting locked oscillations are shown to follow a Farey-tree scenarium.
266 citations
TL;DR: In this paper, a number of general features of non-classical states of light are reviewed, including the properties of photon antibunching and sub-Poissonian photon statistics.
Abstract: A number of general features of non-classical states of light are reviewed. The phenomena of photon antibunching and sub-Poissonian photon statistics are then treated in more detail, including the experimental observations. Quantum effects in spontaneous parametric down-conversion are discussed, and recent experiments dealing with the time intervals between down-converted photons, with the intensity dependence of the cross-correlation function, and with the detection of a localized one-photon state are described. Finally, some quantum effects in the interference of light are discussed.
207 citations
TL;DR: In this paper, the authors present a systematic approach to derive an equation describing the propagation of pulses along a transmission line made of a large number of nonlinear LC-circuits, which correctly captures the leading order effects due the discreteness of the line and describes a two-sided wave propagation, nonlinear wave-wave interactions, and wave-wall interactions.
Abstract: We present a systematic approach to derive an equation describing the propagation of pulses along a transmission line made of a large number of nonlinear LC-circuits. This equation correctly captures the leading order effects due the discreteness of the line and describes a two-sided wave propagation, nonlinear wave-wave interactions, and wave-wall interactions. In contradistinction to previous works, our method is not limited to weakly nonlinear disturbances.
121 citations
TL;DR: The interaction of a single atom with a single quantized field mode is one of the simplest quantum optical models of resonance, yet exhibits a wide variety of non-trivial fundamental features which depend for their existence on field quantization as mentioned in this paper.
Abstract: The interaction of a single atom with a single quantized field mode is one of the simplest quantum optical models of resonance, yet exhibits a wide variety of non-trivial fundamental features which depend for their existence on field quantization. We discuss such problems with special emphasis on reversible spontaneous emission and one-photon Rabi oscillations, photon statistical collapses and revivals of coherent evolution, and the existence of phase-dependent squeezed quantum noise.
121 citations
TL;DR: In this article, the important concepts of fractal dimension and exact and statisical self-similarity and self-affinity are reviewed, and various methods and difficulties of estimating the fractal dimensions and lacunarity from experimental images or point sets are summarized.
Abstract: Mandelbrot's fractal geometry provides both a description and a mathematical model for many of the seemingly complex shapes found in nature. Such shapes often possess a remarkable invariance under changes of magnification. This statistical self-similarity may be characterized by a fractal dimension D, a number that agrees with our intuitive notion of dimension but need not be an integer. A brief mathematical charactrization of random fractals is presented with emphasis on variations of Mandelbrot's fractional Brownian motion. The important concepts of fractal dimension and exact and statisical self-similarity and self-affinity will be reviewed. The various methods and difficulties of estimating the fractal dimension and lacunarity from experimental images or point sets are summarized.
109 citations
TL;DR: In this article, energy levels and radiative transition probabilities in the ground configurations of the sulfur and selenium isoelectronic sequences up to molybdenum and silver, respectively, were calculated.
Abstract: We have calculated energy levels and radiative transition probabilities in the ground configurations of the sulfur and selenium isoelectronic sequences up to molybdenum and silver, respectively. Transition probabilities have been obtained for M1 and E2 forbidden lines within the p4 configurations using electrostatic and spin-orbit integrals for the interactions within this configuration deduced by a fitting procedure to the available experimental energy levels or by graphical inter(extra)polation of Slater parameters along the sequence when the energy levels are unknown. Some of the most important configuration interaction and relativistic effects have been included explicitly using the HFR self-consistent method due to Cowan and Griffin. For most of the ions in the selenium sequence, transition probabilities are reported for the first time. The effects of including configurations with 4f electrons explicitly have been studied for both the 3p3 and 3p4 configurations.
85 citations
TL;DR: A critical review of the literature on similarity solutions of nonlinear Schroedinger equations is presented in this article, where it is shown that the self-similar blow-up solutions discovered hitherto are all associated either with a simple stretching invariance, or with a slightly more complicated conformal invariance and generalizations of the latter.
Abstract: A critical review of the literature on similarity solutions of nonlinear Schroedinger equations is presented. We demonstrate that the self-similar blow-up solutions discovered hitherto are all associated either with a simple stretching invariance, or with a slightly more complicated conformal invariance and generalizations of the latter. This generalized "quasi-invariance" reveals the nature of the blow-up singularity and resolves an old controversy. Most of the previous work has been done on the cubic nonlinearity. We generalize the results to an arbitrary power nonlinearity.
78 citations
TL;DR: In this paper, it was shown that the Dym hierarchy of nonlinear evolution equations is invariant under a class of reciprocal Backlund transformations, which is used to construct a generic auto-Backlund transformation for the Korteweg-deVries hierarchy.
Abstract: It is shown that the Dym hierarchy of nonlinear evolution equations is invariant under a class of reciprocal Backlund transformations. This result is used to construct a generic auto-Backlund transformation for the Korteweg-deVries hierarchy in a novel manner.
72 citations
TL;DR: In this paper, the termination properties of terminating bands of Dy, Er and Yb are reviewed and exemplified on the observed high-spin properties of 158Er and 156Er and the possibility to estimate B(E2)-values in terminating bands from measured feeding times is explored.
Abstract: General properties of terminating bands are briefly reviewed and exemplified on the observed high-spin properties of 158Er and 156Er. The very similar features of the positive parity high-spin spectra of the N = 88 isotones of Dy, Er and Yb are pointed out and discussed. The possibility to estimate B(E2)-values in terminating bands from measured feeding times is explored. The spin contribution from different orbitals is calculated in terminating bands as well as more collective bands. One aim is to get some idea of the interaction between different configurations and to this end we also consider a single-j shell model. The limits of terminating bands in the yrast region when the number of valence nucleons increases is discussed. The usefulness of these results when planning future experimental studies is considered.
TL;DR: In this article, a review of the physics of weak localization is discussed, which represents an interference experiment with conduction electrons split into pairs of waves interfering in the back-scattering direction.
Abstract: The resistance of two-dimensional electron systems such as thin disordered films shows deviations from Boltzmann theory, which are caused by quantum corrections and are called "weak localization" Theoretically, weak localization is originated by the Langer-Neal graph in the Kubo formalism In this review the physics of weak localization is discussed It represents an interference experiment with conduction electrons split into pairs of waves interfering in the back-scattering direction The intensity of the interference (integrated over the time) can be easily measured by the resistance of the film A magnetic field introduces a magnetic phase shift in the electronic wave function and suppresses the interference after a "flight" time proportional to 1/H Therefore the application of a magnetic field allows a time-of-flight experiment with conduction electrons Spin-orbit scattering rotates the spin of the electrons and yields an observable destructive interference Magnetic impurities destoy the coherence of the phase The experimental results as well as the theory is reviewed The role of the spin-orbit scattering and the magnetic scattering are discussed The measurements give selected information about the inelastic lifetime of the conduction electrons in disordered metals and raise new questions in solid state physics Future applications of the method of weak localization are considered and expected
TL;DR: In this paper, the transition probabilities for forbidden lines in the ground configurations of the germanium (4p2) and arsenic(4p3) isoelectronic sequences up to silver (Z = 47).
Abstract: Calculations of energies and transition probabilities are reported for forbidden lines in the ground configurations of the germanium (4p2) and arsenic (4p3) isoelectronic sequences up to silver (Z = 47). Configuration interaction and relativistic effects were included in the framework of the HXR and HFR self-consistent-field methods. Transition probabilities have been obtained in intermediate coupling using parameter values for the 4p2 and 4p3 configurations obtained either by fitting or by extra-(inter)polation when experimental energy levels are missing. Except for Ge I and As I, transition probabilities are reported for the first time for all these ions. A note concerning transition probabilities for Fe XII is also appended.
TL;DR: In this paper, a model of a liquid of long rod molecules is studied and the equations of motion of such a system are remarkably simple and permit simple intuitive pictures of the glass transition to be translated into a theoretical model for molecular diffusivity.
Abstract: Accepting the widely held view that all glass transitions have the same features, a particularly simple model of a liquid of long rod molecules is studied. It is shown that the equations of motion of such a system are remarkably simple and permit simple intuitive pictures of the glass transition to be translated into a theoretical model for molecular diffusivity. The calculation derives the Vogel–Fulcher–Dolittle law which is shown to stem from the co-operative motion of molecules being the only survivor near Tg. Right at Tg it is shown that a power law replaces V–F–D. An analysis is also given of the time relaxation of the system, the Kohlrausch–Williams–Watts law. This however is not critically related to the V–F–D structure, but follows from the averaging over a spectrum of relaxation times.
TL;DR: An overview of progress in the target and ion source techniques at the ISOLDE on-line mass separator is given in this paper, where the production of high intensity beams of mass-separated radioactive nuclei by bombardment of targets with 600 MeV protons and 910 MeV 3He from the CERN synchro-cyclotron is discussed.
Abstract: An overview of progress in the target and ion source techniques at the ISOLDE on-line mass separator is given. The production of high intensity beams of mass-separated radioactive nuclei by bombardment of targets with 600 MeV protons and 910 MeV 3He from the CERN synchro-cyclotron is discussed. Off-line tests performed in order to clarify the release properties of different target materials are described. The targets are metal powders or foils, alloys, carbides, oxides, intermetallic compounds or molten metals. The influence of reactive gases on the release rates and progress in ion-source techniques are also discussed. Recent on-line tests are described in details, and systems are suggested for the production of elements which are not yet available as primary products in on-line mass separators.
TL;DR: In this article, the optical transitions induced by doping poly(3-methylthiophene) or polythiophenes with BF4− or ClO4− were investigated by in-situ spectroscopy in an opto-electrochemical cell.
Abstract: The optical transitions induced by doping poly(3-methylthiophene) or polythiophene with BF4− or ClO4− have been investigated by in-situ spectroscopy in an opto-electrochemical cell. From the number of doping-induced bands and concentration dependence we found evidence that polarons are the primary electronic excitations at doping concentrations up to 1% and that an increasing number of bipolarons is formed at higher concentrations. Both the positions and the intensities of the optical transitions indicate that electron-electron interactions and the Coulomb potential of the dopant ions are relevant.
TL;DR: In this article, the nuclear and electronic magnetic dipole moments of 21Fr and the nuclear ground-state spin of 207Fr have been measured directly by on-line atomic-beam magnetic resonance techniques at the ISOLDE facility at CERN.
Abstract: The nuclear and electronic magnetic dipole moments of 21Fr and the nuclear ground-state spin of 207Fr have been measured directly by on-line atomic-beam magnetic resonance techniques at the ISOLDE facility at CERN. The following results have been obtained: μI(211Fr) = 4.00(8) nm, gJ(Fr, 7s 2S1/2) = 2.00497(9) and I(207Fr) = 9/2. A large deviation of the electronic magnetic moment from the free electron value was found. Using the measured nuclear magnetic moment μI(211Fr), a comparison is made between different theoretical calculations of the magnetic dipole hyperfine constants and with the available experimental data in 211Fr. An analysis of the electric quadrupole interaction is also given. Nuclear magnetic dipole and electric quadrupole moments are deduced for the sequences 207-213Fr and 220-228Fr, using the data on 211Fr as reference values. The nuclear quantities are discussed within the framework of the shell model and the core-quasiparticle model, giving information on the nuclear single-particle structure and on the variation in deformation along the sequences of francium isotopes.
TL;DR: In this article, the theory of linear quantum amplifiers is reviewed and a simplified method using a "faked vacuum" is introduced to derive amplifier master equations and the solution is derived and used as the amplifier transfer function.
Abstract: The theory of linear quantum amplifiers is reviewed. A simplified method using a "faked vacuum" is introduced to derive amplifier master equations. Properties of various amplifiers are summarized. The solution is derived and used as the amplifier transfer function. The Caves' theory for amplifier added noise is discussed. The properties of squeezed states are reviewed, the use of the Wigner function to describe them is advocated. Finally the amplification of squeezed states is discussed in the Wigner representation.
TL;DR: In this article, the decays of strongly neutron rich isotopes of Zn have been studied with the primary aim of nuclear mass determinations, and the experimental results are compared with predicted values of nuclear masses.
Abstract: The decays of strongly neutron rich isotopes of Zn have been studied with the primary aim of nuclear mass determinations. The work has also resulted in considerable information on the previously practically unknown level structure of 75,76,77,79,80Ga. Improved Qβ-values are obtained for 75,76,77,78Zn and 76,78,80Ga. The Qβ-values of 79,80Zn are reported for the first time. The experimental results are compared with predicted values of nuclear masses.
TL;DR: In this paper, the beam-foil excitation technique and the ANDC method for cascade corrections were used to determine the experimental lifetimes of the 2s2p2 2S, 2s 2ns 2S (n = 3, 4, 5) and 2p3 2P0 terms in C II and C III.
Abstract: Using the beam-foil excitation technique and the ANDC method for cascade corrections, we have determined lifetimes of the 2s2p2 2S, 2s2ns 2S (n = 3, 4, 5), 2s2p2 2P, 2s2np 2P0 (n = 3, 4), and 2p3 2P0 terms in C II and the 2s2p 1P0 level in C III. The new experimental lifetimes are in very good agreement with the results of recent theoretical calculations.
TL;DR: In this paper, self-consistent field calculations of wavelengths and transition probabilities along the silicon sequence for elements K to Ti are extended to the 3s-3p and 3p-3d transitions of elements V to Ni.
Abstract: The HXR self-consistent field calculations of wavelengths and transition probabilities previously reported along the silicon sequence for elements K to Ti are extended to the 3s-3p and 3p-3d transitions of elements V to Ni. Ab initio HXR values of Slater parameters have been adjusted by a leastsquare optimization process of the calculated eigenvalues of the Hamiltonian with the available experimental energy levels. New accurate wavelengths and transition probabilities have been derived and six new identifications of solar lines are proposed.
TL;DR: A Mossbauer spectroscopic study on a series of titanium-substituted hematites, (Fe1-xTix)2O3 with x < 0025, is reported in this article.
Abstract: A Mossbauer spectroscopic study is reported on a series of titanium-substituted hematites, (Fe1-xTix)2O3 with x < 0025 It is found that, even in powder samples, Ti influences the Morin transition (TM) quite strongly One percent of Ti is enough to depress TM below 10 K and this is likely true for a homogeneous sample with 05% of Ti too The magnetic ordering temperature lowers with Ti-content
TL;DR: In this article, the fine-structure levels arising from the 2p53s, 3p and 3d configurations of the Ne-like ions, obtained from relativistic multiconfiguration Dirac-Fock calculations, are tabulated for 20 ≤ Z ≤ 54.
Abstract: Energies of the fine-structure levels arising from the 2p53s, 3p and 3d configurations of the Ne-like ions, obtained from relativistic multiconfiguration Dirac-Fock calculations, are tabulated for 20 ≤ Z ≤ 54.
TL;DR: In this paper, the spectrum of six times ionized krypton (Kr VII) has been observed in the 430-1000 A wavelength range and 23 lines have been identified as transitions between levels of the 4s2, 4s4d, 4p2 and 4s 4p configurations.
Abstract: The spectrum of six times ionized krypton (Kr VII) has been observed in the 430-1000 A wavelength range and 23 lines have been identified as transitions between levels of the 4s2, 4s4d, 4p2 and 4s4p configurations. For 13 of the lines the classification is new. Revised values are proposed for three levels while for the rest the uncertainty in the existing level values has been considerably decreased. The results are supported by isoelectronic comparisons along the Zn I isoelectronic sequence. The configurations are interpreted by fitting the theoretical energy expressions to the observed energy levels using least-squares techniques. The parameter values are compared with results from Hartree-Fock calculations.
TL;DR: In this article, the absolute cross sections for single and multielectron processes in 1.8q keV collisions were measured by means of a coincidence time-of-flight technique.
Abstract: Absolute cross sections for single and multielectron processes in 1.8q keV collisions, Arq+ + B → Arr+ + Bs+ + (s + r - q)e- have been measured for the targets Ne, Ar and Kr. By means of a coincidence time-of-flight technique, the charge state of the projectile before and after the collision and the charge state of the target ion are determined. The projectile charge ranges from one to nine, while s at most reaches six (Kr), five (Ar) and four (Ne). The experimental technique is discussed and a simple model for absolute cross sections σq,rs is proposed.
TL;DR: In this paper, a wall stabilized stationary cascade arc served as a plasma source, and the authors measured the broadening parameters of 20 Ar II lines from the 4s-4p and 3d 4p transition arrays and of 19 Xe II lines of the 6s-6p and 5d 6p transition array.
Abstract: Stark broadening parameters of 20 Ar II lines from the 4s-4p and 3d-4p transition arrays and of 19 Xe II lines from the 6s-6p and 5d-6p transition arrays were measured. Additional broadening mechanisms other than Stark effect were taken into account. A wall stabilized stationary cascade arc served as plasma source. Electron densities were determined with high precision from independent measurements with a two-wavelengths Michelson interferometer. The results are compared to experimental data from literature and semiempirical calculations.
TL;DR: Theoretically, the interaction of H2 with metal surfaces gives rise to elastic and inelastic backscattering, physisorption, dissociative and possibly associative chemisorsption as discussed by the authors.
Abstract: The interaction of H2 with metal surfaces gives rise to elastic and inelastic back-scattering, physisorption, dissociative and possibly associative chemisorption Theoretically, the interaction is the simplest example that displays this complete range of properties Experimental study is greatly aided by the availability of the isotopes H2, D2 and HD with their well separated masses and well-spaced rotational spectra H2-metal systems are therefore particularly worthy of study and it would seem feasible through judicious interplay of theory and experiment to understand the interaction in detail This note constitutes a summary of current theoretical ideas and their relation to experiment
TL;DR: In this article, a level scheme was constructed from the studies of γγ-coincidences, the relative excitation function, and γ-ray angular distribution measurements, and a newly observed sequence based on the 1/2+[660] Nilsson orbital was established.
Abstract: High-spin states in 177Re have been populated in the 165Ho (16O, 4n)177Re reaction. A level scheme is constructed from the studies of γγ-coincidences, the relative excitation function, and γ-ray angular distribution measurements. Three decay sequences identified with 5/2+[402], 1/2-[541] and 9/2-[514] Nilsson orbitals have been extended up to spin 29/2+, 49/2- and 33/2-, respectively, and a newly observed sequence based on the 1/2+[660] Nilsson orbital is established. The experimental data are discussed within the Woods-Saxon cranking model. Observed shifts in the band crossing frequencies are interpreted theoretically as being caused by different deformation driving forces of quasiparticle orbitals. B(M1)/Q02 ratios are discussed in connection with quasineutron alignment.
TL;DR: In this article, the phase velocity of low frequency waves in the ionospheric E-region is often lower than the drift speed of the electrons that drive the waves unstable, and the linear instability theory is modified to conform with zero growth rate even above threshold.
Abstract: Comparative measurements indicate that the phase velocity of low frequency waves in the ionospheric E-region is often lower than the drift speed of the electrons that drive the waves unstable. In order to understand these results, the linear instability theory is modified to conform with zero growth rate even above threshold. The result is that the waves travel at the ion-acoustic velocity with an amplitude stabilized at the observed level, and also that the electron gas is substantially heated by the wave.