The atomic-beam laser-rf double-resonance technique has been used to study the hyperfine structure (hfs) of the metastable ${}_{}{}^7{}_{}{}^{}$${\mathit{L}}_{5–11}$ and ${}_{}{}^7{}_{}{}^{}$${\mathit{K}}_4$ states of the 4${\mathit{f}}^4$5d6s configuration in ${}_{}{}^{143,145}{}_{}{}^{}\mathrm{i}$. Four zero-field intervals were measured in each state and the results used to assign the conventional hfs constants A and B. Comparison of the results with predictions of the Sandars-Beck model allowed evaluation of the relevant single-electron radial hfs integrals. These are compared with earlier results from the Nd i atomic ground term and with extrapolations from other rare-earth elements. The unusually large orbital-angular-momentum values (L=7 and 8 for the states studied) do not appear to have introduced any anomalous effects. Ab initio calculations are not yet feasible for the complex 4${\mathit{f}}^4$5d6s levels studied.

We report a clear demonstration of the effect of hyperfine quenching of a forbidden transition by direct comparison of the lifetimes of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ level in the heliumlike isotopes ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}_{}^{26+}{}_{}{}^{}$ and ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}_{}^{26+}{}_{}{}^{}$. We find the quenched lifetime of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ level in ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}_{}^{26+}{}_{}{}^{}$ to be 470(50) ps. From this we deduce the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ energy splitting to be 2.33(15) eV. We also report a measurement of the lifetime of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ level in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}_{}^{26+}{}_{}{}^{}$, which is found to be 70(3) ps.

Becke [J. Chem. Phys. 84, 4524 (1986); Phys. Rev. A 38, 3098 (1988)] has shown that the Hartree-Fock exchange energy for atoms (and molecules) can be excellently represented by a formula K=$2^{1/3}$${\mathit{C}}_{\mathit{x}}$F${\mathcal{J}}_{\mathrm{\sigma }}$ ${\mathrm{\rho }}_{\mathrm{\sigma }}^{4/3}$(r)[1+βG(${\mathit{x}}_{\mathrm{\sigma }}$)]dr, where ${\mathit{C}}_{\mathit{x}}$ is the Dirac constant, β is a constant, G(x) is a function of the gradient-measuring variable ${\mathit{x}}_{\mathrm{\sigma }}$=‖∇${\mathrm{\rho }}_{\mathrm{\sigma }}$‖/${\mathrm{\rho }}^{4/3}$, and the summation is over spin densities ${\mathrm{\rho }}_{\mathrm{\sigma }}$. Becke recommends G(${\mathit{x}}_{\mathrm{\sigma }}$)=${\mathit{x}}_{\mathrm{\sigma }}^2$/[1+0.0253${\mathit{x}}_{\mathrm{\sigma }}$${\sinh }^{\mathrm{-}1}$(${\mathit{x}}_{\mathrm{\sigma }}$)]. It is demonstrated that the kinetic energy can be represented with comparable accuracy by the formula T=$2^{2/3}$${\mathit{C}}_{\mathit{F}}$F ${\mathcal{J}}_{\mathrm{\sigma }}$ ${\mathrm{\rho }}_{\mathrm{\sigma }}^{5/3}$(r)[1+αG(${\mathit{x}}_{\mathrm{\sigma }}$)]dr, where ${\mathit{C}}_{\mathit{F}}$ is the Thomas-Fermi constant, α is a constant, and G(x) is just the same function that appears in the formula for K. Recommended values, obtained by fitting data on rare-gas atoms, are α=4.4188×${10}^{\mathrm{-}3}$, β=4.5135×${10}^{\mathrm{-}3}$. The best α-to-β ratio, 0.979, is close to unity, and calculations with α=β=4.3952×${10}^{\mathrm{-}3}$ are shown to give remarkably accurate values for both T and K. It is briefly discussed how the above-noted equations for K and T can both result from scaling arguments and a simple assumption about the first-order density matrix.

We have investigated the effects of various model polarization potentials in low-energy (below 15 eV) electron-${\mathrm{SiH}}_4$ collisions in which electron-exchange correlation is treated exactly via an iterative procedure. Two models of the parameter-free polarization potential are employed; one, the ${\mathit{V}}_{\mathrm{pol}}^{\mathrm{JT}}$ potential, introduced by Jain and Thompson [J. Phys. B 15, L631 (1982)], is based on the polarized-orbital theory; the other, the correlation-polarization potential ${\mathit{V}}_{\mathrm{pol}}^{\mathrm{CP}}$, first proposed by O’Connel and Lane [Phys. Rev. A 27, 1893 (1983)], is given as a density functional. In this low-energy region, the differential as well as integral cross sections are greatly influenced by such short-range-correlation and long-range-polarization interactions. We found that a local parameter-free model to mimic charge-distortion effects is quite successful if it is determined under the polarized-orbital-type approach rather than based on density-functional theory.

A simple general method is presented whereby measured spectroscopic energy-level data can be used to empirically construct the eigenvectors of intermediate coupling for an arbitrary configuration. These empirical eigenvectors can be used to elucidate the transition rates into, out of, and among the levels of the configuration by separating the effects of intermediate coupling from the radial transition moment. Predictive applications to the ${\mathit{np}}^3$ configurations of the N and P isoelectronic sequences are presented.

Line-shape analysis in absorption spectroscopy provides detailed information on microscopic structure as well as on relaxation processes that take place in the sample. Both aspects are closely intertwined in the framework of the stochastic Liouville equation, where the dynamics of an isolated Hamiltonian system is supplemented with stochastic modulation to account for random interactions with the surrounding medium. Previously, this equation has been solved analytically for a special class of modulation operators of separable form [E. van Faassen, Phys. Rev. A 42, 2785 (1990)]. In this paper the method is extended to include hyperfine couplings in the Hamiltonian, as such couplings are of eminent importance for practical applications in the field of microwave spectroscopy. Again, the equation is rigorously solved by algebraic means. The solution is shown to have a much richer analytical structure than the previous case.

The transition probability of the 358.487-nm transition in neutral uranium has been measured by the line-absorption method using a single hollow-cathode discharge lamp. Our value agrees with that reported by Klose and Voigt [Phys. Rev. A 16, 2032 (1977)] but is surprisingly about four times larger than the value reported by Bieniewski [J. Opt. Soc. Am. B 1, 300 (1984)].

The power spectrum of radiation emitted by a Morse oscillator strongly driven by an intense laser pulse is calculated numerically. It is shown that at laser intensities close to the dissociation threshold, instead of the usual harmonic generation one observes a strong generation of a discrete but dense spectrum. This is a manifestation of resonant nonperturbative effects and can be viewed as a signature of chaotic behavior of the system. The present results suggest the use of nonharmonic generation to measure the onset of chaos in radiation-matter interactions.

The near-photon-number eigenstates introduced by Yuen [Phys. Rev. Lett. 56, 2176 (1986)] link together squeezing, antibunching, and phase properties of light. They are the crescent states generated by the crescent operator introduced here, and physically they represent another explicit example of minimum uncertainty states of the Shapiro-Wagner phase concept.

We present the result of a simple nonvariational configuration-interaction calculation for the energy levels and the radiative lifetimes of the Mg isoelectronic sequence. Emphasis is placed on the nonuniform variation of the radiative lifetimes for a series of singly excited states along the isoelectronic sequence due to the strong configuration mixing between the singly excited series and the doubly excited perturbers. The energy contributions from the bound-continuum type of configurations corresponding to the combination of negative- and positive-energy orbitals for the two valence electrons in a divalent atom are examined in detail within the frozen-core Hartree-Fock approximation. Comparisons with existing theoretical and experimental data are also presented.

We derive generalizations of the semiclassical trace formula of Gutzwiller [J. Math. Phys. 12, 343 (1971)] and Balian and Bloch [Ann. Phys. 69, 76 (1972)] that are valid for systems exhibiting continuous symmetries. In particular, we consider symmetries for which the associated set of conserved quantities Poisson-commute. For these systems, the periodic orbits of a given energy occur in continuous families and the usual trace formula, which is valid only when the periodic orbits of a given energy are isolated, does not apply. In the trace formulas we derive, the density of states is determined by a sum over continuous families of periodic orbits rather than a sum over individual periodic orbits. Like Gutzwiller’s formula for isolated orbits, the sum involves intrinsic, canonically invariant properties of the periodic orbits. We illustrate the theory with two important special cases: axial symmetry and integrable systems.

The spatial power spectra of passively convected scalar quantities in fluid flows are considered for the case in which the flow has smooth large-sclae spatial dependence and Lagrangian chaos. Fundamentally different results apply for the small-diffusivity limit of the ‘‘initial-value problem’’ (in which an initial passive scalar density evolves in time with no passive scalar source present) and the ‘‘steady-state problem’’ (in which a statistically steady passive scalar source is present and one seeks time-asymptotic steady properties). Previous work has shown that the initial-value problem yields a situation where the gradient of the passive scalar tends to concentrate on a fractal. The purpose of this paper is to consider the implications of the prevously obtained fractal properties for the spatial power spectrum of passively convected scalars. The main result of this paper is that for the initial-value problem the spatial power spectrum is related to the fractal dimension spectrum and to the distribution of stretching rates (finite-time Lyapunov exponents) of the flow and is not necessarily a power law. In particular, for the initial-value problem in the case in which the flow has no Kolmogorov-Arnold-Moser (KAM) surfaces, the power spectrum is distinctly not a power law. However, if KAM surfaces are present, the power spectrum for the initial-value problem exhibits a ${\mathit{k}}^{\mathrm{-}1}$ power-law dependence in a range of k values. For the steady-state problem, it is shown that a ${\mathit{k}}^{\mathrm{-}1}$ power spectrum always applies. (This latter result has been previously derived for the steady-state problem and is known as ‘‘Batchelor’s law.’’)

It is shown that the laws of equilibrium statistical mechanics modified for finite number of degrees of freedom are approximately valid for chaotic vibrations of the Hénon-Heiles oscillators.

Configurations generated by the evolution of some one-dimensional cellular automata may be viewed, after many time steps, as particlelike structures evolving in a regular background. A classification of the most frequently observed ‘‘particles’’ is proposed according to their specific behavior. The simplest—a straightforward generalization of the ‘‘kinks’’ in range-1 Rule 18 earlier studied by Grassberger [Phys. Rev. A 28, 3666 (1983)]—exhibit a diffusive motion and annihilate according to simple processes. Others have, in contrast, constant (positive, negative, or zero) velocities. The ‘‘collision’’ of particles with different velocities leads to some ‘‘reactions’’ in which some particles are annihilated and others are created. A detailed description of such ‘‘reactions’’ sheds new light on the large-time behavior of range-1 Rule 54 with a very slow decrease of the particle number, as ${\mathit{t}}^{\mathrm{-}\gamma }$ (γ≃0.15). More ‘‘exotic’’ behaviors are sometimes observed. Some particlelike structures radiate other ‘‘particles.’’ Some ‘‘particles’’ combine to generate a perturbation whose space extension increases with time and can be annihilated through the interactions with other ‘‘particles.’’ These different behaviors could lead to a more precise classification of cellular-automaton rules.

The dynamical properties of a semiclassical model of spin relaxation are carefully studied with the help of computer simulation. It is shown that, as an effect of the reaction field, the relaxation time as a function of temperature ranges from an Arrhenius-like behavior at weak temperatures to a linear power-law behavior at high temperatures. It is also shown that a fairly accurate theoretical prediction of the relaxation time can be obtained in both the low- and high-temperature limit. In the latter regime a simple factorization prescription, although leading to small deviations from the exact equilibrium value for the spin components, is shown to provide the most accurate predictions.

We present a detailed numerical study of certain fundamental aspects of a one-dimensional homogeneous, deterministic Burridge-Knopoff model. The model is described by a massive wave equation, in which the key nonlinearity is associated with the stick-slip velocity-weakening friction force at the interface between tectonic plates. In this paper, we present results for the statistical distribution of slipping events in the limit of a very long fault and infinitesimally slow driving rates. Typically, we find that the magnitude distribution of smaller events is consistent with the Gutenberg-Richter law, while the larger events occur in excess of this distribution. The crossover from smaller to larger events is identified with a correlation length describing the transition from localized to delocalized events. We also find that there is a sharp upper cutoff describing the maximum large event. We identify how the correlation length and this upper cutoff scale with the parameters in the model. We find that both are independent of system size, while both do depend on the spatial discretization. In addition to the magnitude distribution, we present a series of measurements of other seismologically relevant quantities, including the event duration, the size of the rupture zone, and the energy release, and discuss the relationship between our measurements and the corresponding empirical laws in seismology.