Theoretical and semiempirical predictions of fine-structure intervals for the lowest P terms in the Cu, Zn, Ga, and Br sequences are presented for all ions with Z≤92. Through the use of screening parameter reductions of both the existing data base and the ab initio multiconfiguration Dirac-Fock computations reported herein, a new empirical decomposition has been discovered that permits measurements for the Cu sequence to be combined with theoretical computations to make precise predictions for the Zn, Ga, and Br sequences. These predictions are of higher precision than could be obtained solely by ab initio methods, and extend to much higher Z than semiempirical extrapolations alone would permit. These results provide insights into the interaction of the active and core electrons, and test a method that is applicable to many other systems.

The paper describes the experimental investigation of a subclass of quartet levels of the alkali-metal atoms which retain metastability against autoionization and have large radiative yields. Using high-pulsed-power microwaves, we obtain emission spectra of Na, K, Rb, and Cs. In each case, the neutral emission spectrum is dominated by emission from these levels.

We have used two-step, two-color excitation to populate high np singlet Rydberg states of molecular hydrogen under electric-field-free conditions. Sub-Doppler resolution is obtained by exciting the X ${}^1$${\Sigma }_g^{+}$→E ${}^1$${\Sigma }_g^{+}$ two-photon transition with copropagating photons, then further exciting the molecules to high Rydberg states with a narrow-band laser. We have observed transitions to states up to n∼90 for the Rydberg series which converge to the two lowest ionization limits. From an analysis of the energies of the observed transitions we have obtained new results for the first two ionization potentials of molecular hydrogen, with the highest accuracy reported to date. The new values are 124 417.61±0.07 ${\mathrm{cm}}^{\mathrm{-}1}$ for parahydrogen and 124 475.94±0.07 ${\mathrm{cm}}^{\mathrm{-}1}$ for orthohydrogen. Some of the Rydberg states predissociate strongly, apparently due to the influence of perturbing states of low principle quantum number. This is the first observation of such predissociation in Rydberg states of high principle quantum number.

Stark widths and shifts of the most prominent Ne ii spectral lines originating from 13 multiplets have been measured and compared with existing experimental and theoretical results. A linear pinch discharge was used as a plasma source. Electron densities determined with single-wavelength laser interferometry using the visible λ=632.8 nm transition of a He-Ne laser cover the range of (0.30–1.42)×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$. The electron temperature, in the range of 22?0–40?0 K, was determined from the Boltzmann slope of several Ne ii spectral lines and from the relative intensity ratios of several Ne i–Ne ii lines. Experimental Stark width data of Ne ii spectral lines agree well with existing experimental and theoretical results. Stark shift experimental data disagree with existing theoretical data in some cases up to factor of 3. Our data and those of other authors were used to investigate the nature of Stark broadening and shift dependence on the upper-level ionization potential of the corresponding spectral line belonging to 3s-3p and 3p-3d transition arrays and to the np-nd Ne ii, Ar ii, Kr ii, and Xe ii homologous sequence.

Results of relativistic random-phase approximation calculations of photodetachment cross sections and angular-distribution asymmetry parameters are presented for the outer shells of the negative ions ${\mathrm{F}}^{\mathrm{-}}$, ${\mathrm{Cl}}^{\mathrm{-}}$, ${\mathrm{Br}}^{\mathrm{-}}$, and ${\mathrm{I}}^{\mathrm{-}}$ in the photon-energy region from the threshold to about 100 eV. These results are compared with available theoretical calculations and with experimental data.

The total dielectronic-recombination rates for ${\mathrm{Ne}}^{7+}$, ${\mathrm{Ar}}^{15+}$, ${\mathrm{Fe}}^{23+}$, and ${\mathrm{Kr}}^{33+}$, all members of the lithium isoelectronic sequence, are computed in the nonrelativistic, single-configuration, LS-coupling, frozen-core, corona model approximation. Comparison is made with other calculations, and differences are noted and analyzed. Analytic formulas for interpolating the total dielectronic-recombination rates for other members of the lithium isoelectronic sequence are given.

The rate coefficients for the dielectronic recombination of ${\mathrm{Ar}}^{9+}$, ${\mathrm{Fe}}^{17+}$, ${\mathrm{Kr}}^{27+}$, and ${\mathrm{Mo}}^{33+}$, all members of the fluorine isoelectronic sequence, are computed in the single-configuration, LS-coupled, frozen-core, corona model approximation. Comparison is made with other calculations. Analytic formulas which can be used for interpolating the rate coefficients for other members of the fluorine isoelectronic sequence are given.

We consider the solvable model of nonabsorbing nonlinear medium modeled as an anharmonic oscillator interacting with squeezed light described as an SU(1,1) coherent state. We find that the squeezing is eventually revoked and furthermore that the greater the initial state is squeezed, the more rapidly the squeezing is revoked.

We apply our quantum theory of multiwave mixing to the generation of squeezed states of light via three- and four-wave mixing in cavities and in propagation. We compare the cavity predictions to the experimental results of Slusher et al. [Phys. Rev. Lett. 55, 2409 (1985)], finding reasonably good agreement. The squeezing found there is due to the fact that the number operators are driven by resonance fluorescence, which nearly vanishes for the large detunings chosen, while the combination tone operators are driven by relatively large source terms. We give a physical discussion as to why the spectral quantities outside the cavity are given by those inside multiplied by the cavity linewidth. We have found analytic formulas for the variances for arbitrary propagation distances, detunings, and pump intensities. We derive these formulas both from the density operator and from the Langevin methods. To obtain significant squeezing, the propagation distances must be large compared with the resonant Beer’s law length.

We present an exact, analytic solution for the probability of radiative, cooperative transitions of stationary, weakly coupled atoms in strong light fields. Very simple expressions are obtained for pair-emission and -absorption probabilities by use of the ‘‘dressed-atom’’ formalism applied to atoms in solids or nearly at rest in optical traps. Analogies between radiative collisions in gases and the pair transitions encountered in solids, which may be viewed as ‘‘frozen’’ radiative collisions, are explored. Conditions are predicted for the occurrence of electric dipole decoupling in the presence of a suitable rotating electric field, similar to the well-known phenomenon of ‘‘magic-angle’’ decoupling of magnetic spins due to a rotating magnetic field. Observations of this new effect should permit precision determinations of interaction Hamiltonians in optical pair systems.

The recently developed nonlinear complex eikonal approximation, which was previously employed to study dispersively nonlinear resonators, is applied to absorptively nonlinear resonator configurations. Conditions for obtaining optical bistability in molecular absorbers are derived and the photophysical consequences are discussed.

The phase change of an electromagnetic wave propagating through a free-electron laser (FEL) amplifier has been measured. The FEL operated at 34.6 GHz, with both a uniform and a tapered wiggler. The results of the experiment show a nearly constant phase derivative with increasing wiggler length through the exponential gain region and are in good agreement with analytical theory. For the tapered-wiggler amplifier, the phase derivative decreases at a point approximately one third of a synchrotron period past saturation; the decrease is in good agreement with numerical simulation. For the untapered-wiggler amplifier, however, numerical simulations predict an increase in phase derivative past saturation, whereas in the experiment the phase derivative abruptly vanishes. Several explanations for the discrepancy are discussed.

General limits are derived for the achievable brightness and photon density in phase space under very general assumptions. Upper as well as lower limits are given for a classical electric charge radiating in a vacuum, including the case when the emitting charge has velocity approaching zero. Even in the latter case the lower limit given here is in general positive. A figure of merit for photon sources, such as undulators, is defined.

Analytical expressions for the scattering function for a polydisperse Percus-Yevick fluid with Schulz- (Γ-) distributed particle diameters have been obtained. Results obtained with the expression for selected width factors and particle densities are presented. Comparisons have been made with approximations routinely used to model small-angle scattering curves. The expression derived is shown to yield the static structure function as a special case.

We have conducted an experiment on the transition from quasiperiodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior which we have observed is deterministic, that is, it is described by strange attractors. We discuss various problems that arise in computing the dimension of strange attractors constructed from experimental data and show that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50% above the onset of turbulence.

We study the effect of gravity on the Saffman-Taylor meniscus, which appears when air is pushing oil in a horizontal Hele-Shaw cell. The effect enters via the dimensionless (Bond) number G=ρ${\mathrm{gb}}^2$/γ. The existence and the thickness of the wetting films is studied, and the associated pressure jump at the interface is computed. The analysis is carried through by means of asymptotic matched expansions in the small capillary number, scrC=μU/γ. For G<1, there is no correction due to gravity to the jump of pressure across the meniscus and the pressure is proportional to (γ/b)${\mathrm{scrC}}^{2/3}$. For G>1, the finger is released from the bottom plate. The pressure jump is now proportional to √ρgγ ${\mathrm{scrC}}^{2/3}$ and thus independent of the thickness 2b between the plates. We study the meniscus experimentally for two values of G, G=1.1 and 3.3. We obtain a series of different shapes of the meniscus for various values of scrC. For small capillary numbers very good agreement between theory and experiment is found.

The asymmetries, as well as the widths, of spectral line profiles emitted by highly ionized high-Z elements in a dense, laser-produced hot plasma may be of use in determining the density of these plasmas. Three effects which introduce asymmetries into the line shape are the ion-quadrupole interaction, quadratic Stark effect, and fine-structure splitting. In this paper a method is proposed for including the ion-quadrupole interaction. This technique is then combined with procedures for including the quadratic Stark effect and fine-structure splitting to obtain asymmetric Lyman x-ray line profiles which include all three contributions.

Computer simulations have been used to explore the scaling properties of the growth probability measures and harmonic measure for a variety of fractal objects. In all cases we have studied the normalized distribution of growth or contact probabilities, N(P), for clusters with different masses, M, can be scaled onto a single curve using the scaling form ln(PN(P)lnM]=ln(M)g‘(ln(P)/ln(M)). The scaling function g’(x) is related to the function f(α) of Halsey et al. by g’(x)=$D^{\mathrm{-}1}$f(-Dx), where D is the fractal dimensionality of the set on which the measure resides. Here f(α) is the fractal dimensionality of the subset which supports singularities of type α. Similarly, for diffusion-limited aggregation on strips of width L and columns of area L×L we find that ln[PN(P)=ln(L)h(ln(P)/ln(L)), where h(x)=f(-x) and N(P)δP is the number of sites with growth probabilities (also harmonic measure probabilities in this case) in the range P to P+δP. Our results indicate that the ideas recently developed by Halsey et al. and the earlier ideas of Mandelbrot are applicable to a broad range of processes on fractal aggregates as well as to dynamic systems with fractal properties.

Diffusion-limited aggregation without branching is a model of diffusive growth in which tip splitting is absent. The resulting aggregates are sets of needles growing away from the initial deposition plane: They exhibit nontrivial scaling features. This paper contains a detailed study of the model. New results from computer simulations in two, three, and four dimensions are presented, and it is found that, for dimensions larger than 2, the value of the exponent controlling scaling becomes very close to the mean-field theory (continuum approximation) prediction. A theoretical treatment based on ideas close in spirit to real-space renormalization-group methods is discussed in detail. The analog of a Monte Carlo renormalization-group analysis based on this treatment is carried out, yielding predictions for the scaling exponent which agree well with simulation data.

A unit point charge placed within a general cavity in a dielectric medium induces a surface polarization charge density which is determined by a linear inhomogeneous integral equation. As the point source approaches the cavity surface, the polarization charge density becomes dominated by spatially singular terms. The two most singular contributions are calculated in a mean-curvature approximation. These contributions provide an approximate symmetric integral representation for the cavity Poisson-Green function which is exact throughout a spherical cavity in a conducting medium. For a general cavity, the approximation can be improved through the introduction of ‘‘quasi-images.’’ Numerical results are given for a cavity shape which models the geometry of an enzyme with a large indented active site.