An interpretation of the Flory approximation as a coarse graining of the free energy of a polymer chain, recently introduced by R. Dekeyser, A. Maritan, and A. L. Stella [Phys. Rev. A 36, 2338 (1987)] is used for the discussion of the conformational properties of a polymer chain at the FTHETA point in two dimensions. With the inclusion of a short-range nonintersection condition together with long-range three-body repulsion, and the use of scaling invariance arguments, the estimate ${\nu }_{\mathrm{FTHETA}}$=(7/12=0.583. . . is obtained for the scaling of the average end-to-end distance with the number of monomers. This is in very good agreement with experimental and numerical work, and just 2% off the conjectured exact value ${\nu }_{\mathrm{FTHETA}}$=(4/7=0.571. . . .

We study the behavior of chaotic systems at transition points (intermittency and crisis) through their dimension spectra f(α). In the transition regions the finite-statistics f(α) curves display a characteristic doubly peaked structure whose convergence to the asymptotic concave shape occurs for exceedingly large numbers of points. This slowing-down effect is studied for both the Duffing equation and the Hénon map and is used as a guideline in the interpretation of the spectra of NMR-laser experimental data sets.

A growth model is presented to show a phase transition. The drift-diffusion-limited aggregation model with a positive drift proposed by Meakin [Phys. Rev. B 28, 5221 (1983)] is extended to that with a negative drift. When the drift changes from a positive value to a negative value, the structure of the aggregate varies from a dense structure, through the diffusion-limited aggregation (DLA) fractal, to a needlelike structure. In contrast with the crossover from the DLA fractal to the dense structure at a positive drift, at a negative drift the crossover is shown from the fractal structure at short length scales to a one-dimensional structure at longer length scales.

It is shown that the interaction of frequency- and amplitude-modulated optical fields with a two-level atom, as treated by Nayak and Agarwal [Phys. Rev. A 31, 3175 (1985)] and Agarwal and Nayak [J. Phys. B 19, 3385 (1986)], respectively, can be described by the same Bloch equations, and that both have close counterparts in magnetic resonance. The matrix continued-fraction solution for the system is refined, and fluorescence and absorption spectra are explicitly related.

Density-functional theory calculations using the Hartree-Fock system method provide strong theoretical evidence that the negative ions ${\mathrm{Sr}}^{-}$, ${\mathrm{Ba}}^{-}$, and ${\mathrm{Ra}}^{-}$ are stable in the ground states with the odd-parity configurations $n{s}^2\mathrm{np}$ ($n=4, 5, 6$). The dominant relativistic effects have been included perturbatively and are essential in choosing these configurations instead of $\mathrm{}(n-1\mathrm{})\mathrm{dn}{s}^2$ in ${\mathrm{Ba}}^{-}$ and ${\mathrm{Ra}}^{-}$.

We present the first quantum-mechanical calculations of the ionization probability of high-$n$ H Rydberg atoms perturbed by strong bichromatic microwave fields. The quantum-mechanical ionization thresholds agree very well with the experimental findings. The effect of rational approximants to the experimental frequency ratio is studied. We provide evidence to show that for the range of principal quantum numbers and field parameters investigated experimentally, the response of the H atoms to the bichromatic microwave field is quasiperiodic.

A subpicosecond laser is focused to ${10}^{17}$ W/${\mathrm{cm}}^2$ to create an extremely transient Al plasma with a kV radiation time short compared to most of the excitation times. High-resolution spectroscopy is used to analyze the kV line emission from the He- and H-like ions and to determine that the plasma reaches a temperature near 1 keV and cools in less than 10 ps.

We compute above-threshold ionization electron spectra by solving numerically the time-dependent Schrödinger equation of a one-dimensional model atom in an external field, and compare the results with three Keldysh-type models worked out for the same atom. The Keldysh models offer an unreliable representation of the ionization process.

We investigate the interaction between external noise and spatial degrees of freedom for the Kuramoto-Sivashinsky (KS) equation with and without damping, a prototype equation which is known to show weak spatial turbulence and which arises in many areas including flame fronts, flow down an inclined plane, convection between insulating boundaries, etc. We show that the KS equation can be convectively unstable and can lead to noise-sustained structures.

We derive the probability density function for the nearest-neighbor distance of the closest Brownian particle to an isolated trap in one and three dimensions. The asymptotic (in time) density of the nearest-neighbor distance in one dimension is a time-dependent skewed Gaussian function and the mean value of this distance increases asymptotically as $t^{\frac{1}{4}}$. The large-distance form of this function is a simple exponential. In three dimensions the analogous result in the presence of an absorbing sphere is shown to resemble the Hertz density closely at large distances. The asymptotic reaction rate goes as $c$ (density) in three dimensions but as $c{t}^{-\frac{1}{2}}$ in one dimension. The results are related to exciton fusion and reaction kinetics.

The dynamical scaling of the chain-chain aggregation model is investigated in three dimensions. Monte Carlo simulations are performed on a cubic lattice with a diffusion coefficient proportional to $k^{\gamma }$ for a chain of mass $k$. At large times the mean chain mass grows like $t^z$ and the meansquare radius of gyration like $t^{\frac{2z}{D}}$, where $D$ is the fractal dimension of the chains. The relation $z={(1-\frac{1}{D}+\varphi -\gamma )}^{-1\mathrm{}}$, obtained when one assumes that the sticking probability between two chains of mass $k$ is proportional to $k^{-\varphi }$, is checked numerically with $\varphi \mathrm{}\left(3D\right)\mathrm{}\approx 0.72$.

Fermi contact spin densities of the first-row atoms B–F having open-shell p electrons are systematically calculated with simple, physically interpretable wave-function models that include only the dominant configurations together with relevant single excitations that describe polarization effects. All orbitals involved are optimized self-consistently by accurate numerical grid methods to obviate any questions about basis-set incompleteness. It is found that spin polarization of the 1s, 2s, and 2p shells (the latter for oxygen and fluorine only) together with orbital polarization of the 2s shell are the important effects. Core and valence contributions are separately large in magnitude, but nearly cancel one another leading to much smaller net spin densities. The results show good semiquantitative agreement with experiment, implying that true electron-correlation effects play a secondary role in determining the spin densities of these first-row atoms.

The G×(g+h) Jahn-Teller problem, relevant to the instability of icosahedral molecules in fourfold-degenerate electronic states, is investigated. The stationary points of the resulting adiabatic potential energy surface are retrieved by the method of the isostationary function. This method takes advantage of the parent SO(4) symmetry of the G×(g+h) problem under equal-coupling conditions. The structure of the surface depends on the relative strength of the coupling to fourfold- and fivefold-degenerate modes. If the G×g coupling is predominant, five tetrahedral minima are found, forming the vertices of a four-dimensional tetrahedron. If the G×h coupling is the more pronounced, ten trigonal minima are found at the vertices of a Petersen graph. The results are in agreement with the epikernel principle.

Rigorous lower bounds to the average electron radial density 〈ρ〉 in terms of any two moments of the charge density have been found for N-electron systems. Similar bounds to the average electron momentum density 〈γ〉 are also given by means of any two momentum expectation values. These bounds allow us to establish rigorous inequalities to 〈ρ〉 and 〈γ〉 (which have been recently found to be experimentally measurable) and other fundamental and/or measurable quantities such as the electronic energy, the diamagnetic susceptibility, and the Compton profile peak height J(0). The quality of the bounds is analytically discussed and numerically studied within the Hartree-Fock framework. Best bounds turn out to be (1) 〈ρ〉≥〈$r^{\mathrm{-}1}$${〉}^3$/9πN, (2) 〈γ〉≥8[J${\mathrm{}\left(0\right)\mathrm{}]}^3$/9πN. .AE

Lower bounds to the electronic charge density of spherical atoms at the origin, ρ(0), are given in terms of the radial expectation values 〈$r^{\alpha }$〉 and the average electron density 〈ρ〉. Similar bounds are also valid in momentum space. Previous results are also improved, and several relationships among ρ(0), the Coulomb energy, and 〈$r^{\alpha }$〉 values have been derived. The quality of the bounds is analytically discussed and numerically studied within the Hartree-Fock framework.

Simple quadrature formulas are obtained for relativistic continuum normalizations and phase shifts in a screened spherically symmetric central potential, utilizing a relativistic generalized WKB approximation based on the use of Coulomb wave functions as comparison functions. The derivation is based on our similar results for the nonrelativistic case, combined with our recent transformation of the Dirac equation into a modified Schrödinger equation. Excellent agreement is obtained in comparison with exact numerical calculations.

The universal energy relation, discovered for metallic and covalent solids as well as nuclear matter, is tested for diatomic molecules. We find that it applies well to covalent diatomic bonds, but that ionic diatomic bonds are in a distinct class. A simple extension of the universal binding energy relation that includes the effects of ionicity ensues. It yields accurate predictions of spectroscopic data for both ionic and covalent bonds in 150 molecules. The form of the covalent part is given by the universal relation, suggesting an intimate relationship between the energetics of solids and diatomic molecules.

The nucleus is represented as a Kerr-Newman source, under the assumption that the angular momentum of the source is equal to the intrinsic spin angular momentum of the nucleus. The theoretical values of the hyperfine splitting obtained from a solution of Dirac’s equation for this model of the muon, the positron, and the proton agree with the observed values in muonium, positronium, and hydrogen, to within the uncertainty in the respective QED corrections—except for an unaccounted factor of 2. In hydrogen one also has to introduce the observed value of the magnetic moment of the proton. The singularity in Dirac’s radial differential equations is shifted from the origin, where it is located in the case of flat space, to a pair of conjugate points on the imaginary axis of the radial coordinate. Consequently, the energy eigenvalues have a trace of an imaginary part, making the bound states of our model unstable.