Elastic properties of a variety of structures, such as polymers, noble element solids, and solids with very unharmonic interatomic potentials, are dominated by the shape and volume dependence of the entropy. The suggested tethered solid model consists of a periodic array of atoms that interact via potentials with infinite barriers. The potential energy of the system vanishes identically, and its properties are determined by the entropy. Elastic moduli of the solid are strictly proportional to the temperature. The model is used to test some approximate approaches to the problem of entropic elasticity, as well as a ‘‘toy example’’ of emergence of a harmonic response from unharmonic forces.

We show how to build atomic states that mimic the classical Bohr-Sommerfeld elliptic orbits with minimum quantum fluctuations. These elliptic states are uniquely defined from symmetry considerations. They are the coherent states of the SO(4) symmetry group of the Coulomb interaction in three dimensions and are superpositions of the usual spherical states with well-defined weights and phases. They can be experimentally produced from laser excitation of Rydberg atoms in crossed electric and magnetic fields. We finally indicate how to build Coulomb wave packets localized both in space and time.

It is shown that the Bethe parameter $b_K$ for the K-shell ionization of atoms by electrons is the same for various atoms and is numerically twice the value of $b_K$ for the hydrogen atom. Also, a scaling relationship is shown to exist between the oscillator strengths for the K-shell ionization of different atoms and that for the hydrogen atom. Bethe K-shell-ionization cross sections are in good agreement with the experimental data at high energies.

Electron excitation cross sections of ${\mathrm{Ca}}^{19+}$ and ${\mathrm{Ca}}^{18+}$ ions by impact of neutral atoms are calculated with the symmetric eikonal theoretical model. Theoretical results agree with recent experiments.

Transport and reactive properties of a muon swarm in deuterium gas in an electrostatic field are analyzed by solving Boltzmann’s equation over a wide range of E/$n_0$ (ratio of the applied electric field to the gas number density). We find that both the muon-capture rate and the recoil energy of the deuterium molecule after muon capture show significant variation with E/$n_0$. The implications for muon-catalyzed-fusion research are outlined. Muon transport properties are given as functions of E/$n_0$.

The number of interconnections in a neutral network is reduced by eliminating the ‘‘weakest’’ bonds. The performance is then improved by reapplying the learning algorithm.

Construction of spatially chaotic stationary wave trains is discussed in terms of dynamics on a folded solution manifold. The analytic technique employs reduction of a reaction-diffusion system with separated time scales to a singularly perturbed Hamiltonian system to derive a logarithmic next-return map that exhibits domains of chaotic behavior.

The gap map is obtained by introducing a discontinuity at the critical point of a unimodal map on the interval. Truncations due to the discontinuity, onset of chaos, and tangent bifurcation in the gap map are analyzed by means of symbolic dynamics.

As a result of the unusual temperature dependence of the isothermal compressibility of water at low temperature, the structure factor increases with decreasing momentum transfer, below 0.5 A${̊}^{\mathrm{-}1}$. We confirm this behavior with a neutron scattering experiment performed at different temperatures and in isochoric conditions. Neutron scattering conditions allow the obtaining of data almost free of the container contribution. The experimental result is in agreement with the theory describing the hydrogen bond network of water at low temperature.

The Landau-Ginzburg (LG) free-energy-gradient theory is extended to account for domains of intermediate wavelengths. The extension is nonlocal but preserves the universal features of the LG theory, has the same level of complexity, and reduces to it in the small-gradient limit. It also enables one to gain a meaningful insight into the microstructure of a system.

We present simulation results for the fractal dimensionality of the η model for a wide range of values of η. We check the theoretical predictions for the curve $d_f$(η) proposed by Halsey [Phys. Rev. Lett. 59, 2067 (1987)] against the values we get from calculated quantities and find good agreement between theory and the computer experiments.

The dependence of the energy levels of doubly excited states of heliumlike ions on the nuclear charge Z is studied. By expressing the energy levels of doubly excited states for intrashell states in the form of a double-Rydberg formula and for intershell states using the quantum-defect method, we expand the quantum defect in each formula in powers of 1/Z. Using known energy levels for the low-Z ions, we extract parameters of the quantum defect which allow the calculation of accurate energy levels of other ions along the helium isoelectronic sequence.

It is currently thought that the laser cooling of an ordered ion array, an ion crystal, is qualitatively the same as that of a single ion. We show that this assumption is strongly violated in recent experiments in Paul traps, due to ion micromotion. Our analysis demonstrates an unexpected laser damping instability that induces an ion-crystal order-chaos transition and also explains why ion crystals in Paul traps have been limited to less than 100 ions. We directly observe the effects of ion micromotion on the laser cooling of a single trapped ${\mathrm{Ba}}^{+}$ ion by a new technique.

A density-matrix formulation of the ab initio methods of nonrelativistic quantum mechanics is presented. The variational equations for the standard calculational techniques of molecular quantum mechanics are derived from a single expression for the total energy of an N-particle system. A generalization of the Hohenberg-Kohn theorem is proved, showing that the ground-state energy of a many-body Hamiltonian is a functional of the single-particle density matrix and hence of the first-order reduced-density function (the diagonal of which is the particle density of the standard theorem). The theorem is used to develop a new method to calculate the total energy and single-particle properties of the many-body problem.

A modified perturbation procedure for computing relativistic atomic bound-state energies is described, in which the instantaneous Coulomb interaction is included in the unperturbed QED Hamiltonian and the effect of virtual electron-positron pairs and of virtual transverse photons is treated as the perturbation. To illustrate the method in the context of a simple model, a one-electron atom is considered and a ‘‘one-pair’’ approximation is analyzed in detail. The approach is based on the resolvent-operator formulation of many-body time-independent perturbation theory. The removal of divergent vacuum-to-vacuum matrix elements is easily accomplished in this formulation, and it leads rather directly to the derivation of a modified Dirac equation in which all perturbative effects are contained in an effective one-electron potential. A set of integral equations for the evaluation of the effective potential in the one-pair model is derived. These equations have the same structure as the Dyson-Schwinger equations of covariant QED and serve a similar purpose. That is, they allow for the isolation of the divergent self-energy and vertex parts, leaving a finite kernel (the K matrix) which contains the effects of multiparticle intermediate states. In the one-pair model considered here the intermediate states consist of an electron and a virtual pair interacting Coulombically. It is shown that the K matrix can be constructed with the aid of a rigorous minimum principle of the Rayleigh-Ritz type. That such a minimum principle exists appears to be an advantage of the noncovariant Hamiltonian procedure. The inapplicability of standard renormalization methods is, however, a distinct disadvantage. While some progress (the removal of vacuum divergences and the isolation of divergent parts in the integral equation) is reported, a full resolution of the renormalization problem in the Hamiltonian formulation remains to be developed.

Oscillator strengths for electric dipole transitions between singly excited S, P, and D states are calculated via Z-dependent perturbation theory. The transition matrix elements through first order are obtained from variational perturbation first-order wave functions. Second-order expansion coefficients for the matrix elements are then estimated with the aid of several approximants. These matrix elements, together with accurate transition energies, yield oscillator strengths for transitions between all S-P and P-D transitions between states of two-electron ions with principal quantum number up to 9 and for values of the nuclear charge up to approximately 30.

Relative photodestruction cross sections and fragmentation branching ratios of positively and negatively charged aluminum-cluster ions are measured as a function of photon energy for clusters of up to eight atoms. The cross sections and fragmentation branching ratios show a strong dependence on photon energy. For positive ions the cross sections generally increase with photon energy, while for negative ions a pronounced maximum in the cross section is observed near 2.0 eV. Neutral-atom evaporation is a dominant fragmentation pathway for both positive and negative clusters. Positive clusters are also found to evaporate an atomic ion. For the negative clusters, photofragmentation is suppressed for photon energies near the known electron binding energies.

The Dirac equation is solved for a wide class of central potentials by means of a variational calculation involving a scale parameter and a finite basis of orthogonal functions. Instability due to the existence of negative-energy states is avoided and accurate solutions for low-positive-energy states are obtained by an appropriate energy shift and diagonalizing the squared finite Dirac matrix. A basis of 20 states each for the large and small components is capable of 13-place accuracy in the relativistic solution of the hydrogen atom and more than five-place accuracy for a zero-mass quark in a confining scalar potential. In addition to being accurate, the solution is sufficiently rapid to be used on personal computers. The method is also suitable to extension to cylindrically symmetric potentials.

The doubly differential energy and angular distribution of electrons ejected into the continuum from ${\mathrm{H}}^0$,${\mathrm{He}}^{+}$,${\mathrm{He}}^{2+}$(0.2 MeV/u)–Ne,Ar,Kr collision systems are studied. The measured electron distributions are analyzed in a three-dimensional presentation with a series expansion by using a three-dimensional fitting procedure. The coefficients are discussed. Some other parameters of the cusp are also determined and compared with the theory.