Experiments on a ${\mathrm{CO}}_2$ laser with feedback [F. T. Arecchi, R. Meucci, and W. Gadomski, Phys. Rev. Lett. 58, 2205 (1987)] displayed an extraordinary set of instabilities, identified as Shilnikov chaos. We have investigated the stability structure of a theoretical model developed to describe this laser system and carried out an extensive numerical search for the Shilnikov instability. No computational evidence to support the claim of a Shilnikov instability for model parameters corresponding to the experimental region can be found.

A nondegenerate two-photon laser in a cascade three-level atomic system is studied. The difference between the laser and that derived from an effective Hamiltonian is discussed. Photon number distributions about field 1 are presented. The effects of field 2 on field 1 are studied in detail. Field 2 can play a role of gain enhancement or gain reduction for field 1. This is due to two actions of field 2: reducing the population of the intermediate level and changing the detuning really acting upon field 1, which is caused by the ac Stark shift.

An analytic pair potential proposed by Pettifor and Ward is used to calculate the thermodynamic properties of Na, Mg, and Al. The energy, pressure, and bulk-modulus values calculated using the Pettifor-Ward pair potential are in qualitative accord with calculations based on other models.

Derivation of thermodynamic sum rules for systems including charged particles is reconsidered and the validity of the result is examined with respect to the ordering in the powers of the wave number. For mixtures of electrons and ions, it is shown how the aspect of the one-component plasma or the ionic mixture appears when electrons become strongly degenerate.

Madelung energies of typical one-dimensional lattices of charges on a cylinder uniformly charged with neutralizing opposite charges are calculated in order to estimate the cohesive energy of such systems at low temperatures. Results are compared with the values in the limits of large and small radii of curvature, i.e., those of the planar system and the linear chain, and the former is shown to work as a good approximation for cohesive energy in a wide domain of parameters.

A one-dimensional n-step random walk on ${\mathrm{openZ}}^1$ which must not visit a vertex more than k times is studied via Monte Carlo methods. The dependences of the mean-square end-to-end distance of the walk and of the fraction of trapped walks on λ=(k-1)/n will be given for the range from λ=0 (self-avoiding walk) to λ=1 (unrestricted random walk). From the results it is conjectured that in the limit n→∞ the walk obeys simple random walk statistics with respect to its static properties for all λ>0.

An interesting recent article by Caves and Milburn [Phys. Rev. A 36, 5543 (1987)] unfortunately contains—albeit as a side remark only—an assertion that misrepresents the content of an article I wrote [Found. Phys. 16, 351 (1986)] on what I called ‘‘imperfect measurements’’ and on different theories purporting to describe such measurements. The proper perspective is restored here.

We have measured coincidences between x rays and projectiles that have captured one electron in ${\mathrm{F}}^{6+}$ + ${\mathrm{H}}_2$ collisions at projectile energies between 15 and 33 MeV. The cross sections for capture and simultaneous x-ray emission as a function of projectile energy show clear structures. Indications of an unexpectedly high population of high-$n$ states predominantly formed by resonant transfer and excitation (RTE) were found. Above the $\mathrm{KLn} \mathrm{}(n>\mathrm{}1\mathrm{})\mathrm{}$ RTE resonance energies another maximum was observed.

A formula is deduced for x-ray absorption cross sections in circularly polarized laser beams valid for moderate laser intensities. Possibilities of laser-assisted x-ray absorption processes energetically forbidden without the laser are also discussed near the absorption edge.

We consider the front between conductive and stationary convective states in a one-dimensional system exhibiting a subcritical bifurcation and show that it can be pinned to the underlying roll structure. This effect leads to the appearance of confined convective structures of arbitrary length. The pinning originates with the nonadiabatic effect which we study analytically. The pinning of traveling waves is discussed but the confinement, which for that case was observed experimentally, remains unexplained.

We study a shear flow instability in a liquid crystal aligned by the initial flow. A periodic distortion of the director and the velocity field in the plane perpendicular to the flow and the velocity gradient is investigated. We obtain the critical shear rate and the value of the critical wave vector at threshold. We discuss the instability in the case of a conventional liquid crystal and a polymer liquid crystal. Good qualitative agreement with experiment is found and the theory clarifies the observation of banded textures created in many polymer liquid crystals by shear flow.

We use the example of a Stern-Gerlach apparatus to show that the quantum-mechanical measurement problem ceases to be a physical problem for a measuring device with many degrees of freedom in the sense that deviations from wave-function collapse become virtually impossible to detect.

The generalized-exchange local-spin-density-functional theory (LSD-GX) with relativistic corrections of the mass velocity and Darwin terms has been used to calculate statistical total energies for the neutral atoms, the positive ions, and the negative ions for high-Z elements. The effect of the correlation and relaxation correction on the statistical total energy is discussed. Comparing the calculated results for the ionization potentials and electron affinities for the atoms (atomic number Z from 37 to 56 and 72 to 80) with experiment, shows that for the atoms rubidium to barium both the LSD-GX and the quasirelativistic LSD-GX, with self-interaction correction, Gopinathan, Whitehead, and Bogdanovic’s Fermi-hole parameters [Phys. Rev. A 14, 1 (1976)], and Vosko, Wilk, and Nusair’s correlation correction [Can. J. Phys. 58, 1200 (1980)], are very good methods for calculating ionization potentials and electron affinities. For the atoms hafnium to mercury the relativistic effect has to be considered.

The eigenvalue moment method for bosonic systems, recently developed by C. R. Handy and D. Bessis [Phys. Rev. Lett 55, 931 (1985)], is extended to discrete quantum mechanics. The relevant formalism is described and applied in the context of the discretized harmonic and sextic anharmonic potentials. Rapidly converging bounds to the associated ground-state energies are obtained for fixed lattice spacing a satisfying a<O(1).

We present a theory for the definition and the reliable calculation of correlated wave functions of a special class of triply excited states and for their rigorous geometrical analysis. This class is named the three-electron ionization ladder (THEIL) and refers to the simultaneous excitation of three electrons in valence states near threshold. Application to the Li THEIL of ${}_{}{}^4{}_{}{}^{}\mathrm{S}$ ° symmetry reveals impressive localization properties. In analogy with a similar analysis of the ‘‘two-electron ionization ladder,’’ which leads smoothly to the so-called ‘‘Wannier ridge’’ at the E=0 threshold, the present results suggest the existence of a ‘‘hyperridge’’ at E=0 with the following properties: (1) The ion core and the three electrons lie in a plane, (2) ‖${\mathrm{r}}_1$‖=‖${\mathrm{r}}_2$‖=‖${\mathrm{r}}_3$‖, and (3) ${\theta }_{12}$=${\theta }_{23}$=${\theta }_{31}$. .AE

Results of calculations using the non-self-interaction-corrected and self-interaction-corrected generalized-exchange local-spin-density-functional theories are reported and compared to other local-exchange theories. The generalized-exchange theories give most consistent results.

This paper describes an effort to develop further the work of R. McWeeny and C. A. Coulson [Proc. Phys. Soc. London, Sect. A 62, 509 (1949)] to obtain a helium-atom ground-state wave function in momentum space. In the application of Svartholm’s method [N. V. Svartholm, Ph.D. thesis, University of Lund, Sweden (1945)] to the helium momentum-space integral Schrödinger equation, a Feynman-integral evaluation technique is used to start the iteration in the electron-electron interaction term. The resulting correlated momentum-space wave function is used to evaluate the helium-atom ground-state energy and Compton profile.

A general method for solving the stationary one-electron, two-center Coulomb problem with a superimposed (uniform) strong magnetic field is described and applied. For arbitrary orientation of the field with respect to the line connecting the centers, the pertinent Schrödinger equation is solved by evaluating analytically the Hamiltonian matrix in a basis of (nonorthogonal) Hylleraas functions and solving numerically the generalized eigenvalue problem for this matrix. A detailed study of the properties of ‘‘magnetically dressed’’ (diatomic) one-electron molecular orbitals is performed by calculating energies and wave functions for the ${\mathrm{H}}_2^{+}$ and (H-He${)}^{2+}$ systems for field strengths up to about ${10}^8$ T. Molecular-orbital correlation diagrams are presented and discussed, in which dressed-orbital energies are displayed as a function of internuclear distance R at fixed angle θ between field direction and internuclear axis, and as a function of θ at fixed R. Equilibrium internuclear distances and total binding energies are calculated as functions of field strength for the magnetically dressed ${\mathrm{H}}_2^{+}$ system in its lowest gerade and ungerade states at θ=0 and θ=90°. The influence of the magnetic field on molecular binding properties as well as on the separation behavior of molecular orbitals at large internuclear distances is illustrated by means of wave-function plots. Whenever possible, our results are compared to those of previous investigations. The convergence properties of our method are discussed.

We have analyzed the reaction channels for the delayed, unimolecular dissociation of multiply charged clusters made from ${\mathrm{CO}}_2$ and ${\mathrm{C}}_2$${\mathrm{H}}_4$. The smallest observable triply and quadruply charged clusters feature a large probability for fission into at least two charged fragments. The size distribution of heavy, doubly charged fragments from (${\mathrm{CO}}_2$${)}_{\mathrm{n}}^{3+}$, 109≲n≲123, has been analyzed in detail and shows a strong peak at 92% of the precursor size. Delayed fission of doubly charged clusters, however, does not occur on the time scale of the experiment, which is 10≲t≲100 μs with respect to ionization. A simple model, based on a liquid-drop approximation, is proposed. It allows us to calculate the height of the fission barrier for any given precursor ion and fission channel from readily available bulk data. Calculated critical sizes are presented for two-, three-, and fourfold charged clusters of 28 different van-der-Waals–bound or hydrogen-bonded compounds; they agree reasonably well with experimental values. The model also accounts for the strongly asymmetric fission reaction of triply charged ${\mathrm{CO}}_2$ clusters, and for the strong size dependence of their fission rate.