The rate coefficients for the dielectronic recombination of ${\mathrm{Ar}}^{10+}$, ${\mathrm{Fe}}^{18+}$, ${\mathrm{Kr}}^{28+}$, and ${\mathrm{Mo}}^{34+}$ of the oxygen isoelectronic sequence are computed in the single-configuration, LS-coupled, frozen-core, corona-model approximation. Analytic interpolation formulas for the dielectronic-recombination rate coefficients of the oxygen isoelectronic sequence are given, and comparisons are made with other calculations.

Rayleigh scattering by bound electrons is reduced from the free-electron Thomson value at x-ray wavelengths by relativistic effects. To first order this arises from the relativistic increase in mass of the core electrons. The reduction is overestimated by more than a factor of 2 by the commonly used dipole approximation. Inclusion of higher multipole and retardation terms in dispersion analysis resolves reported conflicts between values of the anomalous scattering factor as measured interferometrically and as calculated from attenuation measurements. These considerations further imply that several scattering-factor tabulations in current use for diffraction studies require revision to take relativity fully into account. This correction is particularly significant in regions of anomalous dispersion and at low energies, where the scattering factor is small relative to the atomic number.

We apply our quantum theory of multiwave mixing for the two-photon two-level model to the generation of squeezed states of light. Because of the two-photon transition, a larger number of interaction potentials are present compared to one-photon models, leading to effects absent in the one-photon case. The two most significant of these are the appearance of dynamic Stark shifts and conjugate scattering off the pump induced two-photon coherence. We show that this can lead to almost perfect squeezing, even for low pump intensities and low detunings from the two-photon resonance.

We present analytical results for the steady-state signal and phase-conjugate fields interacting with smoothly varying nondepleted pump waves in a nearly degenerate four-wave-mixing geometry. Signal depletion is retained in the equations and we study the effect that detuning on the input signal from the degenerate pump amplitudes has on the reflected conjugate wave and the transmitted signal wave. A general result is derived for the appearance of spontaneous amplification under weak restrictions on the profile of the degenerate pump fields. The conjugation of the phase front of the signal is studied for exponential and hyperbolic secant functions multiplying the coupling coefficients and comparison is made with corresponding results for square profile pump fields. These results are discussed and their relevance to phase conjugation of pulses is examined.

Treating diffraction effects within the paraxial approximation, we solve the initial-value problem determining the start-up of a single-pass free-electron laser from shot noise in the electron beam. Linearized Vlasov-Maxwell equations are used to derive an equation for the three-dimensional slowly varying envelope function of the radiated electric field. In the high-gain regime before saturation, the output power is expressed in terms of Moore’s exponentially growing guided modes. For a cylindrical monoenergetic electron beam with step-function profile, explicit numerical and analytical calculations have been performed, determining the power in the guided modes. The condition for the dominance of the fundamental mode is discussed. Our solution of the initial-value problem is based upon a Green’s-function technique, and our results are derived despite the lack of orthogonality and completeness of the guided modes. The Green’s function is expanded in terms of an orthonormal set of eigenfunctions of a two-dimensional Schrödinger equation with non-self-adjoint Hamiltonian. In the limit of a long wiggler, the asymptotic representation of the Green’s function is found to be dominated by the contribution of the guided modes. The radiated electric field, and hence the output power, is determined with use of the Green’s function.

A theory is developed for lasing action from ensembles of relativistically or subrelativistically propagating emitters whose motion is bound in the direction(s) transverse to the direction of propagation. These include relativistic electrons and positrons channeled in crystals or other hollow-channel structures, as well as fast ions wherein a bound electron is perturbed by the crystal potential or laser light. Apart from planar-channeled positrons in crystals, the confining potentials for all other emitters in this category are strongly anharmonic. Therefore, their spectral dipolar transitions are nondegenerate, each involving a different pair of nearly discrete levels of the confining potential. This implies that stimulated emission from such systems can exhibit coherence in the Glauber sense. The theoretical framework presented here consists of Heisenberg equations which have the Maxwell-Bloch form with modifications resulting from the high velocity of the emitters. Steady-state semiclassical solutions of these equations are obtained. It is shown that previous approaches, based on the assumption that the cross section for stimulated emission is uniform throughout the system, do not account for the spatial variation of the polarization at high velocities. As a result, these approaches do not yield the correct gain coefficient whenever the characteristic lengths for the dephasing of the dipole oscillation and for emission amplification are comparable. The latter conditions are realizable in structures composed of channels much wider than in crystals. Lasing schemes are investigated and the prospects for achieving gain in these schemes at wavelengths below 100 Å are discussed.

Solutions of the basic equations of a simplified model of the cavity quantum electrodynamics are presented under the condition that the single-photon Rabi frequency is much larger than the cavity decay rate. Such solutions are used to calculate the quantum-statistical properties of the field and atomic observables under a variety of initial conditions involving the states of the field and atom. Effects of increasing cavity damping and of the addition of thermal photons on collapse and revival phenomena are discussed. Phase-sensitive aspects of the cavity field are also treated. Quantum effects are shown to be most easily isolated by sending an atom initially prepared in a dressed state for such a state does not evolve further under the influence of a classical field. The appearance of squeezing in the cavity field is demonstrated. The squeezing is most prominent for a coherently prepared atom passing through an empty cavity. The quantum features of the complex dipole moment and their detectability are also discussed in detail.

Using a self-consistent description of an inhomogeneous electron gas in thermal equilibrium, we formulate a simple model for the stopping power of confined atomic systems at high temperatures. The model is based on previous studies of the energy loss of particles in partially degenerate plasmas. We describe the thermal enhancement of the energy loss in pellet fusion targets, in accord with recent experiments, and we explain this behavior in terms of quantum-mechanical and thermal effects in partially degenerate systems.

Time sequences of the spectral emission from the ASDEX tokamak at the Max-Planck-Institute für Plasmaphysik have been recorded using multichannel survey spectrometers operating over the wavelength range 100–7000 Å. During injection of neutral beams of hydrogen or deuterium, charge-exchange- (CX) excited lines, mostly Δn=1,2 transitions from hydrogenic ions of intrinsic impurity elements or injected trace gases, are prominent throughout this entire spectral region. The charge-exchange origin of the lines is established by the temporal and spatial dependence on the injected beam current and also, in the case of visible transitions, by their relatively large spectral widths. With a beam power of 1.7 MW and an extraction potential of 41.5 keV, excitation of intrinsic impurity ions, e.g., ${\mathrm{O}}^{7+}$ (n<11) and ${\mathrm{C}}^{5+}$ (n<9) occurs routinely while, depending on the plasma conditions, other trace impurities, for example, ${\mathrm{F}}^{8+}$ (n=9), ${\mathrm{Cl}}^{16+}$ (n=13), ${\mathrm{S}}^{13+}$ (n≤15), and ${\mathrm{Kr}}^{25+}$ (n≤22) are also observed. From the absolute intensities of the ${\mathrm{C}}^{5+}$ and ${\mathrm{O}}^{7+}$ CX lines, impurity concentrations are deduced. Comparison of the concentration data derived from the vacuum-ultraviolet and separately from the visible intensities allows an assessment of the theoretical cross sections for charge-transfer recombination into different quantum states. Spectral line profiles of the CX transitions in the visible region involving high-n Rydberg states are consistent with bulk plasma and ion thermal motion. Coincidence between Rydberg levels of different ions with the same effective nuclear charge offers a plausible explanation for the appearance of some visible CX lines in the absence of atomic beams.

After having discussed how integral equations of the Percus-Yevick type can be generated stemming from known approximations of the direct correlation function (DCF), we show that in the case of the hard-sphere (HS) fluid they can be recast into the generalized mean spherical approximation form by using truncated Dirichlet’s series. The analysis is numerically carried through by using present knowledge of second- and third-order approximations of the DCF. The virial and compressibility pressures tend to close on the Carnahan-Starling values, but improvement in the radial distribution functions is noteworthy only in the contact region, while the Waisman thermodynamical consistent approximation appears to be the most accurate one. The mechanical stability of the system is analyzed: For all the considered approximations the HS system appears mechanically stable.

We searched for signs of an instability on the interface between the two phases of a binary-liquid mixture, isobutyric acid and water, after the mixture was quenched further into the two-phase region. Such an instability would be the liquid-liquid analog of the Mullins-Sekerka instability seen in quenched alloys. Never is any dramatic growth observed, but under conditions of small dimensionless quench depth (theta<1.5×${10}^{\mathrm{-}3}$), the intensity of light scattered from the interface grows for small values of the momentum transfer k.

The argon-krypton mixture is studied by equilibrium molecular dynamics (MD) using Lennard-Jones potentials for the molecular interaction. The thermal conductivity λ of the mixture has been determined via the Green-Kubo integrals. By analysis of the partial terms we found that the thermal conductivity of the mixture is well accessible by MD calculations, as the awkward partial cross-correlation function, which contains the partial enthalpies of the components, is negligibly small in comparison with the dominating autocorrelation function. Experimental data for λ of Ar-Kr mixtures are lacking. So we compared with nonequilibrium MD results and with values predicted by an approximate expression derived by Bearman using the thermal conductivities of the pure components. Satisfactory agreement was achieved in both cases.

The isothermal expansion of an ideal gas to fill a container is studied. The gas is initially situated all in one corner of a d-dimensional box and then instantaneously released. The subsequent trajectory and velocity of the center of mass are derived by first deriving the time dependence of the phase-space density distribution function of the system. It is shown that the system is characterized by a long-time (1/t) approach to equilibrium, even though there are no interparticle interactions or energy dissipation. For boxes which have commensurate sides, the trajectory of the center of mass is, in some sense, periodic in its approach to the center of the box. For incommensurate boxes the trajectory exhibits some elements of chaotic motion.

The correspondence, developed in an earlier communication by the author [González, J. Phys. (Paris) 46, 1455 (1985)], between a system of branched polymers in dilute and semidilute solutions of a good solvent on a lattice and a magnetic system consisting of n q-component spins on a related lattice, is extended to include correlation functions and some generalizations. We obtain explicit expressions for the vertex-vertex and monomer-monomer correlations between vertices and monomers belonging to the same or different polymers, in terms of magnetic quantities. We also obtain, in terms of magnetic quantities, the correlation between vertices belonging to the same polymer (pair connectedness). In addition, some general theorems, relating the connectedness length to the radius of gyration of the polymers and the mean cluster size to the pair connectedness, will be proven. Furthermore, we make some generalizations considering explicitly site-bond problems on any lattice. Finally, a discussion is made on the types of gelation transitions that could be described by the model.

We present a general theoretical framework for understanding the geometrical frequency dependence of the impedance of ionic solutions in contact with rough or irregular metallic electrodes. In two dimensions all relevant information regarding the surface is contained in the conformal transformation that maps the rough surface onto a straight line. The ‘‘constant-phase-angle’’ impedance is related to the scaling of current inhomogeneities within a two-scale model of the structure of the metallic surface. The capacitive effects in this model are controlled by a generalization of the ‘‘Parisi matrix.’’

We give a noncovariant Hamiltonian collective-coordinate description of the sine-Gordon breather driven by constant forces. Thresholds for breather decomposition are calculated, including their dependence on the initial phase. Quantitative agreement is obtained with the numerical results presented in a paper by Lomdahl, Olsen, and Samuelsen [Phys. Rev. A 29, 350 (1984)].

The complex dielectric constant has been measured in a room-temperature ferroelectric liquid-crystal mixture. We have resolved the experimental data into the Goldstone mode and the soft mode and for each mode determined the dielectric strength and the corresponding relaxation frequency. The results are compared with the dielectric strength calculated using the extended Landau type of free-energy density proposed by Žekš [Mol. Cryst. Liq. Cryst. 114, 259 (1984)], and it is shown that this calculation is able to describe the experimental data well. We have shown that by reasonable assumptions we can derive a simple relation between the Goldstone-mode contribution to the dielectric susceptibility (${\chi }_2$) and the polarization ($P_0$), tilt (${\mathrm{theta}}_0$), and pitch (p) of the system: ${\mathrm{\chi }}_2$=(${\mathrm{P}}_0$p${\mathit{theta}}_0$${)}^2$/${8\mathrm{K}}_3$${\mathrm{\pi }}^2$), where $K_3$ is a bend nematic curvature elastic constant. We also predict, on theoretical grounds, a small peak of the dielectric strength to exist at $T_c$.

The theory for curvature elasticity in nematics described in an earlier paper [Phys. Rev. A 34, 548 (1986)] is applied to a simple model of Berne and Pechukas [J. Chem. Phys. 56, 4213 (1972)] in which the strength parameter ε(r${^}_{12}$,${\mathrm{\Omega }}_1$,${\Omega }_2$) and the range parameter σ(r${^}_{12}$,${\Omega }_1$,${\Omega }_2$) depend upon the ratio of major to minor ellipsoidal axis and the relative position and orientation of the two molecules. The softness in the repulsion core is found to have a large effect on the value of the Frank elastic constants. The attractive part of the interaction which has the same angle dependence as the repulsive interaction is found to have a small effect on the value of all three constants associated with splay, twist, and bend deformations. Contrary to what has been reported for a single-center, $r^{\mathrm{-}6}$ attractive potential, the attractive part (more accurately the perturbation potential) of this model makes negative contributions to all three elastic constants. The magnitude of this contribution increases with the length-to-width ratio $x_0$ of the molecules. However, the value remains very small compared with that of the reference potential, which is also found to increase with $x_0$ and is always positive. Numerical results for the elastic constants are reported for a range of $x_0$, temperature, and density. It is shown that with better knowledge of the order parameters P${¯}_2$ and P${¯}_4$ and their temperature and density dependence and the potential parameters appearing in the model, one can calculate accurate values of all the Frank constants of any given system. The need to extend the theory to include the flexibility of the alkyl chain and the deviation from the cylindrical molecular symmetry is emphasized.

The generalized Husimi distribution based on coherence-preserving coherent states is defined. We analyze the eigenfunctions of the evolution operator of the quantum kicked rotator in this representation.

The wave function for the 1s2p ${\mathrm{}}^3$P state of the helium atom is found to have an unexpectedly simple nodal hypersurface, symmetric about the z axis when the position of one electron is fixed and independent of the interelectron distance. The six-dimensional configuration space of the electrons is divided by the surface into two geometrically similar regions, but the hypersurface is not a plane of symmetry and points on the hypersurface are not at equivalent sites in the two regions.