Using axially resolved spectra, we have derived temperature and density profiles of sodium-bearing Z-pinch plasmas produced on the Naval Research Laboratory’s Gamble-II generator. The variations in the output power of the Na x 1$s^2$ ${}^1$$S_0$–1s2p ${}^1$$P_1$ line which can be used to pump a Ne ix x-ray laser, are analyzed as functions of mass loading, temperature, and density. The fractional conversion of plasma energy to lasing lines is projected as ${10}^{\mathrm{-}3}$ if an optimum neon lasant plasma can be prepared and pumped to saturation. This would require an increase in load current of less than or equal to 50% from the present 1.2 MA.

We report on a quantitative test of solvability theory in the case of pattern selection for viscous fingering in a rectangular Hele-Shaw cell. We construct an effective two-dimensional theory that properly takes into account the effect of film draining. In the parameter range where the theory is applicable we find excellent agreement between our predictions and the experimental data. This provides the first precise, quantitative assessment of microscopic solvability in a physical system.

The Eden model in many dimensions is studied by means of a theorem by Kramers. The recursion relations for the 1/d correction from an overlapping bond are derived. By inclusion of diagrams containing a four-bond loop in the 1/d correction a new asymptotic behavior for the gyration radius is found.

We consider spatial correlations within multifractals or fractal measures μ(x). Correlation functions such as 〈μ(x${)}^m$μ(x+r${)}^n$〉 are argued to scale as (R/a${)}^{y(m}$,n)(r/a${)}^{\mathrm{z}(\mathrm{m}}$,n), where R is the overall radius of the object and a a short cutoff. The exponents y and z are given in terms of the scaling dimensions $D_q$ of the multifractal. We note that the existence of this single scaling form over the full range of r (a≪r≪R) is incompatible with any description of the measure as a superposition of simple fractal sets of localized singularities.

We investigate the adiabatic eigenfunctions and eigenvalues (and therefore the effective potentials) associated with the hyperspherical harmonic expansion of the wave function for three particles on a line subject to δ-function interactions. Because of the special separability of the potential matrix elements, we obtain the effective potentials as the solutions of a transcendental equation and we also obtain the eigenfunctions in closed form. We demonstrate that the long-range (large hyper-radius ρ) behavior of the effective potentials is qualitatively different from the long-range behavior of the potential matrix elements.

When the (nearly) exact solutions of a Hamiltonian are known, as occurs, for instance, for the electronic Hamiltonian of ${\mathrm{Li}}_2$, the definition of an effective (valence) Hamiltonian may proceed through the direct use of the Bloch equations. Even when intruder-state problems (due, for instance, to the crossing between a valence and a Rydberg state) are no longer divergent behaviors in the quasidegenerate perturbation expansion, they still produce an ambiguity in the choice of the wave operator. Two definitions are proposed, a ‘‘diabatic’’ one, which selects the eigenvectors having the largest components on the model space, and which leads to a discontinuous effective Hamiltonian in the regions of avoided crossings, and an ‘‘adiabatic’’ definition, which follows the same adiabatic root and tends to lose any meaning on one side of the avoided crossing. Both definitions are unsatisfactory if transferability of the effective operators is expected. The recently proposed intermediate Hamiltonians solve this dilemma by realizing some kind of diabatization of the energies of the states crossed by the intruder state. The analysis is illustrated on two molecular problems: the definition of a valence-only effective Hamiltonian for ${\mathrm{Li}}_2$ and the obtaining of a Heisenberg effective Hamiltonian for acetylene.

A finite set of Slater-type orbitals is used as a basis to solve the Dirac equation for atoms in a Dirac-Fock-Slater potential. The energy eigenvalues thus obtained are in good agreement with the results from the numerical solution of the Dirac equation except that a spurious root always occurs for κ>0. It is shown that despite this spurious root the method still gives good approximate atomic energy eigenvalues and wave functions. This implies that the finite-basis-set expansion method can be applied to relativistic atomic structure and atomic collision calculations.

The quasiclassical ground-state energies exhibit typical analytic structures, as well as covariance properties, with respect to certain symmetry transformations. Such symmetries enable us to define corresponding classes of equivalent Hamiltonians. The scaling properties of the underlying phase-space quantum have also been established. Here we shall consider spherically symmetrical Hamiltonians like $p^2$/$m_0$+$C_{n1\mathrm{}}$${/}_1^n$+$C_{n2\mathrm{}}$${/}_2^n$, where $n_1$≠2, & (i=1,2) denote the couplings, whereas $n_i$ are the power exponents. Generalizations towards exact or approximate energy levels, depending on the values of $n_1$ and $n_2$, have also been performed. For $n_1$=2, this procedure leads us to reobtain the exact energy levels for $n_2$=1 and $n_2$=-2, and to propose closed estimates for the other $n_2$ values. The quasiclassical equivalence between the linear plus Coulomb potential and the quartic anharmonic oscillator has also been established.

The time-dependent propagator for the potential V(x)=1/2m(${\omega }^2$$x^2$+${\rho }^2$/$x^2$), x∈${\mathrm{scrR}}^{+}$ is known. It is used in this article to see how certain general ideas about the semiclassical approximation for the propagator are in fact realized. The phenomena demonstrated include caustics at classical focal points, analytic structure of the classical action, complex trajectories for forbidden regions (not forbidden in this instance by energy), and the Langer correction for approximating the centrifugal potential. We also provide an unusual derivation of the solution to a classical problem from its quantum version.

We present a multichannel theory for resonant charge transfer in ion-surface collisions at grazing incidence at intermediate velocities (v≃1 a.u.) taking into account the nonorthogonality of the initial and the final states. Kinematic resonances occur between the atomic projectile levels and the Galilei-shifted conduction band of a metal. The time-dependent Schrödinger equation can be solved in the adiabatic approximation for the slow perpendicular motion ($v_{\perp }$≪1). As an application we calculate the complete n=2 density matrix for H(n=2) following proton scattering at a gold surface at grazing incidence (θ=5°). The shape of the charge cloud around the receding hydrogen atom is determined.

A theoretical study of radiative transitions in molecular collisions occurring in the presence of short laser pulses is carried out within the semiclassical two-state formalism. Transition probabilities are calculated by numerically integrating the Bloch equation for two model systems and the Na-Ar system. At high laser intensities where a short pulse is more effective in inducing transitions than cw radiation, the transition probability exhibits nonlinear character with respect to the pulse intensity. At such high intensities, noncollisional atomic transitions may also be present, which need to be eliminated for an observation of collisional transitions.

The Auger electron emission from ${\mathrm{C}}^{3+}$ and ${\mathrm{C}}^{2+}$ ions after double-electron capture from He, ${\mathrm{H}}_2$, and Xe atoms in a single collision with ${\mathrm{C}}^{5+}$ and ${\mathrm{C}}^{4+}$ ions and after one-electron capture into K-shell excited ${\mathrm{C}}^{4+}$ ions was measured under zero degrees with high resolution. The nl, n’l’ distribution of doubly excited states induced by capture are discussed in the framework of previously established classical over-barrier and Landau-Zener models. Evidence for two-electron transfers in a one-step process is outlined. The spectral features indicate spin conservation during capture, electron transfers with core excitation, contributions from endoergic capture, post-collision line broadenings, and cascade channels.

The excited states of highly charged ions populated by charge transfer are frequently aligned. The alignment of each nl level often reflects the initial alignment due to the collision as well as the alignment of higher levels which cascade down to this level. We adapt the theory of alignment transfer and apply it to analyze the alignment of Lyman radiations following ion-atom collisions. The theory is illustrated using computed alignments of higher levels reported earlier and the results are compared with recent measurements.

The double-photoionization cross sections of molecular hydrogen (${\mathrm{H}}_2$) and molecular deuterium (${\mathrm{D}}_2$) were measured by using the photoion-photoion coincidence method for photon energies ranging from the threshold energy around 50 eV up to, respectively, 140 and 98 eV. The comparison with the recent ab initio calculations of Le Rouzo [J. Phys. B 19, L677 (1986)] indicates that an important part of the double-photoionization process is accounted for by a rigorous description of the electron-electron interaction in the initial state. As a by-product of this work, it was also concluded that double photoionization of hydrogen can be considered as a vertical process and that Franck-Condon approximations are quite valid to calculate the kinetic energy of the resulting ${\mathrm{H}}^{+}$+${\mathrm{H}}^{+}$ fragments.

A multiphoton ionization technique involving third-harmonic generation in phase-matched mixtures of noble gases has been used to make accurate determinations of oscillator strengths for transitions from the ground state to 6s, 6s’, 5d, and 7s levels in Xe and to the 5s’ level of Kr. The method also allows determinations to be made of the absorption coefficients for third-harmonic photons generated in noble-gas mixtures and the vacuum-uv refractive index for the positively dispersive buffer-gas component of the medium, all in the same experiment. The effects of low concentrations of dimers on refractive indexes are also demonstrated. Results are compared with data from other experimental techniques.

Through multiphoton ionization measurements, we have observed the interference of five-photon and internally generated fifth-harmonic excitation processes in ΔJ=1 even-odd parity resonant transitions in Xe and Ar. In agreement with theory, these five-photon resonances are not observable in single-pass laser beams, but are convincingly observed in counterpropagating beams. In the negatively dispersive regions of the 5d${[3/2]}^0$J=1 level of Xe, tunable fifth-harmonic light is generated by phase matching with various buffer-gas mixtures. The fifth-harmonic profiles are in good agreement with calculated phase-matching curves.

The photoionization of the individual L subshells of ${}_{72}{}^{}{}_{}{}^{}\mathrm{Hf}$, ${}_{74}{}^{}{}_{}{}^{}\mathrm{W}$, ${}_{78}{}^{}{}_{}{}^{}\mathrm{Pt}$, ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, and ${}_{82}{}^{}{}_{}{}^{}\mathrm{Pb}$ in the energy regime of the L edges has been studied in detail. Experimentally, the x-ray absorption spectra of thin sample foils were recorded using monochromatized synchrotron radiation. The energy dependence of the absorption is governed in its gross structure by the atomic photoionization with some superimposed oscillatory structure due to solid-state effects. The experimental data are compared to various theoretical predictions for atomic photoionization. Calculations in the framework of an independent-electron approach predict a smooth, power-law-like energy dependence. In contrast, the experimental data show small but significant deviations from such a behavior. The dispersionlike deviations are attributed to electron-correlation effects, as is confirmed by comparative calculations of photoionization with inclusion or omission of the correlations using the computer code of Liberman and Zangwill [Comput. Phys. Commun. 32, 75 (1984)]. The main influence of the correlation effects on the subshell ionization cross sections originates from the dielectric (anti-) screening of the external radiation field. Calculations in the local-density approximation for the response of the atom to the radiation field yield an even quantitative description of the experimental data in a large fraction of the investigated energy range.

Radiative lifetimes for 12 levels in Ni ii are measured using time-resolved laser-induced fluorescence. The lifetimes are used to establish a more accurate absolute scale for earlier transition probability measurements. Issues involved in extending time-resolved laser-induced fluorescence into the vacuum-uv region are discussed.

Narrow (Δλ<5 Å), intense quasicontinuum bands, appearing in emission spectra of highly ionized rare-earth elements between 70 and 100 Å, previously observed in tokamaks and laser-produced plasmas, have been obtained from a low-inductance vacuum spark. The bands shift toward shorter wavelengths with increasing atomic number Z. Using the unresolved transition array model, these bands are identified as primarily 4d-4f transitions in Rh i to Rb i–like ions, although the widths come out too large and the mean wavelengths are much too dependent on ionization stages. Detailed ab initio computations show that the interactions between the 4$p^6$4$d^{N\mathrm{-}1}$4f and 4$p^5$4$d^{N+1\mathrm{}}$ configurations are responsible for the narrowing and the superposition of the transition arrays for the different ionization stages of a given element, in agreement with experimental data.

The fluorescence signal from an atom or molecule following its single-photon near-resonant interaction with a train of N phase-coherent Gaussian pulses is calculated within the rotating-wave and first-order Magnus approximations. The Gaussian line shape will be flanked by Ramsey fringes whose widths are inversely proportional to N, provided the time delay of the train is an integral multiple of the carrier period. The signal intensity is proportional to $N^2$.