The relation of the work of Nagara, Nagata, and Nakamura [Phys. Rev. A 36, 1859 (1987)] to a previous study of the melting of the Wigner crystal is exhibited.

S. Jasty, M. Al-Naghy, and M. de Llano recently presented [Phys. Rev. A 35, 1376 (1987)] an argument to justify the weak divergence of the pressure at random close packing for a classical continuous system with hard cores. Their analysis is based on the behavior of the equilibrium canonical partition function at random close packing. Therefore this approach is erroneous owing to the nonequilibrium nature of the glassy state.

The weak algebraic divergence of the pressure at random close packing in a classical system of hard spheres or hard disks does not rely on the behavior of the equilibrium canonical partition function at such packing, as suggested by M. Alexanian [Phys. Rev. A 37, 4527 (1988)], but rather is a result numerically suggested by the series analysis reported earlier.

We report the first observation of hyperfine structure and isotope shift in autoionizing states. This structure was investigated in the $5d_{\frac{3}{2}}\mathrm{nf} J=4,5\mathrm{}\mathrm{}(n=36-40\mathrm{})\mathrm{}$ barium Rydberg series, excited from the recently localized metastable $5d^2{}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ level. An isotope-selective detection method was used in a cw laser spectroscopic experiment on a collimated atomic beam. The experimental data provide valuable additional information for the analyses of these doubly excited series.

We present the first accurate calculation within a recently developed nonperturbative theory for free-free transitions in intense, high-frequency laser fields, done for modified elastic scattering from a Coulomb potential. The field is assumed to be monochromatic and linearly polarized. In the high-frequency limit of the theory, the scattering takes place from a time-independent, "dressed" Coulomb potential, which contains the frequency and intensity of the field only through a parameter ${\alpha }_0$. The corresponding Schrödinger equation in integral form was solved by the close-coupling method. The cross section depends on the scattering angle $\theta$ and on two other angles defining the orientation of the initial and final momenta ${\mathrm{k}}_i$ and ${\mathrm{k}}_f$ with respect to the electric field. Large deviations from the Rutherford cross section are found in the nonperturbative regime. At small angles θ the deviations appear in the form of characteristic Coulomb interference oscillations, while in backward scattering this pattern is distorted in a way markedly dependent on the orientation of the momenta with respect to the electric field. An unexpected rotation invariance of the cross section around ${\mathrm{k}}_i$ was found for certain "magic" scattering angles $\theta$.

The effect of subshell couplings on $L$-shell ionization cross sections for protons on gold has been estimated in the energy range 0.15-3 MeV. The applied model treats the couplings dynamically solving a set of coupled differential equations which govern the time evolution of the $L$-substate amplitudes. The effect has been found to be particularly large for the $L_2$ subshell, reaching 40% at low collision energies. The results of the calculations were used to correct the cross-section values obtained by Chen and Crasemann in the plane-wave Born approximation with use of Dirac-Hartree-Slater wave functions. The combined theory reproduces the structure observed recently by Jitschin et al. in the energy dependence of the $L_2$- and $L_3$-shell cross-section ratio.

Quantum jumps due solely to spontaneous Raman scattering between the Zeeman sublevels of a single ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}_{}^{+}{}_{}{}^{}$ ion have been observed in the fluorescence emitted by the ion. A theory of quantum jumps for this system predicts that coherences between excited levels cause the ratio of the mean duration of the "fluorescence-on periods" to the mean duration of the "fluorescence-off periods" to be independent of laser intensity. The measured value agrees with the predicted one to within the measurement precision of 2%. The distribution of the durations of the off periods also agrees with theory.

Recently, Handy and Bessis derived, for singular multidimensional Schrödinger equations, infinite sets of hierarchical inequalities fulfilled by the moments of the ground-state wave function. These inequalities, when increasing in number, provide tighter lower and upper bounds to the ground-state energy. This analysis makes use of nonlinear multivariate determinant functionals (Hankel-Hadamard determinants) which define complicated convex sets in the space of the ‘‘missing moments.’’ It is possible to reformulate all the above in terms of linear programming. The previous sets are now replaced by new sets defined by linear inequalities. This new formulation makes the general moment approach highly practical. We describe the general formalism and give a simple one-dimensional example to illustrate it. The three-dimensional quadratic Zeeman problem, in the transition region, is analyzed by this method. Preliminary results for values of the magnetic field B=0.2, 2, and 20 (in atomic units) are given.

A mathematically rigorous approach for the calculation of excited-state energies within the one-particle density-functional formalism is presented. Since the occurring exchange-correlation functional is not exactly known, approximate schemes are proposed and compared with those by other authors. Our approach gives good figures for the harmonic-oscillator potential and it is explained why the agreement with the exact energies is less for the Coulomb potential.

The Schwinger variational method is applied to the static exchange approximation of the electron–hydrogen-atom scattering. Spurious singularities are encountered in singlet scattering processes. The position of the poles is investigated by a simple numerical procedure. Anomalous poles appear in narrow regions of the nonlinear scale parameter. Results are presented which illustrate the behavior of the phase shifts around the spurious poles. No Kohn-type anomalies are encountered in the triplet case. As a byproduct, it is discussed that the Schwinger formula may be approximated in a separable form which is relatively simple but not free of anomalies.

The behavior of an atomic electron in a static magnetic field strong enough to correspond to the transition regime is examined. The field strength is characterized by the parameter L^, the effective component of angular momentum. A Floquet-Mathieu analysis shows that the bifurcation of classical trajectories into elliptical and helical families is related to the 2:1 resonance which occurs at L^=L${^}_T$. Quantum mechanics gives an avoided crossing at L${^}_T$; we examine the nature of the wave functions as L^ passes through the resonance. Semiclassical calculations accurately reproduce the quantum eigenvalues and produce trajectories which underlie the quantum wave functions. The avoided crossing is expressed in semiclassical terms as a switch between elliptical and helical families. The bifurcation of the classical motion means that, at the primitive semiclassical level, some states may be missed and others may be generated in both elliptical and helical representations.

The molecular-orbital (MO) method introduced previously by us [Phys. Rev. Lett. 57, 984 (1986)] to treat two-electron atoms is developed further. The states of systems consisting of two electrons and one positively charged particle are analyzed with use of the interelectronic distance as an adiabatic coordinate in analogy to the interprotonic distance in ${\mathrm{H}}_2^{+}$. The motion of two electrons then separates into rotational, vibrational, and internal motion, the latter being described by MO, exactly as in molecules. Indeed, adiabatic MO potential curves for atomic systems are obtained by scaling the corresponding curves for ${\mathrm{H}}_2^{+}$. Approximate quantum numbers for two-electron states, derived previously by empirical methods or from an ad hoc rovibrational model, arise naturally since the two-center Coulomb problem is exactly separable in MO coordinates and the corresponding nodal surfaces are conserved for all interelectronic separations. In addition, the gerade-ungerade symmetry of MO is exactly preserved and appears as a fundamental symmetry of two-electron states.

Relative excitation rate coefficients of N i and O i are measured using a well-diagnosed Θ-pinch plasma. Levels of n=4 and 5 are included in the measurements for the first time. Experimental values are in satisfactory agreement with theoretical values. A method to deduce the recombination rate coefficient from the He-like ions is suggested from the observations of the effect of recombination on transitions originating from levels of principal quantum number n=4 and 5. Recombination rates of ∼${10}^{\mathrm{-}12}$ ${\mathrm{cm}}^3$ ${\mathit{s}}^{\mathrm{-}1}$ at 69 eV for N i and ∼${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^3$ ${\mathit{S}}^{\mathrm{-}1}$ at 40 eV for O i are deduced. These rates are no larger than the known theoretical rates for radiative, three-body, and dielectronic recombination; charge exchange with hydrogen is suggested as possible explanation.

The cross sections are reported for chlorine negative- and positive-ion production in neutral-chlorine–rare-gas-atom collisions between 10 and 110 keV. The experimental conditions were chosen such that it is unlikely that there was an unknown mixture of metastable states in the neutral beam. The cross section for positive ion production is less for the Kr and Xe targets than for Ar, probably due to competition from target ionization. The negative-ion cross section increases with target mass, so that for a xenon target it is nearly twice the positive-ion cross section between 32 and 100 keV. Thirty percent negative-ion equilibrium charge fractions are predicted.

Strong-coupling S matrices for the anti-Demkov, Nikitin, and Demkov models of nonadiabatic transitions are derived. On this basis, analytic expressions for the channel probabilities, which include the effects of the turning point, are also derived. The two states are assumed quasistationary and coupled by a complex interaction.

Multiple-electron capture as a function of the projectile scattering angle in 90-keV ${\mathrm{Ne}}^{7+}$ collisions on Ne atoms was investigated in the angular range from 1 to 20 mrad by a recoil-ion–projectile coincidence technique which records the final charge states of both product ions. A single-electron-capture probability $P_{\mathrm{SC}(\mathrm{\theta }}$) is determined, which, with application of binomial statistics, provides a good description of measured charge-state distributions for θ<10 mrad. For scattering angles θ>10 mrad, projectile and recoil-ion charge-state distributions are nearly identical, indicating full participation of all L-shell electrons in quasimolecular states. Nearly all electron-capture processes are followed by autoionization, indicating the importance of capture into multiply excited states. We observed a strong angular dependence of the autoionization probabilities.

The 8 ${}_{}{}^2{}_{}{}^{}S$ state of rubidium is selectively populated by stepwise excitation using light from a rubidium lamp and a tunable dye laser. Excitation transfer from the 8 ${}_{}{}^2{}_{}{}^{}S$ to the 6 ${}_{}{}^2{}_{}{}^{}D$ state is studied in a glass cell containing rubidium vapor and noble-gas atoms at different pressures and ground-state rubidium atoms as perturbers. The thermally averaged cross sections for excitation transfer (in units of ${10}^{\mathrm{-}15}$ ${\mathrm{cm}}^2$) are 0.13±0.05, 3.0±1.2, 2.2±0.9, 1.7±0.7, and 4.3±2.6 for the noble gases He, Ne, Ar, Kr, and Xe, respectively, and (6.7±3.0)×${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^2$ for rubidium atoms. The results show that the excitation-transfer cross sections for intermediately excited states cannot be accurately scaled from simple models.

Cross sections have been calculated for electron transfer into the 2s, 2$p_0$, 2$p_1$, and all states of ${\mathrm{He}}^{+}$, and for ionization, in collisions between ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions and H(1s) atoms. Cross sections have also been calculated for electron transfer into the ground state and all states of H, and for ionization, in collisions between protons and ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$(1s) ions. The center-of-mass collision energies range from 1.6 to 40 keV. A coupled-state approach is taken using large triple-center bases of up to 34 states centered on the two nuclei and a third center chosen to be the equiforce point (saddle point of the potential) between the nuclei. The sensitivity of the cross sections to the size of basis is studied, and the ionization cross sections are found to be the more sensitive, particularly at lower energies. The electron-transfer cross sections in most cases are found to agree extremely well with larger-basis molecular-state results at generally lower energies and with double-center pseudostate results at higher energies, as well as with experimental results. The more sensitive ionization cross sections follow the trend of the experimental data, suggesting the considerable importance of saddle-point electrons as previously observed for p-H collisions.