The energies and oscillator strength for the spin-allowed 6$s^2$ ${\mathrm{}}^1$$S_0$–6s6p ${\mathrm{}}^1$$P_1$ transition in neutral ytterbium have been determined by a relativistic Hartree-Fock calculation which includes both intravalence and valence-core correlation effects. The intravalence correlation is found by a multiconfiguration approach in which only configurations involving virtual excitations from the valence shell are admixed. The valence-core correlation is taken into account by a model to represent core polarization by the valence electrons. Intravalence correlation is found to be more important for the transition energy since core polarization lowers both ${6\mathrm{}}^1$$S_0$ and ${6\mathrm{}}^1$$P_1$ energies by roughly the same amount. Core polarization, however, is the stronger influence in determining the oscillator strength. The fact that the calculated transition energy agrees to within 1% with experiment, whereas the calculated oscillator strength is 10% to 20% too high, may indicate that the polarizability of the ${\mathrm{Yb}}^{2+}$ core calculated by Fraga, Karwowski, and Saxena, namely 7.36$a_0^3$, is too small.

The dependence of the associative ionization process Na 3 ${}_{}{}^2{}_{}{}^{}P_{3/2}^{}{}_{}{}^{}$+Na 3 ${}_{}{}^2{}_{}{}^{}P_{3/2}^{}{}_{}{}^{}$→${\mathrm{Na}}_2$${\mathrm{}}^{+}$+$e^{\mathrm{-}}$ on the polarization of the laser light used for Na excitation was independently investigated in Utrecht and Berlin. The purpose of this paper is to clarify discrepancies between earlier experimental results of Kircz, Morgenstern, and Nienhuis, on one hand, and Rothe, Theyunni, Reck, and Tung on the other hand. The new results confirm in general the data of Kircz, Morgenstern, and Nienhuis, and also indicate a dependence of the anisotropy ratios on the relative velocity of the interacting ${\mathrm{Na}}^{\mathrm{*}}$ atoms.

Conditional probability distributions for the ground configurations of alkaline-earth atoms are analyzed using simple analytical functions. The results of this analysis are consistent with those of recent elaborate numerical calculations.

We propose that the recently discovered smectic-$A_R$ phase with a simple rectangular lattice is an example of a ‘‘rippled state’’ in which the order parameter—here the polarization—is the superposition of a constant term and of a modulated one.

A simple power-series method is developed to calculate to large order the Rayleigh-Schrödinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Padé approximants to these series generally avoid the region of the positive real axis 0<λ<${\lambda }^{\mathrm{*}}$, where ${\lambda }^{\mathrm{*}}$ represents the coupling constant threshold. As a result, the Padé sums afford accurate approximations to E(λ) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ‘‘quasioscillatory,’’ but non-Stieltjes, behavior. Accurate values of E(λ) as well as ${\lambda }^{\mathrm{*}}$ for the 1s, 2s, and 2p levels are reported.

A mechanism is described which could explain the recently observed density (φ) and tritium-fraction ($C_t$) dependence of the muon-loss probability in muon-catalyzed d-t fusion. The effect is due to a hypothetical side path in the main catalysis cycle. It is proposed that the lifetime of a bottleneck state in the side path is controlled by ionization resulting from tritium radiolysis. The predicted dependence on φ √$C_t$ then agrees with the experiment.

A 3.34-m plane-grating spectrograph has been used to measure the wavelengths of 11 lines of singly ionized ${}_{}{}^{198}{}_{}{}^{}\mathrm{Hg}$ emitted by an electrodeless discharge lamp in the region 1942–7944 Å. The uncertainty varies from ±0.0003 to ±0.0015 Å. From these wavelengths, accurate values were determined for all levels of the 5$d^{10}$6s, 6p, 6d, 7s, 7p, and 5$d^9$6$s^2$ configurations and for four levels of the 5$d^9$6s6p configuration. By using existing isotope-shift data, values of wavelengths and energy levels for natural Hg ii were deduced. Accurate values for 12 lines of Hg ii in the region 893–2026 Å were calculated from the energy levels.

Using the numerical techniques that have been successful in elucidating the low-lying part of the level scheme of atoms in magnetic fields pertaining to white dwarf stars and neutron stars, we have computed the energies and wave functions of ‘‘circular’’ Rydberg states (i.e., with ‖m‖=n-1) with ‖m‖=24–35 for laboratory fields up to several tens of teslas. We can, therefore, follow a number of physical properties, such as transition frequencies and radiative decay times, of circular states as functions of the magnetic field strength and make predictions that should be verifiable experimentally.

The photon statistics of a free-electron laser at steady state are investigated in the classical regime under the assumption of small gain per pass. A Fokker-Planck–type equation is derived for the photon-number distribution. Strong-signal results are presented, together with analytical expressions for the photon-number fluctuations, and the results are compared to the ordinary laser. It is shown that the radiation is not in a Glauber coherent state, and that the intensity fluctuations are classical, i.e., independent of ħ.

The output voltage amplitude of a nonlinear microwave Fabry-Perot interferometer shows, below a critical value of the driving frequency, a series of aperiodic spikes whose density displays universal scaling behavior. The measured bifurcation diagram and the return map reveal that this type of chaotic motion can be explained in terms of a boundary crisis with repeated reinjection.

Phase diagrams near codimension two (CT) bifurcation points are analyzed. We consider CT points at which two distinct modes become unstable simultaneously. Such a point is expected to occur in a layer of Maxwell fluid heated from below, where one mode is oscillatory and the other one is stationary. We find that the phase diagram exhibits a novel mixed phase in which both stationary and oscillatory modes are present. Moreover, depending on the coupling between the two modes the system may exhibit a direct transition from the conductive to the mixed phase.

A formula for the energy levels of inner electrons in atoms is obtained by assuming that each electron experiences a Coulombic potential appropriate to its particular shell, an approximation that has been shown to result in a 4% error in the atom’s total energy in the limit of large atomic number. Corrections for the non-Coulombic part of the potential, exchange interactions, and relativistic terms are obtained in a manner consistent with the zeroth-order shell-model picture used. Calculated energy levels are then compared with x-ray data for a representative set of atoms from Z=10 to 88 with the result that an average absolute error of 4% is obtained for those levels for which the non-Coulombic potential’s contribution is not too large.

The performance of approximations to the Hohenberg-Kohn-Sham density functionals is tested by comparing with essentially exact results for light atoms (the He isoelectronic series, Be, and Ne). The approximation schemes considered here are the effective gradient schemes due to Langreth and Mehl (LM), and the ‘‘modified weighted-density’’ (MWD) approximation due to Gunnarsson and Jones. Compared to the local density approximation the LM schemes give markedly better exchange-correlation energies and a certain improvement in the density profiles, effective potentials, and orbital eigenvalues. The MWD scheme gives good improvements of the exchange-correlation energies but improves the densities, potentials, and eigenvalues only for the He isoelectronic series. The sensitivity of the MWD scheme with respect to the model pair correlation used, as well as some additional approximations used in practical applications of the MWD scheme, are also analyzed.

Different electric polarizabilities of Ne are calculated by using the complete fourth-order many-body perturbation-theory (MBPT) method and a partly optimized set of Gaussian-type orbital and contracted Gaussian-type orbital basis functions. The results obtained by the MBPT method (dipole polarizability α=2.712 a.u., dipole hyperpolarizability γ=104.6 a.u., quadrupole polarizability C=3.85 a.u., dipole-quadrupole polarizability B=-17.75 a.u.) are considered as the best currently available theoretical estimates. The importance of the electron-correlation contribution is demonstrated by the comparison with the corresponding self-consistent-field Hartree-Fock results (α=2.374 a.u., γ=63.9 a.u., C=3.20 a.u., B=-12.75 a.u.).

The scattering of electrons by ${\mathrm{He}}^{+}$ ions has been studied below the N=2 threshold of the ion. A pseudostate close-coupling method has been used to examine the scattering in the nonresonant and resonant regions. The calculations are performed using an algebraic variational method. Extensive pseudostate basis sets of differing characters are employed. In the nonresonant region, short-range electron-electron correlations are emphasized. In the vicinity of the resonances, the dominant projectile-target electron correlations are comparatively long range. S-, P-, and D-wave phase shifts of high accuracy are obtained for both the singlet and the triplet spin states. The present phase shifts agree very well with those obtained by Shimamura by a variational procedure for the S wave and with those of McGreevy and Stewart by a many-body perturbation method for the singlet P wave. The present phase shifts are in disagreement with the polarized orbital results of Khan et al. Resonance parameters are calculated for 15 S-wave resonances, 16 P-wave resonances, and 19 D-wave resonances with the outer electron extending up to n≃8. Estimates of quantum defects and the reduced widths are obtained for various Rydberg series of the doubly excited states. A number of the high-lying resonances are predicted for the first time. The agreement of the present energy values and the auotionization widths with the available experimental values is excellent.

A dynamical description of spectral shifts and widths of positron planar-channeled radiation is presented. The presence of well-defined valence electron collective oscillations or plasmons as documented in electron-loss spectroscopy is proposed as one mechanism for experimentally observed negative shifts. Qualitative comparison with the experimental data at 55 MeV for diamond, silicon, and LiF is indicated.

Total single-electron-capture cross sections have been measured for impact of ${\mathrm{N}}^{2+}$, ${\mathrm{Ne}}^{2+}$, ${\mathrm{Ar}}^{2+}$, ${\mathrm{Kr}}^{2+}$, and ${\mathrm{Xe}}^{2+}$ at 5–40 keV on Li(2s). The results are compared with other available data and can be quantitatively explained with a modified classical over-barrier transition model, assuming primary-ion-core conservation and taking into account the respective arrangements of available final projectile states.