A bidirectionally emitting ring laser ${(}^{15}$${\mathrm{NH}}_3$ at 376-μm wavelength) exhibits self-pulsing and chaos. The routes to chaos are found to be either a one-frequency–period-doubling route to chaos, or a one-frequency–two-frequencies–phase-locking– period-doubling route to chaos: windows within the chaotic range, the same as reported for a two-roll Bénard convection cell experiment. In single-mode operation an instability is observed under conditions compatible with the Lorenz model.

An analytic solution of the Vlasov equation in the one-dimensional case is presented for electrons in the potential electric field of a high-frequency monochromatic plasma wave with an arbitrarily large amplitude. The phase velocity of this wave is assumed to be appreciably higher than the electron thermal velocity. The ambipolar potential due to charge separation is taken into account and the form of the electron distribution function on the boundary need not be Maxwellian.

A density functional for inhomogeneous single-component fluids capable of describing both the short-range structure as well as coexistence phenomena such as wetting and drying is derived. The formalism utilizes a coarse-grained reference density $n_0$(r→) in addition to the full density n(r→). Equilibrium profiles are obtained by finding the extrema of the density functional with respect to both densities. Density profiles for a Lennard-Jones fluid at both a hard wall and a 3-9 wall near the complete wetting transition are presented.

The multiconfiguration Dirac-Fock (MCDF) method is used to calculate excitation energies, Landé g values, and hyperfine-structure (hfs) constants for the lowest multiplets of the 4$f^N$6$s^2$ configurations of neutral rare-earth atoms. Although no adjustable parameters are used, the results are in rather good agreement with experiment. The calculated excitation energies and dipole hfs constants (using the known moment values) differ from experiment by typically 5%, and the g values by 0.1%. Relative to quadrupole moment values determined from muonic-atom hfs or Coulomb excitation, the calculated electric-quadrupole hfs is typically (30±2)% too large, consistent with a Sternheimer shielding factor (not included in the MCDF calculations) of $R_{4f}$=+0.23. The calculated J dependence for all four observables is generally in good agreement with experiment for the ground multiplets. Particular cases where the MCDF results are less accurate are identified and discussed.

A charge perturbation method for the calculation of static electric dipole polarizabilities (α) is used to investigate the polarizability of the lithium dimer (${\mathrm{Li}}_2$). A series of studies are reported, which include all-electron self-consistent-field (SCF) and configuration-interaction calculations for a range of bond distances, the role of core correlation, and the effects of inclusion of d orbitals in the atomic orbital basis. Final values of the isotropic and anisotropic components of α, averaged over the ground vibrational state, are 209 and 170 a.u., respectively. The latter is 2.5 times the SCF value.

The calculation of recoil corrections to the Lamb shift in hydrogen is carried out by treating the Dirac electron in the presence of the nuclear Coulomb and convection potentials. The leading Dirac equation and its solutions were given by Grotch and Yennie many years ago. A systematic derivation of recoil corrections to the leading Lamb shift leads to results in agreement with previous work. New terms of order α(Zα${)}^5$$m^2$/M are derived by examining recoil corrections to higher-order radiative level shifts. These reduce the theoretical Lamb shift in the hydrogen n=2 state by about 2 ppm. It is expected, however, that additional contributions of the same order will also arise from corrections to the external-field approximation as well as from nonradiative recoil.

Statistical electron angular correlation coefficients τ=2〈 ${\mathcal{J}}_{?}^{}$, have been obtained for the atomic systems ${}_2{}^{}{}_{}{}^{}\mathrm{He}$ through ${}_{14}{}^{}{}_{}{}^{}\mathrm{Si}$, within the Hohenberg-Kohn-Sham density-functional formalism. These are computed with use of the spectral sum rules obtained from the pseudoexcitation spectrum employing the recent formulation of the time-dependent Kohn-Sham theory due to Bartolotti. Various approximations to the exchange-correlation energy functional are used and for first-row atoms, a comparison is made with the highly accurate correlation coefficients recently obtained by Thakkar. The present τ values show closer agreement with those of Thakkar with increasing number of electrons.

A classical equivalent of the Born-Oppenheimer approximation, commonly used in molecular quantum mechanics, is demonstrated to supply highly visualizable dynamic potentials which make obvious the localization of regular trajectories in nonintegrable Hamiltonian systems. Simultaneously, the approximation supplies a zeroth-order Hamiltonian $H_0$ with a small correction $H_1$ which is implicitly called for in perturbation analysis that assigns local actions. The smallness of $H_1$ can be used without extensive calculation to study the regions of action space where regularity exists. The methods used supply a unity to classical and quantum treatments of regularity in Hamiltonian systems. The basic ideas of the presented approach are illustrated on the example of librators and precessors of the Hénon-Heiles system.

Regularity in the quantum stadium is explained.

A spinless, nonrelativistic hydrogen atom coupled to an electromagnetic field is considered. The interaction is taken in the minimal-coupling form, and the ground state of the coupled system is obtained by straightforward perturbation theory. The form of the cloud of virtual photons surrounding the atom is studied through the quantum-mechanical average on this state of an appropriately defined coarse-grained energy-density (CGED) operator W(r→). The properties of W(r→) are studied in order to show that this operator can give a reliable description of the shape of the virtual photon cloud. The quantum-mechanical average of W(r→) is obtained analytically and exactly, and the CGED is shown to consist of an infinite number of spherically symmetric contributions, each originating from the set of virtual transitions induced by the vacuum fluctuations between the bare atomic ground state and all the bare atomic eigenstates belonging to a given subshell. This yields a shell and subshell structure for the virtual photon cloud, each of them characterized by a different behavior of the CGED as a function of the distance from the atom. The details of this structure are studied both analytically and numerically, and the results obtained are compared to those pertaining to virtual clouds in other fields of physics.

We have extended the von Barth–Hedin local-spin-density theory to treat the relativistic spin-polarized case as proposed by Doniach and Sommers. This extension permits us to do actual numerical calculations on atomic and solid-state systems. A technique for integrating the resulting coupled Dirac equations is presented. As a test the theory is applied to the study of the magnetic and electronic properties of some rare-earth ions. We analyze the relativistic and spin-polarization effects on the 4f spin densities and evaluate the polarization effect on the core electrons. Tables of form factors for the first seven rare-earth ions are also presented.

A simpler version of the formulas given by the author for the expansion of Slater-type orbitals (STO’s) about a point displaced from the orbital center is derived. By utilizing these formulas, extremely compact analytical expressions are established for multicenter electron-repulsion integrals over STO’s. The final results are of a simple structure and are, therefore, especially useful for machine computations.

Using crossed beams of polarized electrons and polarized hydrogen atoms we have investigated the effect of spin exchange on 90° elastic scattering from 4.4 to 30.3 eV and impact ionization from 14.1 to 197.0 eV. Our results suggest that the range of validity of various theoretical approximation methods is more restricted than had been assumed previously.

Measurements are reported for the dissociative attachment process $e^{\mathrm{-}}$(ε)+${\mathrm{CCl}}_4$→${\mathrm{Cl}}^{\mathrm{-}}$+CCl ${}_3{}^{}{}_{}{}^{}$ and the attachment process $e^{\mathrm{-}}$(ε)+${\mathrm{SF}}_6$→${\mathrm{SF}}_6$${\mathrm{}}^{\mathrm{-}}$ at electron energies ε of below threshold to 140 milli-electron-volts, and at resolutions of 6 and 8 meV full width at half-maximum, respectively. Resolution-limited narrow structure is observed in both molecules at energies below 10 meV, similar to structure reported earlier in attachment to 2-${\mathrm{C}}_4$${\mathrm{F}}_6$ and ${\mathrm{CFCl}}_3$. We ascribe this structure to the divergence of the attachment cross section in the limit ε,l→0. At the present limits of resolution, the attachment cross sections ${\sigma }_A$(ε) at the lowest energies are consistent with the Wigner threshold law for s-wave attachment in which ${\sigma }_A$(ε)∼${\epsilon }^{\mathrm{-}1/2}$. Comparisons are given with experimental collisional-ionization (high-Rydberg-state attachment) results, electron-swarm unfolded cross sections, and earlier threshold photoionization data. Comparisons are also made for ${\mathrm{SF}}_6$ with several theoretical calculations of the thermal attachment cross section.

${\mathrm{Li}}^{+}$ ions, accelerated to energies between 1 and 20 keV, pass through thick vapor targets of Mg, Sr, and Cs. The ions that emerge into a narrow, forward-directed cone are electrostatically separated into three charge-state components: ${\mathrm{Li}}^{\mathrm{-}}$, ${\mathrm{Li}}^0$, and ${\mathrm{Li}}^{+}$. The principal results over this energy range are the following: (1) The negative fraction peaks at 5% near 5 keV for a Cs target, and is less than 1% in Mg and Sr targets; (2) for Sr and Cs targets, the beam is greater than 90% neutral; and (3) for a Mg target, the beam does not neutralize at the lowest energies studied, remaining mostly positive between 1 and 10 keV.

A time-of-flight electron transmission spectrometer was employed to measure the absolute total electron-scattering cross section (elastic plus inelastic, integrated over all angles) for molecular hydrogen for incident electron energies from 1 to 50 eV. A complete error analysis is included. Comparisons are made with recent measurements and calculations.

Measurements have been made of the cross section for electron-impact single ionization of the ions ${\mathrm{Ti}}^{2+}$, ${\mathrm{Fe}}^{2+}$, ${\mathrm{Ar}}^{2+}$, ${\mathrm{Cl}}^{2+}$, and ${\mathrm{F}}^{2+}$, spanning the range of energies from below threshold to 1500 eV. Indirect processes such as excitation-autoionization contribute substantially to the cross section for ${\mathrm{Ti}}^{2+}$, while such contributions are less pronounced for the other species. Comparisons with available theoretical predictions and with the Lotz semiempirical formula are presented. Expansion coefficients and formulas for generating ionization rate coefficients in the temperature range ${10}^4$${<10\mathrm{}}^7$ K are included for each ion.

Total electron-capture cross sections have been measured for collisions of ${\mathrm{Al}}^{\mathrm{q}+}$ (q=2–10) with H and ${\mathrm{H}}_2$ in the 20–120-eV/amu energy range. The general trend of the cross sections for both H and ${\mathrm{H}}_2$ is an approximately linear increase with ionic charge state. The ${\mathrm{Al}}^{2+}$+H and ${\mathrm{Al}}^{3+}$+H systems were investigated theoretically using the molecular-orbital method with a pseudopotential to represent the ${\mathrm{Al}}^{3+}$ ion core. Coupled-channel calculations realize good agreement with experiment. An anomalously small cross section for ${\mathrm{Al}}^{2+}$+H is attributed to the fact that of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }$ and ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }$ entrance channels, only the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }$ molecular state contributes to the cross section.

Ll, Lα, Lβ, and Lγ x-ray-production cross sections have been measured in elements Ta, W, Au, Hg, Tl, Pb, Bi, Th, and U for 60-keV photons. The measured values have been interpreted in terms of photoelectric cross sections, fluorescence yields, Coster-Kronig transition probabilities, and radiative decay rates. A fairly good agreement is found between the experimental and calculated values.

Excitation of 0.05–2.5-keV H atoms in H+Ne collisions has been examined by measuring the absolute emission cross sections for Balmer-α, Balmer-β, and Lyman-α radiations resulting from the collisions. Lyman-α emission was also observed when an electric field was applied in the interaction region to investigate excitation of H atoms to the (metastable) 2s state. The radiation polarization for each of the above emissions was measured. A new method for absolute calibration of the Lyman-α detector is described, and Lyman-α emission cross sections for ${\mathrm{H}}^{+}$+Ar and $e^{\mathrm{-}}$+${\mathrm{H}}_2$ collisions are compared with previous results, the latter reaction giving a significantly smaller cross section than generally accepted. The peculiar behavior of the H+Ne interaction indicated by the measurements is discussed.