We present a systematic scheme of improvement on the hypernetted-chain (HNC) equations, based on the density-functional formalism of correlations in high-density, classical plasmas. We show by a numerical comparison that the proposed scheme significantly improves the HNC results and leads to predictions almost identical to the exact Monte Carlo results.

We present the Hamiltonian structure of two-fluid electrodynamics, with the Hamiltonian functional equaling the energy. The Poisson bracket on functionals of the fluid variables and the electric and magnetic fields is bilinear, antisymmetric, and satisfies the Jacobi identity.

$K\alpha$ emission has been measured from plane multilayered disk targets irradiated by nanosecond C${\mathrm{O}}_2$-laser pulses at peak irradiances of 7.5 × ${10}^{14}$ W ${\mathrm{cm}}^{-2\mathrm{}}$. Absolute levels of hot-electron preheat have been determined.

A unified treatment of the total time regime of the decay of an unstable macroscopic state is derived by functional integral methods. A new one-variable integral representation for the conditional probability is obtained. Previous results with only a limited range of validity are contained as special cases. Further, the evolution of initial states in the vicinity of the instability point is studied.

A direct method is described for obtaining conditions under which certain $N$-degree-of-freedom Hamiltonian systems are integrable, i.e., possess $N$ integrals in involution. This method consists of requiring that the general solutions have the Painlevé property, i.e., no movable singularities other than poles. We apply this method to several Hamiltonian systems of physical significance such as the generalized Hénon-Heiles problem and the Toda lattice with $N=2\mathrm{} \mathrm{and} 3$, and recover all known integrable cases together with a few new ones. For some of these cases the second integral is written down explicitly while for others integrability is confirmed by numerical experiments.

The extra-electron binding energies of the ground-state monatomic negative ions with $Z<\mathrm{}86\mathrm{}$ are calculated using the self-interaction correction (SIC) to the local spin-density approximation (LSD) for exchange and correlation. The results agree reasonably with experiment, and the errors reflect the familiar "interconfigurational energy error" common to LSD and SIC. Some of the rare earths, e.g., Ce and possibly Gd, are predicted to form stable negative ions. In addition we have the following: (1) Relativistic (other than spin-orbit) contributions to the electron affinities are included and discussed. In Au the relativistic effects boost the calculated affinity from 1.5 to 2.5 eV. (2) The doubly negative ions ${\mathrm{O}}^{2-}$ and ${\mathrm{Te}}^{2-}$ are predicted to have no stable ground state. (3) Electron affinities are calculated for a few excited atomic states. (4) The calculated ground-state densities $n\left(r\right)\mathrm{}$ of all the neutral atoms and negative ions are monotonically decreasing functions of $r$. (5) Corrections to the random-phase-approximation electron-gas correlation energy are shown to cancel out of SIC calculations for atoms.

Two muonium states have been found in diamond. "Normal" muonium shows an isotropic hyperfine interaction with a coupling constant $\frac{A}{h}=3711\mathrm{}\pm 21$ MHz. "Anomalous" muonium is described by a $〈111〉$ axially symmetric spin Hamiltonian with coupling constants extrapolated to 0 K $\frac{\left|A_{\parallel }\right|}{h}=167.98\mathrm{}\pm 0.06$ MHz and $\frac{\left|A_{\perp }\right|}{h}=392.59\mathrm{}\pm 0.06$ MHz. $A_{\parallel }$ and $A_{\perp }$ are of opposite sign, and they exhibit a temperature dependence describable by a Debye model. The amplitudes of the three anomalous muonium hyperfine transitions is zero applied field increase with increasing temperature and show relative variations which give information about muonium formation and indicate that anomalous muonium is the most stable state for muons in diamond. These diamond results are compared with those from the isostructural materials silicon and germanium.

The time dependence of the muon spin polarization is calculated for situations where transitions occur between the different (paramagnetic or diamagnetic) muon states which have been observed in semiconductors. It is shown that under suitable experimental conditions the transition rates can be measured with high accuracy.

The energy of the ground electronic state of $\mathrm{H}_2^{}{}_{}{}^{+}$ is studied as a function of the internuclear separation $R_{12}$, the angle, $\theta$, between the molecular axis and the magnetic field, and the field strength $B$. For small $B$ the molecular diamagnetism reaches its maximum value when $\theta =\frac{\pi }{2}$ and $R_{12}\cong 5$ Bohr radii. This maximum value is about 50% greater than the diamagnetism of an isolated H atom. At large $B$ the molecule shrinks due to magnetic compression of the electron wave function, and the molecular vibration frequencies increase substantially. A strong diamagnetic torque appears which tends to align the molecular axis along the field. This gives rise to a zero-point rotational oscillation about $\theta =0\mathrm{}$ whose energy can substantially exceed that of the zero-point vibrational oscillation. The calculations presented indicate that even if the protons had infinite mass, the molecule would become unstable to dissociation at $\theta =\frac{\pi }{2}$ in fields $\gtrsim 1.6\times {10}^{11}$ G.

We study a perturbative semiclassical expansion for the energy levels of the hydrogen atom in a magnetic field. A recursion relation is derived for the calculation of the ground-state energy in each azimuthal subspace. Four terms of the series have been obtained analytically and higher-order corrections have been computed by numerical iteration of the recursion relation. The semiclassical series yields accurate results for field strengths up to the intermediate region, and a simple Shanks extrapolation extends its applicability into the region of very strong fields. A similar calculation for the Stark Hamiltonian is also outlined.

Although the electromagnetic Casimir forces are customarily explained in terms of the vacuum radiation field, they may also be understood in terms of radiation reaction, without explicit reference to the vacuum field. In particular, the Casimir forces may be obtained if one recognizes that the radiation reaction field of a dipole on itself depends on where the dipole is located, for this field is determined by the modal characteristics of the surrounding space. Only in infinite free space does the field of radiation reaction have a spatially invariant meaning. The fact that the Casimir forces may be understood in terms of either the vacuum electromagnetic field or the field of radiation reaction is an example of the general fluctuation-dissipation relation between the two concepts. These ideas are illustrated with derivations of several "vacuum-field effects," including the Casimir-Polder attraction of an atom to a conducting wall and the van der Waals force between two atoms.

It is well known that including the coordinate $r_{12}$ in the wave function is essential in obtaining highly accurate results for the low-lying bound states of two-electron systems. In this work we calculate the energy, wave function, oscillator strength, radial expectation values, and mass-polarization effect for helium bound states by using simple configuration-interaction basis functions. Our results show that the advantage of the $r_{12}$ coordinate is lost quickly in going from $S$ to $D$ states. In most cases, the results of this work give substantial improvement over previous calculations where $r_{12}$ is not included. For ${}_{}{}^{1,3}{}_{}{}^{}D$ states the results presented here are among the best in the literature.

For the first time, the impact-parameter dependence for $K$-shell ionization was measured for relativistic projectiles, although in an indirect way. Experimentally, channeling of GeV projectiles was used to gradually exclude close-encounter processes. In the present experiment, the Lorentz $\gamma$ factor varied between ∼2 and ∼100; in this region, the contribution from distant collisions becomes increasingly important and amounts to about 50% of the total yield for $\gamma \sim 100$. The experimental data are compared to theoretical calculations of impact-parameter distributions, and the agreement is fair for both positive and negative particles.

We extend the theory of light scattering from an atom undergoing collisions to the case of strong laser fields, where the expansion in powers of $\Omega {\tau }_c$ that was used formerly in a series of papers by Burnett et al. breaks down. In particular we consider in detail the conditions necessary to relate the observable quantities to intense-field collisional rate constants in a dressed-state basis (such as those calculated by Light and Szöke). We also show (following Rabin and Ben-Reuven) that by studying the spectrum emitted by the atoms in the presence of a strong field one may measure the collisional rates for transfer between the dressed states of atom plus radiation field.

A theory for small-angle scattering of arbitrary medium- or high-energy atoms or ions by atomic hydrogen is described. Results are obtained in terms of the known closed-form and easily calculable Glauber-approximation scattering amplitudes for electron-hydrogen collisions and for collisions between the nucleus (treated as one charged particle) of the ion or atom and the hydrogen atom, and in terms of the transition form factor of the arbitrary ion or atom. Applications are made to the angular differential cross sections for the excitation of atomic hydrogen to its $n=2\mathrm{}$ states by singly charged ground-state helium ions having velocities of roughly between ½ and 1 a.u. The differential cross sections are obtained in terms of electron-hydrogen amplitudes and the known ${\mathrm{He}}^{+}$ ground-state form factor. Comparisons are made with other calculations and with recent measurements. The results are in good agreement with the data. It is seen that the effect of the ${\mathrm{He}}^{+}$ electron is to produce significant constructive interference at most energies.

Previously reported ten-state perturbed stationary-state calculations for ${\mathrm{C}}^{6+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions are extended by increasing the basis to include all molecular states correlating to the principal levels $n=3,4, \mathrm{and} 5$ of the final ${\mathrm{C}}^{5+}\mathrm{}\left(\mathrm{nlm}\right)\mathrm{}$ atomic ion. This allows cross sections to be computed for the angular momentum sublevels, $l$, of each of the above $n$. The H-atom energy range extends from 13 eV to 27 keV. Adiabatic calculations are done for energies below 1.3 keV, and partially diabatic calculations are done at higher energies. The inclusion of states with magnetic quantum number $m\ge 2$ in the new basis leads to significant increases in the $n=5\mathrm{}$ capture cross section even at rather low energies. Two translational factors, which depend on the internuclear separation, are employed in the construction of the scattering basis. One is used for the state which correlates to $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$; the other is used for all states correlating to states of ${\mathrm{C}}^{5+}$. For purposes of comparison, cross sections are also computed for the same scattering basis, with the use of the method of Bates and McCarroll and the method of Piacentini and Salin. The heavy-particle motion is treated semiclassically, with the use of Riley's average approximation at energies below 1.3 keV and the straight-line impact-parameter method at higher energies. As in the ten-state calculations, it is shown that adiabatic and diabatic formulations lead to rather different values for the cross sections at the higher energies. The results are compared with the experimental and theoretical cross sections obtained by other researchers.

Electron-impact excitation of inner-shell electrons followed by autoionization can dominate the total ionization cross sections in certain cases. We have made calculations to investigate this phenomenon for transitions of the form $n{p}^{6}n{d}^m\to n{p}^{5}n{d}^{m+1\mathrm{}}$ in ions of the transition series of elements. We predict such excitations lead to enhancements of the total cross section of more than an order of magnitude in the triply ionized species of Ti, Zr, and Hf in accord with recent crossed-beam experiments. In these cases, the predicted and measured positions and shapes of the resonances agree quite well; however, the magnitude of the theoretical cross sections is overestimated in the distorted-wave, dipole approximation used here. The effects of other kinds of excitation-autoionization transitions are considered, and trends along the first transition series are discussed.

It is argued that a valuable method of observing certain types of surface-atom interactions may lie in mechanical torques generated through the spin-orbit relaxation of valence electronic spins of optically pumped atoms at surfaces. The unusual feature of this phenomenon is that the less probable spin-orbit relaxation becomes highly visible as compared with the much more rapid paramagnetic relaxation, because of an enhancement, typically by as much as a factor ${10}^9$, in the torques delivered to mechanical structures, by virtue of a very large effective moment arm. Spin-orbit relaxation operates through an exchange of translational momentum which, in turn, can be identified with the delivery of a gigantic angular momentum (in units of $\hslash$) relative to a distant axis about which mechanical motion is referred. The spin-orbit relaxation strongly depends upon the atomic number of the surface atoms and the strength of interaction with the optically pumped atoms. Being dominated by high-atomic-number surface atoms, spin-orbit-relaxation rates may not be too strongly influenced by minor surface contamination of lighter-weight optically active atoms.

Total scattering cross sections have been measured in the same apparatus for positrons and electrons colliding with ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and C${\mathrm{O}}_2$ using a beam transmission technique. The projectile impact energies range from 1 - 500 eV for $e^{+}-{\mathrm{H}}_2,2-500\mathrm{}$ eV for $e^{-}-{\mathrm{H}}_2,0.5-750\mathrm{}$ eV for $e^{+}-{\mathrm{N}}_2,2.2-700\mathrm{}$ eV for $e^{-}-{\mathrm{N}}_2,0.5-60\mathrm{}$ eV for $e^{+}-{\mathrm{CO}}_2$, and $2-50$ eV for $e^{-}-{\mathrm{CO}}_2$. The onset of positronium formation is clearly seen by an abrupt rise in the total cross sections for positrons colliding with each of the molecules at the respective positronium-formation thresholds. The positron measurements are compared with the electron measurements at intermediate energies for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$. This comparison reveals a merging of the cross sections for ${\mathrm{H}}_2$ at energies above 200 eV, while for ${\mathrm{N}}_2$ the electron results remain higher than the positron results at all energies. Estimates are made of potential experimental errors, as well as the experimental resolution for discrimination against projectiles scattered at small forward angles.

A two-step laser excitation technique was used to investigate the collisional broadening and shift of excited-state potassium transitions. Measurements were also made to determine that the broadening and shift constants were unaffected by optical pumping and saturation effects. Values for the argon collisional-broadening and shift constants for the potassium $4p-\mathrm{ns} \mathrm{}(n=8-11\mathrm{})\mathrm{}$ and $4p-\mathrm{nd} \mathrm{}(n=6-9\mathrm{})\mathrm{}$ transitions were determined from line-shape measurements. The values of these constants (in units of ${10}^{-9\mathrm{}}$ rad ${\mathrm{s}}^{-1\mathrm{}}$ ${\mathrm{atom}}^{-1\mathrm{}}$ ${\mathrm{cm}}^3$ at 110°C) and their one-sigma statistical uncertainties are $\left\{\right({4P}_{\frac{1}{2}}-{8S}_{\frac{1}{2}}): \gamma =17.03\mathrm{}\pm 0.15, \beta =-14.58\mathrm{}\pm 0.29 ;\}\left\{\right({4P}_{\frac{3}{2}}-{8S}_{\frac{1}{2}}): \gamma =17.45\mathrm{}\pm 0.24, \beta =-14.71\mathrm{}\pm 0.30 ;\}\left\{\right({4P}_{\frac{1}{2}}-{9S}_{\frac{1}{2}}): \gamma =17.29\mathrm{}\pm 0.15, \beta =-24.16\mathrm{}\pm 0.15 ;\}\left\{\right({4P}_{\frac{3}{2}}-{9S}_{\frac{1}{2}}): \gamma =17.35\mathrm{}\pm 0.12, \beta =-24.16\mathrm{}\pm 0.09 ;\}\left\{\right({4P}_{\frac{1}{2}}-{10S}_{\frac{1}{2}}): \gamma =15.62\mathrm{}\pm 0.07, \beta =-29.49\mathrm{}\pm 0.22 ;\}\left\{\right({4P}_{\frac{3}{2}}-{10S}_{\frac{1}{2}}): \gamma =15.80\mathrm{}\pm 0.11, \beta =-29.86\mathrm{}\pm 0.27 ;\}\left\{\right({4P}_{\frac{1}{2}}-{11S}_{\frac{1}{2}}): \gamma =12.69\mathrm{}\pm 0.09, \beta =-33.66\mathrm{}\pm 0.11 ;\}\left\{\right({4P}_{\frac{3}{2}}-{11S}_{\frac{1}{2}}): \gamma =12.85\mathrm{}\pm 0.17, \beta =-35.10\mathrm{}\pm 0.23 ;\}\left\{\right({4P}_{\frac{1}{2}}-{6D}_{\frac{3}{2}}): \gamma =13.75\mathrm{}\pm 0.27, \beta =-8.28\mathrm{}\pm 0.16 ;\}\left\{\right({4P}_{\frac{3}{2}}-{6D}_{\frac{5}{2}}): \gamma =15.15\mathrm{}\pm 0.41, \beta =-8.96\mathrm{}\pm 0.10 ;\}\left\{\right({4P}_{\frac{1}{2}}-{7D}_{\frac{3}{2}}): \gamma =18.60\mathrm{}\pm 0.21, \beta =-16.00\mathrm{}\pm 0.18 ;\}\left\{\right({4P}_{\frac{3}{2}}-{7D}_{\frac{5}{2}}): \gamma =19.64\mathrm{}\pm 0.25, \beta =-15.16\mathrm{}\pm 0.21 ;\}\left\{\right({4P}_{\frac{1}{2}}-{8D}_{\frac{3}{2}}): \gamma =19.94\mathrm{}\pm 0.09, \beta =-24.14\mathrm{}\pm 0.22 ;\}\left\{\right({4P}_{\frac{3}{2}}-{8D}_{\frac{5}{2}}): \gamma =19.80\mathrm{}\pm 0.06, \beta =-24.16\mathrm{}\pm 0.18 ;\}\left\{\right({4P}_{\frac{1}{2}}-{9D}_{\frac{3}{2}}): \gamma =17.40\mathrm{}\pm 0.13, \beta =-30.17\mathrm{}\pm 0.28 ;\}\left\{\right({4P}_{\frac{3}{2}}-{9D}_{\frac{5}{2}}): \gamma =17.50\mathrm{}\pm 0.27, \beta =-29.47\mathrm{}\pm 0.12 .\}$ The overall accuracy of these measurements is estimated to be about 5%.