Relativistic electron streams are shown to be both electrostatically and magnetically self-focusing; the electrostatic component can dominate. Moreover, steady-state reverse currents exist allowing steady-state stream currents in excess of the Alfvén limit. Many diverse phenomena (ion acceleration, stepped beam head and net current behavior, strong microwave generation) can be quantitatively understood as simultaneous-pinch phenomena. Limiting energies for axial acceleration of ions are given. Stream radius, focal length, limiting current, stream particle temperature, and plasma particle densities are calculated from initial conditions and are in agreement with experimental data. Conditions for target-implosion fusion studies are specified.

The theory of translational diffusion in nematic liquid crystals is developed from the standpoint of hydrodynamics and molecular-hydrodynamic interactions. The anisotropy of the diffusivity is obtained and related to the orientational order parameter, viscosity coefficients, and the detailed molecular geometry. Liquid-crystal hydrodynamics, Riemannian geometry, and molecular chain space are utilized in the theoretical development. The results for the diffusivity parallel and perpendicular to the director in $p$-azoxyanisole (PAA) at 125°C are $D^{\parallel }=4.3\mathrm{}\times {10}^{-6\mathrm{}}$ and $D^{\perp }=3.1\mathrm{}\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^2$/sec, respectively, giving an anisotropy ratio $\frac{D^{\parallel }}{D^{\perp }}=1.4\mathrm{}$. In addition, the temperature dependence of $D^{\perp }$ is obtained, using available viscosity data. $D^{\perp }$ ($D^{\parallel }$) shows an increase (decrease)—corresponding to the decrease in order parameter—as the isotropic transition temperature is approached.

With the use of the Herivel-Lin variational principle to describe incompressible inviscid fluids, a fluctuation Hamiltonian is derived in terms of a complex field $\Psi (\overrightarrow{\mathrm{r}}, t)$ representing the fluid. The source-free part of the field current describes the velocity field. The field interaction is found to be of current-current type, i.e., ${({\Psi }^{*} \mathrm{grad} \Psi -\mathrm{c}.\mathrm{c}.\mathrm{})}^2$ instead of the commonly used ${\left|\Psi \right|}^4$ type. The pressure, together with a complete energy-momentum tensor of the $\Psi$ field, is introduced, depending on the boundary conditions. The latter imply a long-range interaction near the onset of turbulence. Viscosity is taken into account by proper extension of the equation of motion of $\Psi (\overrightarrow{\mathrm{r}}, t)$, which turns out to be of the Landau type. This equation is solved exactly for laminar plane shear flow. The eddy interaction in $k$ space for fully developed turbulence is given together with a model Hamiltonian for the effects of viscosity. Finally the transient behavior of the $\Psi$-field amplitude of a fixed spatial mode near the onset of turbulence is compared with experiments.

The longitudinal and transversal current-current correlation functions of simple classical liquids are expressed in terms of restoring forces and frequency-dependent relaxation kernels within the frame-work of Mori's theory. The spectra of the relaxation kernels are approximated by the decay of one-mode excitation into pairs of two longitudinal modes and into pairs of one longitudinal and one transversal mode. The decay vertex is given by an irreducible three-particle distribution function which is approximately expressed in terms of two-particle distribution functions taking three-particle hard-core correlations into account. The resulting nonlinear integral equations are solved by iteration for liquid argon parameters and the obtained current excitation spectra are compared with the curves found by computer simulations and by neutron scattering experiments.

Neutron inelastic scattering data from a monatomic liquid can be directly translated into a pair interaction. This requires accurate experimental determination of the zeroth and fourth moments of $S(\kappa , \omega )$. The iterative calculation works because the Fourier transform of the fourth moment gives a good zeroth approximation to the second derivative of the potential. Recent molecular dynamics data on liquid rubidium are used to illustrate the method. Experiments should be carried out to exploit this method.

Through a detailed analysis of the second Born amplitude, an alternative derivation of Kroll and Watson's low-frequency result for the multiphoton bremsstrahlung process is given.

The usual dipole approximation for the transition probabilities for hydrogen atoms is derived from the exact transition probabilities by considering $j=1\mathrm{}$ photons only, neglecting retardation, and using an identity derived from the wave equation for the radial wave function for the atom.

We have measured the lifetimes of ($1s2p$) ${}_{}{}^3{}_{}{}^{}P_{0,2}^{}{}_{}{}^{}$ in heliumlike fluorine in a search for the nuclear-spin-induced quenching of the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ state. Both fine-structure decays ($2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^3{}_{}{}^{}P_{0,2}^{}{}_{}{}^{}$) were observed following foil excitation of a 15-MeV F beam. Within experimental error (±10%) the two states have the same lifetime (10 nsec) in agreement with theoretical $2p-2s$ $E1\mathrm{}$ decay rates.

The hyperfine structure of the $8{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ and the $9{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ has been measured by a multistep excitation method using a dye laser. Our measured values for the magnetic dipole coupling constant are $A({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}, 8{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})=32.12\mathrm{}\left(11\right)\mathrm{}$ MHz and $A({}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}, 9{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})=23.19\mathrm{}\left(15\right)\mathrm{}$ MHz.

Recently Rajagopal and Sudarshan proposed a generalization of Marcinkiewicz's theorem to quantum systems. From it they conclude that approximation schemes, such that the irreducible equal-time correlation functions vanish for all orders larger than $l$ but are nonvanishing for some $l$ larger than 2, are inconsistent with basic positivity conditions on the density operator. We show that this statement is false for fermion systems. For boson systems the statement is correct and its extension to irreducible correlation functions for unequal times can be made plausible; a fully rigorous proof does not yet seem available, however. The possibility is briefly discussed that an extension of Marcinkiewicz's theorem may hold for fermion systems, provided one confines his attention to equilibrium states of such systems.

Numerical evaluation of high-order terms in the Born series for an attractive Yukawa potential is accomplished with a transform described in an earlier paper. Born terms through order five are computed at high energy and through order seven at low energy. These are resummed using a variational functional for the $T$-matrix elements suggested by Rabitz and Conn to give good agreement with the existing numerical study of Walters.

The Brueckner-Goldstone many-body theory is applied to study the photon-atom reaction $\mathrm{He}\left(1\mathrm{}{s}^2\right)+\gamma \to {\mathrm{He}}^{++}\left(1\mathrm{}{s}^0\right)+e+e$. An expression for the double-photoionization cross section is derived. The result is used to obtain the angular distribution of the ejected electrons. The effect of final-state correlation is examined.

The Auger electron spectrum of HF in the gas phase has been measured and the peaks identified with the transitions to the expected final states in H${\mathrm{F}}^{++}$. The relative energies and intensities are quite similar to those for the Auger spectrum of the isoelectronic atom neon. The additional features appearing in the HF spectrum are explained in terms of perturbations to ${\mathrm{Ne}}^{--}$ or ${\mathrm{F}}^{-}$ by an adjacent proton. The ionization potentials of HF have been measured by photoelectron spectroscopy. The energy-loss spectrum for 710-eV electrons incident on HF has been determined and the peaks identified with the expected excited states in the HF molecule.

The fine structure of the oxygen ${}_{}{}^3{}_{}{}^{}P$ ground state is computed using a rather simple multiconfiguration wave function. The approach is similar to that used in previously reported fine-structure calculations for the lowest nitrogen ${}_{}{}^2{}_{}{}^{}D$ and ${}_{}{}^2{}_{}{}^{}P$ states, and similar results are obtained, accounting for about 80% of the difference between the Hartree-Fock result for the spin-orbit coupling parameter and the value indicated by experiment. The contribution due to spin-spin coupling is also considered.

Self-consistent-field wave functions and energies have been used to obtain an interpretation of the $\mathrm{KLL}$ Auger spectra of C${\mathrm{H}}_4$. The computed Auger energies are in good agreement with observed values. The multiplet structure and splittings of the final states of C${\mathrm{H}}_4^{+2\mathrm{}}$ are shown to play a key role in determining the spectra. For the first time, symmetry assignments have been made for the final states of the Auger transition peaks in a molecule.

We have determined the radiative lifetimes of the $n=5-13\mathrm{}$, $s$ and $d$ states of Na by pumping the desired level with two resonant photons derived from two dye lasers excited by the same ${\mathrm{N}}_2$ laser. The lifetimes increase approximately as the cube of the effective quantum number, and are in good agreement with a Coulomb-approximation calculation.

We give a general nonperturbative treatment of cooperative emission in systems of $N$ two-level atoms, starting from first principles and including inhomogeneous broadening. In particular, we study superfluorescence, which is defined as the cooperative spontaneous emission, i.e., radiation rate proportional to $N^2$, from an atomic system initially excited with zero macroscopic dipole moment and a uniform population difference between the excited and the fundamental states. The atomic system is described by means of collective dipole operators. A fundamental justification is given for the existence of damped "quasimodes" of the mirrorless active volume. The damping of such modes is simply due to the propagation of the Maxwell field, which escapes from the active volume. A general atom-field master equation is derived for the system atoms plus field inside the active volume, described, respectively, in terms of collective dipole operators and quasimode operators. An important feature of this equation is that inhomogeneous broadening simply appears via a time-dependent atom-field coupling constant. In this paper we give a semiclassical treatment of such a master equation. For a pencil-shaped geometry of the active volume, generalized Maxwell-Bloch equations are derived for the envelopes of the radiation inside the active volume and polarization. Such equations take into account the two directions of propagation of the radiation and the inhomogeneous broadening. Suitably phrasing our initial condition in semiclassical terms, we find that propagation effects can be neglected at all times and the generalized Maxwell-Bloch equations reduce to a simple pendulum equation. On the basis of the discussion of the pendulum equation, we conclude that superfluorescence occurs when (i) the length $L$ of the active volume is much larger than a suitable threshold length $L_T$ (this condition ensures that the dephasing atomic processes occur on a time scale much larger than the times characteristic of the cooperative emission); (ii) the length $L$ is smaller or of the same order of a suitable cooperation length $L_c$ (this condition ensures that cooperative spontaneous emission dominates stimulated processes, which give radiation proportional to $N$). For $L\ll L_c$, one has a hyperbolic-secant superfluorescent pulse; for $L\approx L_c$, as one has in the recent experiments of Skribanowitz et al., one finds oscillations in the cooperative decay and in the radiation emission. Such oscillations are due to the contribution of stimulated processes. For $L\gg L_c$, this contribution increases. As a consequence one gets more oscillations in the radiated intensity, which becomes proportional to $N$, so that superfluorescence effects disappear.

Measurement of $v=1-0\mathrm{}$, $P$-branch 3.4-μm DF absorption spectra is made for a 0.1- to 500-Torr range of pressure. A cw DF laser is used as a light source, and laser intensity transmitted by DF gas is recorded in order to determine the absorption. The laser frequency is tunable over an interval which corresponds to a Doppler width. This permits measurement of the frequency dependence of transmitted light intensity for each line in the spectra, from which determination of absorption at precisely the absorption peak frequency is made. This latter determination permits evaluation of Einstein-$A$ and linewidth ${\nu }_L^0$ dependence on pressure. The results obtained for $v=1-0\mathrm{}$, $P\left(5\right)\mathrm{}$ through $P\left(10\right)\mathrm{}$ spectra are ($A$ in ${\sec }^{-1\mathrm{}}$, ${\nu }_L^0$ in ${\mathrm{cm}}^{-1\mathrm{}}$ ${\mathrm{atm}}^{-1\mathrm{}}$): for $P\left(5\right)\mathrm{}$, $A=28\mathrm{}\pm 4$ and ${\nu }_L^0=0.46\mathrm{}\pm 0.08$; $P\left(6\right)\mathrm{}$, $A=34\mathrm{}\pm 4$ and ${\nu }_L^0=0.45\mathrm{}\pm 0.07$; $P\left(7\right)\mathrm{}$, $A=31\mathrm{}\pm 4$ and ${\nu }_L^0=0.29\mathrm{}\pm 0.05$; $P\left(8\right)\mathrm{}$, $A=35\mathrm{}\pm 4$ and ${\nu }_L^0=0.24\mathrm{}\pm 0.04$; $P\left(9\right)\mathrm{}$, $A=31\mathrm{}\pm 4$ and ${\nu }_L^0=0.17\mathrm{}\pm 0.03$; and $P\left(10\right)\mathrm{}$, $A=34\mathrm{}\pm 4$ and ${\nu }_L^0=0.13\mathrm{}\pm 0.02$. These values for $A$ and ${\nu }_L^0$ are in excellent agreement with corresponding theoretical values.

Adaptation of the momentum-space Schrödinger-Coulomb Green's function for second-order perturbation calculations of the bound-state energy levels of hydrogenic atoms is demonstrated. The numerical viability of the formulas derived is proven by recalculating the contribution in second order of the spin-spin operator to the hydrogen hyperfine-structure residual $R=\frac{(8\mathrm{}{\nu }_{2S}-{\nu }_{1S})}{{\nu }_{1S}}$. Application to positronium hyperfine structure is discussed.

Using a modification of the trapped-electron technique, we have measured the total intensity of electrons inelastically scattered from helium as a function of both incident and final energies near the ionization threshold. We find that a "cusp," which appears in the scattered electron intensity at the ionization threshold for electrons of near-zero final energy, decreases in visibility as the energy of the scattered electrons increases. For scattered-electron energies greater than about 2.0 eV, the intensity is smooth through the ionization threshold. The physical reason for the cusp is the formation of states with two excited and strongly correlated electrons. These experiments define the range of excess energies above the ionization threshold for which correlation effects are important, and hence measure the energy range of validity of the Wannier law of threshold ionization.