The results obtained in a previous article [Phys. Rev. A 23, 1365 (1981)] for the optical Hanle effect of an atomic beam (no Doppler broadening) are extended to the case of a dilute gas with Doppler width greater than the collision or natural width. It is shown that the optical Hanle effect is independent of the Doppler width for the case where the strong-field detuning is larger than the Rabi frequency and the weak-field excitation detuning. Analytical results are obtained for a $J=0\mathrm{}\to J=1\mathrm{}$ transition.

The lethargic regime of a swept-gain laser amplifier is investigated theoretically to determine the procedure for passing over to the conventional limit $T_1\left(\mathrm{level}\mathrm{lifetime}\right) \gg T_2 \left(\mathrm{phase}\mathrm{memory}\mathrm{time}\right)$ of laser amplifiers. The calculation is done with a model in which the transit time of the atoms $t_0$, is less than $T_1$, which is soluble in closed form. The conventional limit is taken as $t_0\to \infty$. The general and conventional limits involve contradictory conditions of operation; nonetheless, both agree with experiment. This apparent contradiction is resolved by our finding that the conventional limit is a singular case.

Exact and explicit formulas relating equilibrium polymerization (with excluded volume and polymer rings) and Ising models with even multispin interactions in any dimension are given. It is concluded that equilibrium polymerization either belongs to the Ising universality class or is a first-order transition. Numerical, mean-field evaluations disfavor the latter.

This paper reports finite-frequency density modifications due to the electron Bernstein wave at the upper-hybrid resonant layer of a magnetoplasma. Envelope solitons consisting of nonlinear density perturbations together with localized Bernstein wave envelopes are found to exist.

We have performed a fully relativistic calculation, using the Dirac-Fock approximation, of energy levels and excitation energies for several ions in the promethium isoelectronic sequence. Our results verify the overall predictions on level ordering of the Hartree-Fock calculations, which included some relativistic effects perturbatively. Some differences were found concerning the atomic number at which the ground state of the ion has alkali-metal-like configuration.

A high-energy expansion is obtained for nonrelativistic phase shifts in a screened Coulomb potential, expressing their difference from the corresponding point Coulomb phase shifts as quadrature integrals over the potential. The result exhibits the role of small- and large-distance regions of the potential in determining these phase shifts.

The absolute yield of beam-foil-excited Rydberg states is measured, with the use of field-ionization techniques, for 125-MeV sulfur ions. The result, which agrees with a simple estimate, is compared with yields inferred from recent measurements of delayed $K$ x rays.

A highly polarized ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ atomic beam is produced by optical pumping with the use of either a multimode cw dye laser or a single-mode ring dye laser followed by a double-passed acousto-optic modulator. Electron-spin polarizations of 0.72 to 0.90 are obtained.

The dynamics of Ginzburg-Landau (or "potential") systems driven away from equilibrium and subjected to noise is simulated numerically. It is found that the Fourier spectrum does not always have its peak at the wave number corresponding to the absolute minimum of the potential. This is explained heuristically on the basis of an entropy type of argument.

The measured attractor of a driven $R-L$-varactor system is found to be self-replicating and inconsistent with a simple logistic map. A calculation based on a standard model of a varactor diode is in qualitative agreement with the data.

We study the global dynamics of nonlinear networks made up of synchronous threshold elements. By writing a master equation for the system, we obtain an expression for the time dependence of its activity as a function of parameter values. We show that with both excitatory and inhibitory couplings, a network can display collective behavior which can be either multiple periodic or deterministic chaotic, a result that appears to be quite general.

The attractor of the chaos in a driven nonlinear dissipative circuit is observed. The attractor is made of a curve imperfectly folded many times. The crisis effect, the sudden onset of chaos caused by the collision of the subband attractor with the unstable periodic orbit, is verified experimentally.

The functional renormalization group is used to show that a wide class of dynamical systems displays spectra with a $\frac{1}{f^{\delta }}$ divergence. Cutoffs introduced by stochastic or deterministic perturbations have universal features as well. Numerical support is presented.

The single-particle equations of motion are used to study the stimulated emission from a tenuous relativistic electron beam propagating in the combined solenoidal and variable-parameter longitudinal wiggler magnetic fields produced near the axis of a multiple-mirror (undulator) field configuration. The specific case of constant field amplitude and variable wiggler periodicity is studied. It is found that the efficiency of radiation generation can be increased by orders of magnitude relative to the case where the wiggler periodicity is constant. This is due to the fact that the phase velocity of the ponderomotive potential in which the electrons are trapped is decreasing, allowing the electrons to exchange energy with the radiation field.

The expression for the dipole moment of an atom or a centrosymmetric molecule in the vicinity of a perfect metallic surface is given at any distance. The near-zone (London) and the far-zone (Casimir) limits of these results are also considered.

The unrestricted Hartree-Fock (UHF) method is shown to be a special case of the saddle-point variational method for atoms and molecules containing inner-shell vacancies. Numerical results determined by this method are presented for excited electronic states of ${\mathrm{B}}^{+}$ and ${\mathrm{B}}^{2+}$ atomic ions. These results are compared to experimental Auger energies and to independently calculated results based on the saddle-point variational method without the UHF approximation.

We report on a nonadiabatic calculation of the few lowest $J=0\mathrm{}$ states in the ${\mathrm{H}}_2^{+}$ molecule done within the framework of the generator-coordinate method. Substantial accuracy is achieved with the diagonalization of matrices of very modest dimensions. The resulting wave functions are strongly dominated by just a few basis states. The computational scheme is set up so as to take the best advantage of good analytical approximations to existing adiabatic molecular wave functions.

The density-functional theory relates the ground-state properties of an $N$-electron system to a universal functional of the charge density. In this paper we discuss a functional which avoids the problems of the Hohenberg-Kohn theory. We show that this functional can be calculated exactly, at least in principle. We present an upper bound for this functional, which is applied to the case $N=1\mathrm{}$ and to the jellium problem. This upper bound is exact for $N=1\mathrm{}$.