We have measured the yield of convoy electrons produced by 2-MeV/u C projectiles incident on C foils as a function of target thickness (0.8-50 μg/${\mathrm{cm}}^2$) for incident charge states $q_i=4\mathrm{}-6$ and exit charge states $q_e=4\mathrm{}-6$. Normalizing the yields measured in coincidence with ions of exit charge state $q_e$ to the total number of projectiles exiting with charge state $q_e-1\mathrm{}$ we conclude that the target-thickness dependences found support the model of electron loss to the continuum as the dominant convoy-electron production mechanism even for bare projectiles incident on the thinnest targets. For equilibrium-thickness foils the electrons are lost predominantly from excited states.

We have directly measured the effect of $p$-orbital spatial alignment on the associative-ionization (AI) cross section in $\mathrm{Na}\mathrm{}\left(3p\right)+\mathrm{Na}\mathrm{}\left(3p\right)\mathrm{}$ collisions as a function of collision velocity in crossed atomic beams. Our measurements show that anisotropy in the cross section grows rapidly with velocity and that AI increasingly favors $p$-orbital alignment of both partners parallel to the laboratory collision axis over all other possible relative laboratory orientations.

The spectrum of degenerate Rydberg states of an $n$-manifold of the hydrogen atom when placed in crossed (perpendicular) electric and magnetic fields (the diamagnetic term is disregarded) is shown to conicide with that of a charged-particle harmonic oscillator in a magnetic field. A mechanical counterpart is identified as the gyropendulum. These correspondences give further insight into the nature of Rydberg states in external fields.

We report on an interferometric frequency measurement of the ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}_2^{}{}_{}{}^{}$ absorption line which has been used as a reference in Doppler-free two-photon spectroscopy of the positronium $1{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ transition. The measurement relies on a comparison with a nearby, previously calibrated line of ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}_2^{}{}_{}{}^{}$. The result, 616803 545.98(71) MHz, lowers the observed value of the positronium $1{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ interval to 1233607 142.9(10.7) and lessens the agreement between theory and experiment.

A two-step process using internal conversion and fluorescence to stabilize the $6P_{\frac{3}{2}}11d$ autoionizing state of barium has been observed. The internal conversion produces very highly excited autoionizing Rydberg states, which then emit fluorescence to produce singly excited, bound states. Inclusion of this process should bring calculations closer to agreement with recent measurements of dielectronic recombination.

Photoelectrons that leave the residual Pb ion in the $6s^{2}6p\left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)$ and $6s^{2}6p\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)$ states were observed from the ionization threshold (7.42 eV) to 12 eV. Partial and total cross sections were obtained, the latter also from ion measurements. The $6p_{\frac{1}{2}}$ cross section was found to be unexpectedly small near threshold (${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$), but strongly enhanced near the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ threshold associated with the admixed $6p_{\frac{3}{2}}$ configuration. The $6p_{\frac{3}{2}}$ cross section is unusually large at threshold.

The decay of squeezed quantum fluctuations of a system coupled to a dissipative environment is discussed. For a model where the heat bath consists of an infinite set of harmonic oscillators, exact results for the time evolution of the mean-square fluctuations are obtained for arbitrary bath temperature and arbitrary damping strength.

We have computed the Stark-broadened profiles of the first two Balmer lines ($n=3,4\mathrm{}\to 2$) of ${\mathrm{C}}^{5+}$. Plasma conditions span the electron density range $n_e={10}^{17}-{10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$, and $T=20\mathrm{}-300$ eV. The calculations include ion-dynamic effects, which we find are very important at the lower densities for ${\mathrm{H}}_{\alpha }(n=3\mathrm{}\to 2)$. At the higher densities, the dynamic profiles approach the static ones.

We observe a resonance behavior of oscillations prior to Hopf bifurcations in an autonomous system. The system studied is a barium sodium niobate crystal in which voltage oscillations are induced by a periodically modulated current density. The resonance behavior is measured as a function of the dc-offset current density. The shape of the resonance peak and its dependence on the dc offset are found to be in fair quantitative agreement with recent theoretical studies.

Uniform convergence to an effective Fokker-Planck equation for weakly colored noise is proved. Corresponding constraints on the correlation time for the colored noise are obtained. Examples of bistable nonlinearities are presented and discussed.

It is shown that the formation of stationary waveforms in a driven nonlinear microwave resonator with dissipation can be attributed to the generation and parametric amplification of Korteweg-de Vries (KdV) solitons by a pump wave traveling in the same direction. The interaction process and the soliton propagation are described on the basis of a perturbed KdV equation which is solved numerically. The results of an approximate analysis are compared with measurements performed on a transmission line resonator.

The first-passage time problem for a general non-Markovian process driven by a dichotomic Markov noise is solved. An equation for the probability to be found in an interval without ever having left this interval is deduced. Exact results for first-passage time moments are obtained.

We use the zero-core-contribution model to calculate the photoelectron spectra of three anions with complex electron configurations: ${\mathrm{Sc}}^{\mathrm{-}}$, ${\mathrm{Y}}^{\mathrm{-}}$, and ${\mathrm{Pd}}^{\mathrm{-}}$. Electrons can be detached from s, p, and d shells in ${\mathrm{Sc}}^{\mathrm{-}}$ and ${\mathrm{Y}}^{\mathrm{-}}$. Detachment occurs from s and d shells in ${\mathrm{Pd}}^{\mathrm{-}}$, which is further complicated by having bound states with two different electron configurations. The complex electron configurations of all these ions result in a variety of peaks with widely different intensities within each spectrum. The intensities of these peaks are accounted for by the zero-core-contribution model. The spectrum of ${\mathrm{Pd}}^{\mathrm{-}}$ provides a unique test of the rule for determining the core radius given in previous papers using this model.

A study is made of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ autodetaching states of ${\mathrm{H}}_2$${\mathrm{}}^{\mathrm{-}}$ from the viewpoint of ${\mathrm{H}}^{\mathrm{-}}$+H, rather than the usual viewpoint of e+${\mathrm{H}}_2$. The model proposed in this work is a Feshbach-type formalism with two differences from previous studies. Guided by the structure of ${\mathrm{H}}^{\mathrm{-}}$+H states at larger internuclear separations, Q space is defined by taking the singlet spin pair to be the pair of electrons on one center, rather than the pair of electrons in the lowest molecular orbital. These two specifications are the same at large separations, but depart from one another in the autodetaching region. It is suggested that such a Q space is more appropriate to the consideration of collisions of ${\mathrm{H}}^{\mathrm{-}}$ on H than are the conventional ${\mathrm{H}}_2$${\mathrm{}}^{\mathrm{-}}$ states obtained from the e+${\mathrm{H}}_2$ reaction. A second departure from previous works is the strengthening of the asymptotic condition on the Feshbach Q operator to require that 〈$p_r^2$+V(r)〉 is less than zero for the diffuse electron, where V(r) is the full Hartree-Fock potential produced by the core, including the Hartree-Fock parts of the 1/$r_{\mathrm{ij}}$ terms. This condition makes the diffuse electron unable to escape from the system unless it absorbs energy from the core or converts centrifugal motion into radial motion. Finally, it is shown that differential charge-exchange experiments for ${\mathrm{H}}^{\mathrm{-}}$ on H can provide an experimental measurement of the energy difference between the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ states and perhaps give some indication of their lifetimes as well.

In continuation of previous work explicitly demonstrating the basic quantum-mechanical principles of the static and the time-dependent superposition of spinors, a new double-resonance coil experiment is described, where a spin-flip process associated with an exchange of energy quanta happens in both beams of a perfect-crystal neutron interferometer. It is shown that under the given circumstances of neutron self-interference coherence is preserved in spite of the energy transfer to every neutron, which may stimulate renewed epistemological discussions about the interpretation of quantum mechanics. Furthermore quantum beating on a macroscopic time scale has been observed by introducing an exceedingly small energy difference of 8.6×${10}^{\mathrm{-}17}$ eV between the two interfering beams. According to the statistical accuracy of the data thereby an energy sensitivity of 2.7×${10}^{\mathrm{-}19}$ eV has been achieved.

We present a theoretical treatment for the two-electron interaction in the alkaline-earth atoms. The most important element in this procedure is the introduction of a nonlocal interaction potential for states of fixed total spin S and total orbital angular momentum L. The orbital wave function generated in this potential is capable of prediagonalizing the N-particle Hamiltonian matrix with respect to a given two-electron configuration series (i.e., a series of configurations with one valence electron in fixed orbital nl and the other one with fixed orbital angular momentum l’ but variable principal quantum number n’). With this procedure, we will show that the wave function for each state is well represented by a simple superposition of a few neighboring configurations. The effectiveness of this approach to include higher excited states in a simple calculation is demonstrated in its application to the ${}_{}{}^1{}_{}{}^{}\mathrm{P}$ states of the Mg atom.

This paper discusses some initial steps toward the goal of finding explicit procedures for calculating, to a good approximation, the minimum kinetic energy consistent with a given particle density ρ(r) for a system of fermions. The strategy proposed begins by separating the desired kinetic energy into a sum $T_W$+$T_{\mathrm{theta}}$, where $T_W$≥0 is the Weizsaaumlcker energy F $d^3$r ‖∇ρ${\Vert }^2$/8ρ , and $T_{\mathrm{theta}}$≥0. Approximations are applied to $T_{\mathrm{theta}}$ alone, and are sought in the form of interpolations that will be nearly correct in two limits: small departures from uniform density, for which exact results are known from linear-response theory, and cases where a region containing no more than one particle of a given spin becomes isolated from the rest of the distribution by regions of nearly vanishing density. Only highly nonlocal functionals can behave properly in either of these limits. A few other conditions for satisfactory approximations to $T_{\mathrm{theta}}$ are noted. Some explicit interpolation formulas are offered for one-dimensional problems, and are tested on a variety of examples; one such is found to give kinetic energies to within a few percent in nearly all cases examined. More detailed tests are possible by comparing correct and approximate potentials yielding a given density, or correct and approximate densities for the ground state of a given potential; tests on the position dependence of kinetic energy density, however, are physically meaningless. A few remarks are offered on the additional problems that beset extension of the scheme to three dimensions; foremost among these is that of computational tractability.

Lifetime measurements, based on the method of beam-foil spectroscopy, together with careful corrections for cascade effects, have in recent years yielded the line strength of the 2$s^2$ ${\mathrm{}}^1$S–2s2p ${\mathrm{}}^1$P° transition in Be-like ions with uncertainties ranging from 3.4% to 8.1% in Bei–O. By applying a method of isoelectronic smoothing of line strengths, similar to those earlier used for excitation energies and transition wavelengths, we have reduced the experimental uncertainties by about a factor of 2, to 1.9–3.6 % for these transitions. The fitted results are in excellent agreement with the best theoretical data. The applicability of this method to other isoelectronic sequences is briefly discussed.

We calculate the shifts in the orbital frequency and damping constant for a charged particle in a cyclotron motion that is highly localized near the center of a lossy spherical cavity. In consequence of the spherical geometry, a simple closed form for the frequency shift and damping time is obtained, and the dissipation of a cavity with finite conductivity can be treated exactly. The spherical cavity has a simple mode structure that correlates frequency shift and damping-constant minima. This correlation provides a simple prescription for minimizing the shifts. However, because the modes are more sparsely spaced than are those of the cylindrical cavity treated earlier which models present Penning traps, the overall effects are larger for the sphere.

The Wei-Norman algebraic techniques for time-ordering problems are applied to the study of the evolution of quantum states ruled by a harmonic-oscillator Hamiltonian with a time-dependent frequency. The slowly varying frequency case is studied; the adiabatic theorem is rederived together with higher-order corrections. The analogy with the propagation of a paraxial beam through a self-focusing fiber is also pointed out.