It is shown, in the context of a double-slit experiment, that small nonlinearities of the Schrödinger equation, considered recently by Weinberg [Phys. Rev. Lett. 62, 485 (1989)], will in general allow a simultaneous measurement of particle paths and interference, unless the nonlinearities are of a special form such that nearby initial states remain so at all later times.

The convexity of the spherically averaged electron density ρ(r) of neutral atoms with Z≤54 is numerically studied in a Hartree-Fock framework. It is found that ρ(r) is convex for Z=1, 2, 7–15, and 33–44, while for the rest of the atoms it presents a small ‘‘nonconvex’’ region. Second, rigorous relationships between the values of the single-particle density and its first derivative at the origin and the radial expectation values 〈${\mathit{r}}^{\mathit{k}}$〉 for a convex ρ(r) are derived. These conditions are valid for any many-body system whose spherically averaged single-particle density is convex. Finally, for atomic systems, these determinantal conditions together with the electron-nucleus cusp condition are used to obtain novel upper and lower bounds to ρ(0) by means of two or more expectation values. The quality of the new lower bounds is better than that of the corresponding ones known up to now. In particular, the convexity bound (1/6π)(〈${\mathit{r}}^{\mathrm{-}2}$${\mathrm{〉}}^2$/〈${\mathit{r}}^{\mathrm{-}1}$〉) to ρ(0) improves by a factor of 4/3 the accuracy of the corresponding bound obtained from the property of monotonic decrease of ρ(r).

Using a saddle-point method the 1s2s2s2p ${}_{}{}^3{}_{}{}^{}$P ° states of Be-like systems are calculated for atomic systems with nuclear charge from Z=4 to 10. We used up to 260 terms and 29 various orbital and spin-angular-coupling partial waves in the wave function. Our results for O v, 423.95 and 435.96 eV, give an unambiguous confirmation of the identification of the most detailed analyzed experimental data, 423.9±0.2 and 435.9±0.2 eV. Our result for Be i, 101.10 eV, confirms the experimental identification at 101.02±0.1 eV. The result for C iii, 243.27 eV, agrees with the experimental measurement at 243.2±0.2 eV. The result for B ii, 161.36 eV, lies so close to the strong lithiumlike line at 161.24±0.1 eV that a greater resolution is needed to resolve them. Possible misidentifications in the literature are also discussed.

We have measured the hyperfine constants A${(}^2$${\mathit{S}}_{1/2}$), A${(}^2$${\mathit{P}}_{1/2}$), and A${(}^2$${\mathit{P}}_{3/2}$) for ${\mathrm{Ca}}^{+}$. We compare our results with the calculations of Mårtensson-Pendrill and Salomonson [Phys. Rev. A 30, 712 (1984)], who used many-body perturbation theory (MBPT). The agreement between our results and MBPT calculations for ${\mathrm{Ca}}^{+}$ is about 3%, which is comparable to similar comparisons reported for Cs [S. Blundell, in 2 Relativistic, Quantum Electrodynamic, and Weak Interaction Effects in Atoms, AIP Conf. Proc. No. 189, edited by Walter Johnson, Peter Mohr, and Joseph Sucher (AIP, New York, 1988)].

Consider the nonuniformly scaled electron density ${\mathit{n}}_{\lambda }^{\mathit{x}}$(x,y,z)=λn(λx,y,z), with analogous definitions for ${\mathit{n}}_{\lambda }^{\mathit{y}}$ and ${\mathit{n}}_{\lambda }^{\mathit{z}}$. It is shown that it is generally true that ${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }^{\mathit{x}}$]≠${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }^{\mathit{y}}$]≠${\mathit{E}}_{\mathrm{xc}}$[${\mathit{n}}_{\lambda }^{\mathit{z}}$], where ${\mathit{E}}_{\mathrm{xc}}$ is the exact exchange-correlation energy. A corresponding inequality also holds for the correlation component of ${\mathit{E}}_{\mathrm{xc}}$ when the correlation component is defined in one of the meaningful ways. In contrast, equalities always hold for the local-density approximations to these exact functionals. In other words, the local-density approximations for exchange correlation and for correlation alone do not distinguish between nonuniform scaling along different coordinates.

The asymptotic dependence of the second-order Born term on the collision energy E is reexamined. In contrast to previous work, a relativistic free-particle propagator is used, and allowance is made for the spectator electrons of the target by means of a screened potential. These modifications do not change the behavior of the capture cross section like (lnE${)}^2$/E.

We derive a shakeoff-like expression for double ionization induced by fast charged projectiles that includes higher-order contributions of the Born series. The resulting shakeoff amplitude is about twice as large and has the opposite sign when compared to that of the shakeoff term defined by the first Born approximation. This analysis permits the determination of the relative phase between the shakeoff and double-scattering contributions to double ionization.

The effect of He, Ar, and Xe admixture into ${\mathrm{SF}}_6$ gas on the absorption of 16.26-μm laser radiation is reported. Helium suppresses 16.26-μm absorption in ${\mathrm{SF}}_6$, whereas Ar and Xe enhance the absorption.

We analyze the phase-fluctuation measurements of Gerhardt et al. [Phys. Lett. 49A, 119 (1974)] on the phase fluctuations of a microscopic radiation field using the Hermitian phase-difference operator of Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)]. The predictions are in agreement with the measurements.

The electron-energy spectra for electrons emitted from ${\mathrm{Ar}}^{+}$-Kr and ${\mathrm{Kr}}^{+}$-Ar collisions have been measured for projectile energies of 0.4, 0.8, and 1.6 MeV. The spectra show a peak, or peaks, attributable to L-vacancy production in the AR ions superimposed on a continuous portion of the electron spectra. This continuous portion, which decreases with increasing electron energy, extends to electron energies in the 600–800-eV range. The data show some events for which electrons with more than twice the normal ${\mathit{L}}_{2,3}$-MM Auger energies are emitted, and their origin is not clear. They might be due to the decay of ${\mathit{L}}_1$ vacancies or to the filling of a vacancy in a molecular orbital during the collision. An Auger process in which two 2p vacancies are filled with the subsequent emission of only one electron, an ${\mathit{L}}_{2,3}$${\mathit{L}}_{2,3\mathrm{-}}$MMM transition, might contribute to the spectra above 400 eV. The association of the major peak with Ar L-vacancy production is in contrast to a recent paper in which the peak, together with the higher energy electrons, was attributed to quasimolecular electron emission, specifically, filling of 4sσ and 4pπ molecular-orbital vacancies during the collision.

Exchange effects are included exactly in these vibrational close-coupling calculations using a new separable representation, and short- and long-range interactions using a parameter-free correlation-polarization potential. Differential cross sections are similar to measurements, but differ as to the location of the threshold peaks, the relative importance of rotationally elastic versus inelastic transitions, and the validity of a critical assumption made in the electron-beam energy calibration. Polarization at intermediate distances is critical and the angular distribution of scattered electrons is anisotropic both near and well above threshold.

We report cross-section measurements of the associative-ionization process, Na(3${\mathit{p}}^2$${\mathit{P}}_{3/2}$)+Na(3${\mathit{p}}^2$${\mathit{P}}_{3/2}$)→${\mathrm{Na}}_2^{+}$+e as a function of velocity, alignment, and orientation in the collision energy range from 300 to 5 K. Two independently tunable laser beams select narrow velocity classes of excited sodium in a well-collimated atomic beam. Circular and linear polarization of the excitation lasers permits alignment and orientation of the excited atoms in the two velocity classes. The excitation functions show pronounced differences reflecting different molecular pathways to the final product, and they bridge the energy range between conventional and ‘‘cold’’ collision dynamics.

We have renormalized our previously reported 0° cross sections for zero resonant transfer and excitation calculation using high-resolution Auger spectroscopy (RTEA), d${\mathrm{\sigma }}_{\mathrm{RTEA}}$(0°)/dΩ, obtained in 0.25–2-MeV/u collisions of ${\mathrm{F}}^{6+}$ and ${\mathrm{O}}^{5+}$ ions with ${\mathrm{H}}_2$ by normalizing to calculated binary-encounter electron yields rather than the usual Ne K Auger yields. The renormalized data are found to be in good agreement with recent angular-dependent impulse-approximation calculations of RTE, showing the importance of alignment and the small influence of interference between RTEA and elastic electron scattering for a 0° observation.

The observation of modulational instability of optical waves in the normal dispersion region has been accomplished through the copropagation of two nonlinearly coupled, orthogonally polarized visible waves in a strongly birefringent optical fiber. Intensity autocorrelations exhibit ∼3.5-THz oscillations on both waves, and each wave spectrum develops a single shifted frequency sideband. The results agree well with an analysis of coupled nonlinear Schrödinger equations.

We show that laser and maser action is possible using atoms that have been prepared in dressed states. We develop the microscopic theory and derive the Fokker-Planck equation for the field distribution for such a laser (maser) system.

Coupled integral equations for bound states of two spin-0 bosons are derived variationally from scalar quantum electrodynamics, using an ansatz which incorporates the transverse photon degrees of freedom of the electromagnetic field. The equations are decoupled approximately and then solved perturbatively as well as numerically. A perturbative eigenenergy formula for particles of arbitrary masses, including all the corrections of order ${\mathrm{\alpha }}^4$, is obtained. A variational solution of the wave equation is used to determine eigenvalues and eigenfunctions at arbitrary coupling for the 1s and 2p states of the equal-mass and ${\mathit{m}}_{\mathit{K}}$/${\mathit{m}}_{\mathrm{\pi }}$ cases. Radial s-state excitations are calculated using the basis-state expansion method. In the limit where one particle becomes infinite our equation turns out to be the same as the weak-field limit of the Klein-Gordon-Coulomb equation.