An integral representation for the spherically averaged electron density ρ(r) of atoms and molecules is proposed. Only the order k of the monotonicity of ρ(r) was assumed to be known. This representation is used to bound the mth derivative ${\mathrm{\rho }}^{\left(\mathit{m}\right)}$(r), m>=2, by means of the values of the density ρ(r) and its first derivative ρ’(r). Particular consequences of this general result are (i) lower bounds of the curvature ρ’’(r) at any value of r and (ii) atomic cusp-type inequalities for the derivative ${\mathrm{\rho }}^{\left(\mathit{m}\right)}$(0) of any order m [i.e., inequalities which allow one to bound such derivatives at the nucleus by means of the nuclear charge Z and the value of the density ρ(0)]. For example, it is obtained that the value (2Z${)}^2$ρ(0)(k-2)/(k-1) is a lower bound to the curvature of the electron density at the nucleus. Some of these results are compared with other recent findings of similar nature and are numerically analyzed by means of the highly accurate 204-term Hylleraas wave functions in several heliumlike atoms.

The widely used near-Hartree-Fock functions of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)] are compared with the newer functions of Bunge et al. [At. Data Nucl. Tables 53, 113 (1993)] by means of different measures of functional distance on the charge density ρ for the atoms He to Xe. The results are correlated with the energy improvement, and an empriical relation between the linear deviation in the first derivative of ρ and the total energy is reported.

We generalize the existing description of collision-induced atomic S⇆P transitions by spin-polarized electrons on spin-polarized target atoms. Analysis of existing experimental and theoretical data on the 3s⇆3p transitions in Na determines how closely the ‘‘perfect scattering experiment’’ has been achieved to date. Using a newly developed inversion technique, we demonstrate to what extent the various scattering amplitudes can be extracted from present experiments, and how state-of-the-art theory can be used to remove the remaining ambiguities.

A pseudorotating state of ${\mathrm{Li}}_5$ observed in a recent EPR experiment is investigated using the local density functional method. The calculated isotropic spin population indicates that a planar ${\mathit{C}}_{2\mathit{v}}$ structure is more consistent with the experimental result than a suggested trigonal bipyramid. A new pseudorotating state based on the planar structure is proposed.

We present a quantum-mechanical study of the dynamics of collisions of cold atoms in a (magneto-) optical trap valid in the linear intensity regime. We find further evidence for a discrepancy with results of the semiclassical optical-Bloch-equation method at lower collision energies and detunings, referred to as ‘‘quantum suppression’’ in previous work. We find a strong dependence on the detuning: for the lowest energies considered the suppression factor ranges from more than three orders of magnitude for Δ=-${\mathrm{\Gamma }}_{\mathrm{at}}$ to a factor 2 at Δ=-10${\mathrm{\Gamma }}_{\mathrm{at}}$. The fraction of atoms surviving at small interatomic distances for a single l value can in good approximation be described by a simple formula in the form of a product of a Landau-Zener excitation function and a WKB survival factor. Summed over partial waves this formula allows a relatively easy calculation of loss rates in a two-channel linear-intensity description. The role of such an approach in a future more complete treatment including hyperfine channels is pointed out.

A pair of light quanta with different colors (155.9-nm difference in center wavelength) generated from parametric down-conversion was injected collinearly into one input port of a Mach-Zehnder interferometer. Coincidence interference behavior was studied over a wide range of optical path differences of the interferometer. A measurement of 75% interference visibility with oscillation of the pump frequency for a large optical path difference of the interferometer (43 cm) is the signature of a quantum two-photon entangled state, which reflects both particle and wave nature of the light quanta in one experiment.

I show that, in the case of both one- and two-photon resonances, a many-cascade two-photon correlated-spontaneous-emission laser can generate light exhibiting phase and photon-number squeezings. Optimizing the mean photon number in the cavity with respect to a phase factor sin[1/2(n-1)θ]/sin(1/2θ), we find that the maximized mean photon number and its squeezing increase with increasing the top populations ${\mathrm{\rho }}_{\mathit{n}\mathit{n}}^{\mathit{a}}$ of the active atoms. However, the photon-number squeezing may decrease, increase, or not change when increasing the number n-1 of lower, almost degenerate atomic levels, depending on the relative phase θ of lower atomic states determined by the optimization conditions. The phase squeezing has a maximum value with increasing n-1 and ${\mathrm{\rho }}_{\mathit{n}\mathit{n}}^{\mathit{a}}$.

Stapp has recently presented a revised algebraic version of his (and others’) earlier nonlocality arguments. Stapp’s argument would seem to be an improvement over traditional arguments because he assumes only the so-called parameter-independence condition, but neither determinism nor the so-called outcome-independence condition. We show that, in fact, Stapp’s argument rests on a logical fallacy.

The logical structure of my recently proved nonlocality theorem [Phys. Rev. A 46, 6860 (1992)] is examined from the perspective of the theory counterfactual conditionals. It is shown in detail why the argument of Dickson and Clifton [preceding Comment, Phys. Rev. A 49, 4259 (1994)] does not substantiate their claim.

An inequality is deduced from local realism and a supplementary assumption. This inequality is violated by the predictions of quantum mechanics for experiments with low-efficiency detectors.

A mechanism is proposed for fragmentation resulting from positron-induced ionization of polyatomic molecules at energies below the threshold for producing positronium. The mechanism is supported by calculation, and by comparison with experimental data.

The dissociative ionization of organic molecules, induced by positrons having energies below the positronium threshold (0.5–3 eV), has been studied. Cross sections for the ionization-fragmentation processes increase as positron energies decrease. The data reveal that the energy required for dissociative ionization is supplied by the annihilation process, and that fragmentation occurs by breakage of C-C single bonds in preference to double and triple bonds.

Double-differential cross sections (DDCS’s) for the production of binary-encounter electrons (BEE’s) are reported for 30-MeV ${\mathrm{O}}^{\mathit{q}+}$+${\mathrm{O}}_2$ collisions. The BEE DDCS’s were measured at θ=0° with respect to the beam direction for projectile charge states q=4–8. The measured BEE DDCS’s were found to increase with decreasing charge state in agreement with other recent BEE results employing simpler ${\mathrm{H}}_2$ and He targets. Impulse-approximation calculations of BEE production for θ=0°–45° are also presented, in which it is assumed that target electrons undergo elastic scattering in the screened Coulomb field of the projectile ion. These calculations are shown to be in agreement with our data at θ=0° where only 2s and 2p target electrons are considered.

Complicated potential deformations performing a desired changing of the decay rates of quasistable states (resonance widths) or deleting chosen bound states are explained surprisingly simply. Exotic stalactitelike potential deformations ‘‘carrying’’ the chosen states through potential barriers are elementary constituents of the general theory of resonance management.

A set of previously measured helium (e,2e) coincidence ionization differential cross sections obtained over an exceptionally wide range of outgoing electron angles has been decomposed into tensorial angular components. A technique has been used which is familar in nuclear physics for the analysis of cascade decay correlations but which does not appear to have been applied previously to atomic scattering or ionization processes. The amplitudes of the angular components, and their variation with energy, give information of a new type on the interplay between the incident and outgoing electrons.

The interaction between two cavity resonant nonlinear processes in an intracavity ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$ medium is studied, namely frequency doubling of a pump field of frequency ${\mathrm{\omega }}_1$ and subsequent down-conversion of the second harmonic to a pair of photons of frequencies ${\mathrm{\omega }}_1$±Δ. A closed set of semiclassical equations of motion for appropriately chosen quantities of the full system is derived and an explicit stationary solution is given. Its features and stability are discussed, the most striking being a stable plateau in the second harmonic, i.e., the field of frequency ${\mathrm{\omega }}_2$=2${\mathrm{\omega }}_1$ becomes independent of the pump field ${\mathit{scrE}}_1$, provided ${\mathit{scrE}}_1$ is larger than a certain threshold value. It is demonstrated that undamped self-pulsing can only prevail, if the ratio of the rates of second harmonic generation over and parametric down-conversion exceeds a value which depends solely on the relative damping rates of the second harmonic and fundamental, which yields a tentative theoretical explanation of the experimentally observed quenching of the self-pulsing.

We analytically and numerically examine the stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity in a uniform saturable self-focusing medium. It is shown that the fundamental bound state of the family is stable to a symmetric perturbation but unstable to an asymmetric perturbation (that breaks the azimuthal symmetry of the beam, i.e., transverse instabilities). The higher-order states are also found to display transverse (modulation) instabilities. The development of the instabilities is shown to lead to the emission of filaments which spiral away from the center of the dark spot as stable entities.

A scheme for the preparation of nonclassical states of motion in a three-dimensional harmonic ion trap is proposed. The technique is based on adiabatic passage along dressed energy levels of the strongly coupled ion-trap system by varying the laser frequency.

Degenerate four-wave mixing in dense sodium vapor under conditions of strong pressure-induced Zeeman pumping is investigated. Thermal diffusion and its interplay with the Zeeman light shift are found to be responsible for the generation of a grating mechanism that is not sensitive to thermal washout. The effect can be observed experimentally after eliminating the influence of radiation trapping by the use of nitrogen as a buffer gas. Under these conditions large nonlinearities are produced which also influence the propagation of the signal wave via collision-aided circular birefringence.

It is demonstrated that the following two postulates are inconsistent: (1) the locality postulate, stating that if two physical systems are noninteracting then no real change can take place in one system in consequence of anything that may be done to the other one; and (2) the hidden-variable postulate, stating that a physical quantity has a pre-existing definite value before a measurement. The proof is based on a particular Mach-Zehnder interferometer in which the first beam splitter is an analyzer of circular polarizations. A left-handed beam of light propagates in this interferometer through only one optical path and does not interact with the interferometer’s phase shifter. Still, it is shown that, having detected the photon in one of the output ports of the interferometer, an acceptance of the above hidden-variable postulate implies that we know what would have been the result of the measurement had we chosen a phase shift α+π instead of α: The photon would be with certainty detected in the other port. It follows that the phase shifter deterministically influences the behavior of photons at the second beam splitter. The proof is formulated for a single-photon state. Another difference with respect to the ordinary proofs of the Bell theorem is the fact that the alternative settings of the phase shifter correspond to measurements of the same observable (in all other proofs one considers simultaneously the values of complementary observables). The proof is formulated without any use of inequalities and no additional assumption such as ‘‘the emptiness of the path not taken’’ is made.