It is argued that the proofs [W. D. Sharp and N. Shanks, Philos. Sci. 60, 488 (1993); O. Cohen, Phys. Rev. A 51, 4373 (1995); D. J. Miller, Phys. Lett. A 222, 31 (1996)] of the general nonvalidity of the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz rule [Y. Aharonov, P. G. Bergmann, and J. L. Lebowitz, Phys. Rev. 134, B1410 (1964)] are perfectly valid, and that Vaidman’s rejection of these proofs [L. Vaidman, Phys. Rev. A (Comment for which this paper is the Reply)] is unsustainable. It is demonstrated that Vaidman’s proposed formulation of “counterfactual probability,” on which his rejection of these proofs depends, is problematic and inconsistent in several respects.

We analyze a quantum observable $f$ given by the time average of a dynamical variable F along a Feynman path. We show that $f$ can be described by a (generalized) wave function satisfying the Schrödinger-like equation and measured by a meter similar to that of von Neumann. A connection with operators is established. Examples include the particle’s momentum, energy and the fractional traversal time.

This paper shows how analogs of the Greenberger-Horne-Zeilinger experiment, which demonstrates the impossibility of certain types of local hidden-variable theories in quantum mechanics, can be performed using nuclear magnetic resonance on spins in molecules at finite temperature. Because of their microscopic nature, these experiments cannot rule out the presence of nonstandard interactions that could cause classical variables to imitate quantum variables. Instead, they are designed to reveal the peculiarly quantum-mechanical correlations on which the Greenberger-Horne-Zeilinger effect is based.

A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration.

We present a finite-size scaling approach for the calculations of the critical parameters of the few-body Schrödinger equation. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we added detailed calculations for the critical screening length and the critical exponents for the Yukawa potential.

Angle-resolved Auger and valence photoelectron spectra of HCl were measured over a 14-eV-wide photon-energy range across the Cl $2p$ ionization thresholds. Auger decay spectra of dissociative core-excited states were observed to change with photon energy, reflecting a change in the rate of dissociation. Auger electron spectra at the first Rydberg states were analyzed and the evolution of the resonant Auger to the normal Auger decay distorted by postcollision interaction was examined. Valence photoionization channels were shown to resonate strongly at the photon energies of the core-to-Rydberg excitations. Angular distributions of the photo- and Auger electron lines were derived; strong fluctuations of the β values of the 2π photoline were observed at some Rydberg resonances. Anisotropy of the Auger decay at the ${\sigma }^{*}$ and Rydberg excitations was found to be different, with the latter showing uniformly negative β values.

We present accurate calculations for the single and double photoionization of helium from the threshold to the high-energy limit. At low and intermediate energies, we use the ab initio hyperspherical close-coupling method, which is extended up to 1 keV by introducing an energy-dependent reaction region. At high energies we employ an accurate Hylleraas initial state and a 3$C$ correlated final-state wave function. The 3$C$ wave function is shown to be correct to leading order in $Z/k.\mathrm{}$ We find good agreement with recent experiments over the entire energy range. The two calculations merge at $\sim 1\mathrm{keV}$ to within 5%.

Tunable infrared laser spectroscopy of ${\mathrm{Al}}^{-}{(3p}^2{}^3{P}_J)$ has yielded an improved value for the electron affinity of aluminum and experimental data on the previously unobserved fine structure of the ionic ground state. The electron affinity is determined to be $3491.0\left(4\right)\mathrm{}{\mathrm{cm}}^{\mathrm{-}1}$ [432.83(5) meV], and the $J=0-1\mathrm{}$ and $J=1-2\mathrm{}$ splittings are found to be 22.7(3) and $45.7\left(2\right)\mathrm{}{\mathrm{cm}}^{\mathrm{-}1},$ respectively. The result for the electron affinity is in substantial disagreement with a very recent experimental investigation. Our work also indicates that isoelectronic extrapolations for the ionic fine structure were accurate within uncertainties, and is in good agreement with recent calculations of the electron affinity.

We use a full coupled-channels method to calculate collisional properties of magnetically or optically trapped ultracold ${}^6\mathrm{Li}.$ The magnetic-field dependence of the $s$-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at $B=0.08\mathrm{}\mathrm{T}$ and $B=1.98\mathrm{}\mathrm{T}.$ We show that the exact coupled-channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.

We present direct experimental evidence for the localization of atoms cooled and trapped in a three- dimensional optical superlattice. As in the case of solid-state superlattices, we are able to tailor the characteristics of the optical potential wells. In particular, we impose a long-range modulation to the depth of the potential wells whose size remains in the optical wavelength range. The cooling mechanism in this configuration accumulates the atoms in the deepest wells. Images of the resulting separated denser atomic planes (distance $\simeq 70$ $\mu \mathrm{m}$) have been obtained both by detecting the fluorescence and by observing the shadow of the cloud.

The ability to support metastable current-carrying states in multiply connected settings is one of the prime signatures of superfluidity. Such states are investigated theoretically for the case of trapped Bose condensed alkali-metal gases, particularly with regard to the rate at which they decay via thermal fluctuations. The lifetimes of metastable currents can be either longer or shorter than experimental time scales. A scheme for the experimental detection of metastable states is sketched.

We present a theoretical study of dissociative photoionization of H${}_2$ and D${}_2$, with emphasis on resonant effects through intermediate doubly excited states. The theory coherently includes competition between the different dissociation and ionization channels, and makes use of $B$-spline functions to represent both the electronic and nuclear motions. We show that strong interference effects between resonant and nonresonant amplitudes are responsible for unidentified peaks observed in recent experimenal works, and that, for photon energies smaller than 28 eV, the various peaks can be explained in terms of a single ${}^1{\Sigma }_u^{+}$ doubly excited state.

We consider a separable approximation to the Schrödinger equation for the three-body Coulomb problem and found its exact solution above the ionization threshold. This wave function accounts for different possible asymptotic behaviors and reduces to the well-known product of three two-body Coulomb waves (C3) for scattering conditions. The momenta and position-dependent modifications recently proposed for the Sommerfeld parameters, as an improvement to the C3 model, are analyzed. We show how these changes can be included in our model as a suitable physically based variations in the separable approximation for the wave equation.

Dissociation cross sections of H${}_2$ for high-energy electron impact (100–1000 eV) producing $H\left(1s\right)\mathrm{}$, $H\left(2s\right)\mathrm{}$, and $H\left(2p\right)\mathrm{}$ for excitation from the ground vibrational state $\mathrm{}(v=0\mathrm{})\mathrm{}$ to the continuum of the $B^1{\Sigma }_u^{+}$, $B^{\prime }{}^1{\Sigma }_u^{+}$, and $C{}^1{\Pi }_u$ states were computed in the first Born approximation. Configuration-interaction electronic wave functions were used and vibrational degrees of freedom taken in account. The dissociative excitation cross sections as a function of the continuum energy for each final state were presented, and the accuracy of the wave function, including the importance of relaxation effects and the validity of the Franck-Condon approximation, is analyzed in comparison to available previous theoretical results. The computed dissociation cross sections were compared to experimental results making use of the separation of the various breakup channels proposed by Ajello, Shemansky, and James [Astrophys. J. 371, 422 (1991)]. The obtained cross sections to produce $\mathrm{H}\mathrm{}\left(2p\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ fragments via dissociative excitation to the $B$ and $C$ states have agreed well with the decomposed experimental results within the error bars. The dissociation cross sections to produce $\mathrm{H}\mathrm{}\left(2s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ through the $B^{\prime }$ state were in most cases somewhat larger than the reported experimental error bars. In the most favorable case our theoretical $B^{\prime }$ dissociation cross section was 3.1% within the reported error bar at 300 eV electron impact energy. A possible experimental reason for this discrepancy was raised.

We have developed a simplified relativistic configuration-interaction method to calculate the dielectronic recombination (DR) cross sections and rate coefficients. In this method, the infinite resonant doubly excited states can be treated conveniently in the framework of quantum defect theory. Here we report a systematic study of DR rate coefficients of hydrogenlike isoelectronic sequence with atomic number $2<~Z<~79.$ The behavior of the DR rate coefficients along the isoelectronic sequence is studied. The results are compared with the Burgess formula and other theoretical works. Because of its relativistic treatment, our method can be applicable for arbitrary $Z$ ions and the validity of the widely used Burgess formula can be examined, e.g., for the ion with $Z>~36,$ the results calculated from Burgess formula would be larger by a factor of 2.

Positronium-formation cross sections from positron-hydrogen collisions are calculated by solving a set of close-coupled, time-dependent partial differential equations. These cross sections are determined by propagating a time-evolving wave packet on a two-dimensional radial lattice and then projecting the wave function onto the stationary states of the atom. Calculations are performed through $L=8\mathrm{}$ and are extrapolated for $L>~9$ at energies of 30, 40, and 50 eV. Using distorted-wave calculations to determine ionization cross sections at these higher energies, we are able to extract approximate positronium-formation cross sections from the transfer ionization cross sections. Comparisons are made with experiment.

Calculations of $1s$ electron inner-shell photoionization from the ${1s}^{2}2s{}^2{S}^e$ Li ground state have been performed using recent developments of the $R$-matrix code with a 19-term target representation for incident photon energies up to 130 eV. This photon energy range allows important resonances in the partial cross sections due to ${1snln}^{\prime }{l}^{\prime }$ autoionizing states to be obtained. Theoretical resonant results are compared with recent experimental measurements of Kiernan et al. [J. Phys. B 29, L181 (1996)] in the $1s2l$ threshold region. Partial cross sections, branching ratios, and asymmetry parameters are also compared outside the resonant energy range with previous theoretical results of Lisini, Burke, and Hibbert [J. Phys. B 23, 3767 (1990)], who used the $R$-matrix code with an 11-term target representation, as well as the corresponding experimental results of Ferret et al. [Phys. Rev. A 36, 3172 (1987)], Langer et al. [Phys. Rev. A 43, 1652 (1991)], and Cubaynes et al. (private communication).

A combined experimental and theoretical investigation of collision-induced dissociation (CID) of the quasi-one-electron system ${\mathrm{Na}}_2^{+}$ He at 80 eV center-of-mass energy is presented. This study, complemented by additional measurements with an ${\mathrm{H}}_2$ target, provides a detailed analysis of the competition between the two basic CID mechanisms: via excitation of electronic states of the ${\mathrm{Na}}_2^{+}$ molecular ion and via momentum transfer to one of the ${\mathrm{Na}}^{+}$ core. The experimental method is based on a combined coincidence and time-of-flight technique, resulting in a complete measurement of the velocity vectors of the two fragments and giving a full determination of the collision parameters. The theoretical analysis is based on the so-called nonadiabatic quantum molecular dynamics, developed recently. This theory treats self-consistently and simultaneously classical atomic motion and quantum electronic transitions in dynamical processes of atomic many-body systems using time-dependent density functional theory. It allows one to simulate the experiment in microscopic detail and, thus, provides a deep insight into the excitation and dissociation mechanism. The combined theoretical and experimental analysis can later be extended to more complex systems like larger molecules or clusters.

Total cross sections for electron scattering by ${\mathrm{CH}}_4$ molecules in the energy range 400–5000 eV have been measured with experimental errors of about 3%. The method was based on a transmission-beam technique, and a detailed error source analysis is included. Present results have been compared with available experimental and theoretical data. The dependence on electron energy of the total cross sections obtained shows an asymptotic behavior with increasing energies, in agreement with the Born-Bethe approximation. In addition, an analytical formula is provided to extrapolate total cross sections to higher energies. Finally, total cross-section values have been partitioned into elastic and inelastic (ionization and neutral dissociation) processes.