We show that various experimental configurations using correlated photon-number states are predicted to violate many forms of Bell’s inequality. This test is potentially one of macroscopic quantum mechanics in that violations are predicted for situations where large numbers of photons are detected at a single detector at a time. The configurations also allow higher-spin tests of quantum mechanics. We indicate how the violations of Bell inequalities might be achieved with both parametric amplification and parametric oscillation. The effect of photodetection inefficiencies is analyzed. In order to investigate the potential for Bell-inequality tests in the high-intensity regime of recent experiments where detection efficiencies may be very high, we introduce a simple model for the effect of electronic noise that introduces a poor resolution of the photon number detected.

Using the Shannon information theory and the Bayesian methodology for inverting quantum data [K. R. W. Jones, Ann. Phys. (N.Y.) 207, 140 (1991)] we prove a fundamental bound upon the measurability of finite-dimensional quantum states. To do so we imagine a thought experiment for the quantum communication of a pure state ψ, known to one experimenter, to his colleague via the transmission of N identical copies of it in the limit of zero temperature. Initial information available to the second experimenter is merely that of the allowed manifold of superpositions upon which the chosen ψ may lie. Her efforts to determine it, in an optimal way, subject to the fundamental constraints imposed by quantum noise, define a statistical uncertainty principle. This limits the accuracy with which ψ can be measured according to the number N of transmitted copies. The general result is illustrated in the physically realizable case of polarized photons.

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable system a deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite-dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrödinger equation. Applications to the harmonic oscillator in a flat space and in a curved space with constant curvature, the Kepler problem in a flat or curved space, the Fokas-Lagerstrom potential, the Smorodinsky-Winternitz potential, and the Holt potential are given. The method shows how quantum-algebraic techniques can simplify the study of quantum superintegrable systems, especially in higher dimensions.

Spectra of laser-produced plasmas of the elements from tin to iodine contain weak bands of quasicontinuum overlaid by weak emission lines in the 70–120-Å region. Multiconfiguration-Dirac-Fock calculations show that these features are consistent with theoretical spectra for 4${\mathit{d}}^{\mathit{N}\mathrm{-}}$4${\mathit{d}}^{\mathit{N}\mathrm{-}1}$(5f+6p) transitions in a number of adjacent ion stages which are predicted to produce unresolved transition arrays (UTA) in this spectral region. Moreover, the calculations predict a gradual decrease of 4d-5f oscillator strength with increasing ionization up to the eleventh spectrum where Jgf(4d-5f)≊0. However, inclusion of configuration interaction effects between the 4${\mathit{d}}^9$nf levels showed that 4${\mathit{d}}^9$4f and 4${\mathit{d}}^9$5f mixing shifts this minimum to the thirteenth spectrum. The theoretical data were then parametrized within the UTA formalism and the different order moments corresponding to weighted mean energy, variance, and skewness coefficient evaluated.

Fluorescence and excitation spectra arising from transitions between excited states of the HgCd exciplex molecule were produced in a mixture of Hg and Cd vapors following pump-and-probe laser excitation. The vapor mixture, contained in a sealed quartz cell, was irradiated by pulsed pump (3261 Å) and probe (4300–4750 Å) laser beams, delayed by 450 ns relative to one another. The fluorescence bands were recorded with a monochromator, a photomultiplier, and a digitizing oscilloscope controlled by a microcomputer. In addition to the previously reported and analyzed ‘‘blue-band’’ fluorescence that can be excited with a single laser, we observed short-lived and structured fluorescence bands as well as the corresponding excitation bands in the blue spectral region, which we assigned to transitions between specific states of HgCd. An analysis of the bands yielded the vibrational constants for some of the states, as well as their relative internuclear equilibrium separations. These results provide an initial basis for the draft of a partial potential-energy diagram consisting of spin-orbit states correlated to the 5 ${}_{}{}^3{}_{}{}^{}$P manifold in Cd.

The soft-x-ray uranium emission in the 60–200-Å range recorded from a high-temperature (∼1 keV) low-density (∼${10}^{13}$ ${\mathrm{cm}}^{\mathrm{-}3}$) tokamak plasma has been analyzed by comparison with theoretical level structure and line-intensity calculations. In an extension of previous work [Finkenthal et al., Phys. Rev. A 45, 5846 (1992)], theoretical U xxv, U xxx, U xxxi, and U xxxii n=5 to n=5 spectra have been computed for the relevant plasma parameters. Fully relativistic parametric potential computer codes have been used for the ab initio atomic-structure calculations, and electron-impact excitation rates have been computed in the distorted-wave approximation. 5s-5p spectral lines and quasicontinua of U xxx, U xxxi, and U xxxii are identified in the 165–200-Å wavelength band. An unambiguous line identification is hampered by theoretical uncertainties and the blending of emission from adjacent charge states.

We propose a theoretical frame to handle trapping problems in phase-modulation fluorometry. Applying operator manipulations, we arrive at a ‘‘perturbation’’ expansion in a straightforward and systematic manner. Furthermore, we show that the numerical implementation of this approach can be enhanced by the reduction technique. Following this approach, we carry out some numerical investigations and the results appear to be instructive. Finally, we point out how to generalize the method to the cases of several fluorescence species and differential phase fluorometry.

In analogy to the local-density approximation of the density functional, a transfer of electron correlation from the homogeneous electron gas to inhomogeneous systems is realized through a density-dependent Jastrow factor. This approach enables a strictly variational treatment with respect to the inhomogeneous systems. We have adjusted the density-dependent Jastrow factor on the basis of electron-gas Jastrow factors, determined within a Fermi hypernetted-chain approximation. We applied it to the isoelectronic series He to ${\mathrm{Ne}}^{8+}$ where 83–90 % of the correlation energy was recovered, taking into account a supplementary density-dependent one-particle Jastrow factor, which allowed an approximate conservation of the Hartree-Fock density. Within our simple application we are able to describe the electron correlation of different systems by means of a single Jastrow factor, which depends on the interelectronic distance and the electron densities at the positions of the electrons.

In order to analyze the differential correlation energies among the lowest ${}_{}{}^2{}_{}{}^{}$S(4${\mathit{s}}^1$), ${}_{}{}^2{}_{}{}^{}$D(3${\mathit{d}}^1$), and ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$(4${\mathit{p}}^1$) states of ${\mathrm{Ca}}^{+}$, configuration-interaction calculations have been carried out for the three states. The results reveal that the ${}_{}{}^2{}_{}{}^{}$D state has a larger core-valence correlation energy by 0.66 and 0.91 eV and a smaller core-core correlation energy by 0.38 and 0.39 eV than the ${}_{}{}^2{}_{}{}^{}$S and ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ states, respectively. Based on an analysis of the computed correlation energies in terms of contributions by various excitation types, the differential core-core correlation energy is interpreted as the difference in the contribution from the 3${\mathit{p}}^2$→dd’ excitation between the ${}_{}{}^2{}_{}{}^{}$D state and the others. The 3s intrashell correlation energies as well as the 3s-3p intershell correlation energies are uniformly equal among the three states.

We find the unitary operator for diagonalizing the Hamiltonian of a triatomic linear molecule. The unitary operator is expressed in a coordinate representation that brings convenience for deriving the density matrix ρ(${\mathrm{x}}_1$,${\mathrm{x}}_2$,${\mathrm{x}}_3$;${\mathrm{x}}_1^{\prime }$,${\mathrm{x}}_2^{\prime }$,${\mathrm{x}}_3^{\prime }$,β). The unitary transformation approach is simple because the derivation can be reduced to the calculation of two independent harmonic-oscillator density matrices and one free-particle density matrix. The average of the potential energy and the kinetic of the molecule is calculated by using the density matrix.

It is shown that a time-dependent external four-vector potential ${\mathit{a}}_{\mathrm{\mu }}^{\mathrm{ext}}$(r→t) and a conserved external four-current ${\mathit{j}}_{\mathrm{\mu }}^{\mathrm{ext}}$(r→t), with a given fixed initial state of the combined condensed-matter–electromagnetic system, lead, respectively, to a conserved self-consistent four-current density ${\mathit{J}}_{\mathrm{\mu }}$(r→t) and a self-consistent four-vector field ${\mathit{A}}_{\mathrm{\mu }}$(r→t), such that a map (${\mathit{a}}_{\mathrm{\mu }}^{\mathrm{ext}}$,${\mathit{j}}_{\mathrm{\mu }}^{\mathrm{ext}}$)→(${\mathit{J}}_{\mathrm{\mu }}$,${\mathit{A}}_{\mathrm{\mu }}$) is invertible under certain simple conditions. With this as a basis, the stationary action principle is used to derive the self-consistent equations for the electron and the electromagnetic fields appropriate for a description of the combined condensed-matter and electrodynamic systems, where real or virtual pair creation is ignored.

The gradient-free correlation functional derived in a previous work [E. I. Proynov and D. R. Salahub, Phys. Rev. B 49, 7874 (1993)] is combined with two different exchange counterparts—the standard local-spin-density (LSD) exchange and a modified LSD exchange derived in the spirit of the local thermodynamic approach in density-functional theory (DFT). These exchange-correlation schemes are tested on a set of small molecules. The obtained binding energies are on average comparable to those of the gradient-corrected ones used currently in the DFT code demon. The equilibrium geometries produced by our functionals are superior and on average very close to the experimental ones. The required computer time is comparable to that of the Vosko, Wilk, and Nusair LSD scheme [Can. J. Phys. 58, 1200 (1980)].

The excited electronic states with the magnetic quantum numbers 4≤‖m‖≤10 of the hydrogen molecular ion are investigated. In the field-free case the lowest electronic states with ‖m‖≥5 possess purely repulsive potential-energy curves and are, therefore, unbound. In the presence of a strong magnetic field the shape of these electronic states changes drastically. For parallel internuclear and magnetic-field axes we observe well-pronounced potential wells that contain many vibrational states; the corresponding electronic states are, therefore, strongly bound. The coupling of the electronic degrees of freedom to the ionic center-of-mass motion is estimated.

There is a class of quadruply excited states of ${}_{}{}^5{}_{}{}^{}$${\mathit{S}}^{\mathit{o}}$ symmetry where electronic motion is highly correlated and where the electrons tend to form a tetrahedron as the excitation energy increases toward the four-electron ionization threshold. This conclusion has been reached following ab initio state-specific calculations in Be, for the lowest energy state of each intrashall manifold n, of the energies, the average radii ${\mathit{r}}_{\mathit{n}}$, and the average interelectronic angle ${\mathrm{\theta }}_{12}$. In order to calculate ${\mathrm{\theta }}_{12}$, a general theory is developed, applicable to arbitrary N-electron atomic states. The value of ${\mathrm{\theta }}_{12}$ is straightforward to compute, and is given from a prescription transforming the expression for the two-electron interaction energy of the state to a formula for the probability density of cos${\mathrm{\theta }}_{12}$. The state-specific calculations for each n, up to n=6, were done by the multiconfigurational Hartree-Fock method where all configurations with ${\mathit{n}}_1$=${\mathit{n}}_2$=${\mathit{n}}_3$=${\mathit{n}}_4$ are included. For n=3, the main configuration 3s3${\mathit{p}}^3$ has a weight of 0.90 while ${\mathrm{\theta }}_{12}$=103.3°. As n increases, electron correlation increases relative to the Coulomb nuclear attraction. With increasing degeneracy, many configurations with high orbital angular momenta mix heavily, and ${\mathrm{\theta }}_{12}$ increases.

For example, for n=6, the 6s6${\mathit{p}}^3$ configuration has a weight of only 0.59 and ${\mathrm{\theta }}_{12}$=106°. In this case, doubly, triply, as well as quadruply excited configurations with respect to ${\mathit{nsnp}}^3$ contribute to the wave function significantly. Finally, these four-electron ionization ladder states have a simple energy spectrum, given to a very good approximation by ${\mathit{E}}_{\mathit{n}}$=-A’/${\mathit{n}}^2$ (${\mathit{n}}^{1/2}$∼${\mathit{r}}_{\mathit{n}}$), where A’ is a constant. In conjunction with our earlier results on the geometry and the spectra of special classes of doubly and triply excited states, this finding leads to the conclusion that for highly correlated electronic motion the spectrum is dictated essentially by one dynamical variable, the average radius from the nucleus.

The survival probability P(t) of hydrogenic wave packets for some choices of strong external electric and magnetic fields is studied. The recursive residue generation method, in combination with complex dilation and a Laguerre basis, is used to calculate the local density of states from which P(t) is computed via a Fourier transform. P(t) is calculated both for a single initial ‖8p0〉 state and for an initial radial hydrogenic wave packet centered around n=15. In the first case only, in principle, a single n manifold is involved in the dynamics, while in the latter case several n manifolds contribute. The different choices of initial states lead to significantly different results. The choice of fields was made in order to exemplify various patterns of behavior. Results similar to those obtained here were found in recent experiments by Broers and co-workers [Phys. Rev. Lett. 71, 344 (1993); Phys. Rev. A 49, 2498 (1994)]. The results presented in this work are quantum-mechanical calculations of hydrogenic wave packets in strong fields that include the effect of finite lifetimes on P(t).

The energies of the bound states and energies and widths of autoionizing resonant states of helium are calculated within the s-wave model, where the individual orbital angular momenta of both electrons are zero. The energies of the bound 1sns states differ from the corresponding energies in real helium only via a small n-independent shift Δμ in the quantum defects, which amounts to Δμ=0.011 for singlet states and Δμ=0.004 for triplet states. The quantum defects of more than 50 bound and resonant states with singlet or triplet symmetry are reproduced by an empirical four-parameter formula to within an rms deviation of less than 0.016. The normalized widths of the autoionizing Nsns resonant states increase with the smaller quantum number N, and the widths of the singlet states tend to become larger than the separation of successive resonances in the Rydberg series for N≊8. Effects of interference of Rydberg series can be described in the framework of multichannel quantum-defect theory. In the 7sns singlet series of resonances, interference due to the 8s8s perturber inhibits autoionization by more than three powers of 10. Semiclassical quantization based on unstable periodic orbits reproduces the energies of states with equal or similar quantum numbers rather well in a standard application of the cycle-expansion technique and very well in an application using only three nonretracing periodic orbits.

The isotope shift for the Zeeman ${\mathit{g}}_{\mathit{J}}$-factor ratio, including relativistic corrections of orders ${\mathrm{\alpha }}^2$, ${\mathrm{\alpha }}^2$m/M, and ${\mathrm{\alpha }}^3$, is calculated to high precision using variational wave functions. The finite-mass corrections coming from the mass scaling and from the mass polarization term are treated exactly. The result is ${\mathit{g}}_{\mathit{J}}$${(}^3$He, 2 ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$)/${\mathrm{g}}_{\mathrm{G}}$${(}^4$He, 2 ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$)=1+2.708 439 694 74(76)×${10}^{\mathrm{-}9}$. Our calculation significantly improves the previous theoretical prediction of Barkley and Hegstrom [Phys. Rev. A 14, 1574 (1976)] for this isotope shift.

P-odd and P,T-odd transition amplitudes for the two almost degenerate levels of opposite parity with J=10 and E=19 797.96 ${\mathrm{cm}}^{\mathrm{-}1}$ are calculated. Our result for the P-odd amplitude of the interaction with the weak charge of the nucleus is (70±40)(-i) Hz. The P,T-odd amplitude caused by the electric dipole moment of the electron ${\mathit{d}}_{\mathit{e}}$ is (1.2±0.5)×${10}^{23}$ Hz/(e cm). We also calculated g factors and hyperfine constants A and B for several levels. These results are in good agreement with experiment. The calculated lifetime of 6 μsec for the positive parity level is reasonably close to 8 μsec measured by D. Budker et al. [Phys. Rev. Lett. 70, 3019 (1993)].

The energies and wave functions of the Be-like 1${\mathit{s}}^2$2snp (n=2,3) ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ and ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,1,0}^{\mathit{o}}$ states are calculated with a full-core plus correlation method for ions from B ii to Ne vii, Mg ix, and Si xi . The relativistic corrections and fine structures are calculated with the first-order perturbation theory. Higher-order effects are estimated. The calculated excitation energies (relative to the 1${\mathit{s}}^2$2${\mathit{s}}^2$ ground state) are compared with the experiment. Intermediate coupling between the ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ states is also considered. Most of the predicted ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{\mathit{J}}^{\mathit{o}}$ energies agree with the experiment to within a few ${\mathrm{cm}}^{\mathrm{-}1}$. The fine-structure splittings of the 1${\mathit{s}}^2$2s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,1,0}^{\mathit{o}}$ states calculated in this work all agree with the best experimental data in the literature. Our results show that for systems of Z≥9, it is critically important to consider intermediate coupling. For Si xi , it shifts the 2s2p ${}_{}{}^{3,1}{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ levels by 86 ${\mathrm{cm}}^{\mathrm{-}1}$ and the 2s3p ${}_{}{}^{3,1}{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ energies by 193 ${\mathrm{cm}}^{\mathrm{-}1}$. The predicted 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ energies are slightly higher than the experimental data; the discrepancy increases from 14 ${\mathrm{cm}}^{\mathrm{-}1}$ for Z=5 to 93 ${\mathrm{cm}}^{\mathrm{-}1}$ for Z=14.

Starting from very accurate many-body wave functions, we have constructed essentially exact densities, exchange-correlation potentials, and components of the total energy for helium and two-electron ions. These density-functional results are compared to the corresponding quantities obtained from a variety of commonly used approximate density functionals, namely, the local-density approximation and various generalized gradient approximations, in order to test the accuracy of the approximate functionals. Although the generalized gradient approximations yield improved energies compared to the local-density approximation, the exchange and correlation potentials (especially the latter) obtained from the generalized gradient approximations are in poor agreement with the corresponding exact potentials. The large-distance asymptotic behavior of the exact exchange-correlation potential to O(1/${\mathit{r}}^4$) is found to agree with theoretical predictions. The short-range behavior of the exchange-correlation potential is very close to quadratic. The prospects for improved generalized gradient approximations are discussed.