We use the convergent close-coupling formalism to calculate the double-to-single-photoionization cross-section ratio in helium for photon energies from threshold up to 400 eV. Our results for the velocity and acceleration forms of the electromagnetic interaction operator are very close, and lie in between the measurements of Dörner et al. [Phys. Rev. Lett. 76, 2654 (1996)] and Levin et al. [Phys. Rev. Lett. 76, 1220 (1996)].

The $R$ matrix with pseudostates method has been used to study $e^{-}$-He collisions at low and intermediate energies up to 80 eV. Since target correlation effects and target continuum states are both accurately represented by this method, the associated program package can now be used to obtain reliable results at intermediate energies for more complex atomic and ionic targets, which are urgently required in many applications.

We study the anomalous diffusion resulting from the standard map in the so-called accelerating state, and we observe that it is determined by unusually large times of sojourn of the classical trajectories in the fractal region at the border between the chaotic sea and the acceleration island. The quantum-mechanical breakdown of this property implies a coherence among so slightly different values of momentum as to become much more robust against environment fluctuations than the quantum localization corresponding to normal diffusion. © 1996 The American Physical Society.

An extension of Feynman’s rule, relating probability amplitudes and probabilities in two-photon interferometry, has been proposed recently [G. Jaeger et al., Phys. Rev. A 48, 1023 (1993)]. It would be interesting to analyze the validity of this rule in other physical situations not considered by these authors. In particular, we show in this paper that the extended rule cannot be applied to the gedanken two-slit experiment. This result suggests the existence of two quantum regimes, differentiated by the validity of the generalized rule. The distinguishability of one particle and the visibilities of one-particle and two-particle interferences are calculated. © 1996 The American Physical Society.

While both diamagnetic and Stark spectra of hydrogen can be analyzed accurately in terms of classical orbits, in nonhydrogenic atoms the multielectron core induces additional spectral modulations that cannot be analyzed reliably in terms of standard periodic orbit-type theories. However, by extending closed-orbit theory to include core-scattered waves consistently, both diamagnetic and Stark photoabsorption spectra of nonhydrogenic Rydberg atoms at constant scaled energy can be analyzed semiclassically using only the closed orbits of the corresponding hydrogenic systems. Frequencies and amplitudes of the core-scattered modulations, as well as corrected amplitudes for contributions from repetitions of primitive hydrogenic orbits, are found to be in excellent agreement with quantum results. We consider whether these nonhydrogenic systems correspond to quantum chaos. © 1996 The American Physical Society.

We discuss the advantages of using the approximate quantum Fourier transform (AQFT) in algorithms which involve periodicity estimations. We analyze quantum networks performing AQFT in the presence of decoherence and show that extensive approximations can be made before the accuracy of AQFT (as compared with regular quantum Fourier transform) is compromised. We show that for some computations an approximation may imply a better performance. © 1996 The American Physical Society.

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most difficult (time and space consuming) part of Shor’s quantum factorizing algorithm. We show that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorized. © 1996 The American Physical Society.

We develop a transformation theory in quantum physics, where the transformation operators, defined in the infinite-dimensional Hilbert space, have right-unitary inverses only. Through several theorems, we discuss the properties of state space of such operators. As one application of the right-unitary transformation (RUT), we show that using the RUT method, we can solve exactly various interactions of many-level atoms with quantized radiation fields, where the energy of atoms can be two levels, three levels in Λ, V, and ≡ configurations, and up to higher (>3) levels. These interactions have wide applications in atomic physics, quantum optics, and quantum electronics. In this paper, we focus on two typical systems: one is a two-level generalized Jaynes-Cummings model, where the cavity field varies with the external source; the other one is the interaction of a three-level atom with quantized radiation fields, where the atoms have Λ-configuration energy levels, and the radiation fields are one-mode or two-mode cavities. © 1996 The American Physical Society.

A general approach to Bell-type inequalities for trichotomic observables is presented. With this formalism, which explicitly includes no-counts events, we show that the limits of all Bell-type inequalities are functions of the supplementary assumptions. This approach enables us to include in the causal and local theory the same assumptions used in the quantum-mechanical analysis of an experiment, and to deduce the inequality that must be satisfied by any local realistic model incorporating these assumptions. We prove that, using the quantum-mechanical assumption of ‘‘random nondetection’’ in the causal and local approach, a generalized Bell-type inequality is deduced whose upper limit can be violated by the quantum-mechanical predictions for symmetrical experimental setups involving detectors with quantum efficiency greater than 0.811. © 1996 The American Physical Society.

An effort is continued to define quantum probabilities for continuous histories. The sum-over-paths approach used in Prog. Theor. Phys. 87, 77 (1992) is critically reviewed, improved, and applied again. Consistency between wave nature and particle nature is the criterion used to judge the definability of the probabilities and is formulated as the path classifiability condition (C1) and the no-interference condition (C2). A set of classes of histories satisfying these two conditions is considered as a space-time analog of observables. In particular, Feynman’s paths for a nonrelativistic particle are considered as histories and the definability of probabilities for classes of paths is investigated, where classes are defined by classifying paths according to their behavior with respect to a rectangular space-time region Ω≡ΔX×ΔT. Confining ourselves to cases where C1 is satisfied, we examine C2 for some sets of classes of paths. Although C2 does not hold in general, some examples are found where C2 holds. In all the examples, the initial wave function is restricted. In some examples, the location of Ω and/or the potential in the region also affect the success of C2. Due to these restrictions, the resultant probabilities for classes of paths take reasonable values. A puzzling example in which probabilities cannot be defined for histories contrary to intuition is resolved by considering an appropriate coarse graining of classes of paths. Considering a rectangular potential barrier, we show that the reflection and the transmission probabilities are special cases of probabilities for histories, and also that probability densities of transmission and reflection times cannot be defined. This study may be taken to be a study of the consistent-histories approach not with discrete histories defined by products of projection operators but with continuous histories defined by Feynman’s paths in configuration space. © 1996 American Institute of Physics.

Potential curves of the ${\mathrm{K}}_2$ and NaK molecules have been computed in the framework of pseudopotential methods, over a wide range of interatomic distances. At short internuclear distances, the agreement with experimental data is excellent, the mean deviation between theoretical and experimental spectroscopic constants being 1% for the two alkali dimers. At large interatomic separation, wells and avoided crossings are observed in adiabatic potential curves of highly excited states correlated to the asymptotes close to K[4p]+K[4p] and Na[3p]+K[4p]. For example, the well depths of the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states reach 2650 ${\mathrm{cm}}^{\mathrm{-}1}$ for ${\mathrm{K}}_2$ and 4330 ${\mathrm{cm}}^{\mathrm{-}1}$ in the case of NaK. We demonstrate that they correspond to pseudocrossings between covalent states (dissociating into K[nl]+K[n′l′] or Na[nl]+K[n′l′]) and ionic states (correlated to ${\mathrm{K}}^{+}$+${\mathrm{K}}^{\mathrm{-}}$ for ${\mathrm{K}}_2$, ${\mathrm{Na}}^{+}$+${\mathrm{K}}^{\mathrm{-}}$, or ${\mathrm{Na}}^{\mathrm{-}}$+${\mathrm{K}}^{+}$ for NaK, the negative ion being in the ground state or an autoionizing state). As for ${\mathrm{Na}}_2$, these structures may play a crucial role in the interpretation of low-energy collisions. © 1996 The American Physical Society.

We present comprehensive calculations of the electronic structure of selected first-row atoms in uniform magnetic fields of strength ≤${10}^{10}$ G, within a flexible implementation of the Hartree-Fock formalism. Ground-state and low-lying excited state properties are presented for first-row atoms He, Li, C, and ion ${\mathrm{H}}^{\mathrm{-}}$. We predict and describe a series of ground-state quantum transitions as a function of magnetic field strength. Due to its astrophysical importance, highly excited states of neutral He are also computed. Comparisons are made with previous works, where available. © 1996 The American Physical Society.

The K${\mathrm{\beta }}_2$ x-ray spectra of zirconium, niobium, molybdenum, and palladium bombarded by 150 and 300 keV electrons were measured with a high-resolution transmission curved crystal spectrometer. Multiconfiguration Dirac-Fock calculations were used for the decomposition of the experimental spectra into the K${\mathrm{\beta }}_2$${\mathit{M}}^0$ (diagram) and K${\mathrm{\beta }}_2$${\mathit{M}}^1$ (satellite) components. The probabilities of energy dependent (direct Coulomb and two-step) processes were estimated from the differences in the satellite line yields for electrons and photons. The satellite yields are found to be considerably enhanced in comparison with those for the proton-induced ionization recently measured and analyzed in the same way [T. Ludziejewski et al., Phys. Rev. A 52, 2791 (1995)]. This result indicates the importance of multielectron effects in the K plus M shell ionization by energetic projectiles. © 1996 The American Physical Society.

We develop a model for the lowest optically allowed excited states of molecules in which the basic orbital structure consists of a rigid skeleton of localized bonding electrons, and mobile electrons that participate in bonds between like atoms. (For aromatic molecules this is the σ-π separability principle.) We demonstrate via fully interacting tight-binding calculations that for such molecules the optically allowed excited states involve linear combinations of states with at least one set of paired electrons and one vacant site. These pairing effects, which are strongly influenced by electron-electron interactions, have a dramatic effect on the optical spectrum because of a symmetry property of the dipole operator. We employ a model consisting of a particle and a hole on the molecule, corresponding to the paired and empty site, which interact via a repulsive on-site pseudopotential. This produces states with small probability for particle-hole pairing and therefore mimics the excited states accurately. The model is applied to real systems and excellent agreement with experiment is found. © 1996 The American Physical Society.

We show in this paper that the use of an extended coupled-cluster functional leads to a more desirable stationary-response formulation for molecular properties than that obtained by the use of an expectation-value functional. We make a detailed formal and numerical analysis of relative suitability of both the functionals. In particular, we investigate the extent of size-separation error using a truncated expectation-value functional and examine the relative accuracy and convergence of the two functionals in extracting molecular properties. We have also compared the results obtained by the use of these two functionals with the nonvariational coupled-cluster results. © 1996 The American Physical Society.

The conjecture by Collins that the correlation energy ${\mathit{E}}_{\mathrm{corr}}$ is proportional to the information entropy as defined by Jaynes is examined. We present numerical evidence supporting this conjecture by computing atomic information entropies from highly correlated wave functions of configuration-interaction (CI) type for members of the lithium isoelectronic series. Sequences of increasingly larger basis sets are used to show how ${\mathit{E}}_{\mathrm{corr}}^{\mathrm{CI}}$ (CI correlation energy) is related to ${\mathit{S}}_{\mathrm{Jaynes}}$. © 1996 The American Physical Society.

Explicit segment level formulas (in terms of 3-j and 6-j symbols) for the matrix elements of a symmetrized combination of two U(2n) generators (also known as a two-electron spin-orbital replacement operator) are derived in a spin-orbital basis. [A basis symmetry adapted to the subgroup U(n)×U(2) of U(2n).] The matrix elements of a single U(2n) generator are also determined. Using the above-mentioned matrix elements, all the spin-dependent terms of the Pauli-Breit Hamiltonian can be included into quantum chemistry calculations. The matrix elements are evaluated by first expressing the spin-orbital states as Yamanouchi-Kotani states and then applying a graphical form of Wick’s theorem and the graphical method of spin algebras. © 1996 The American Physical Society.

Application of the perturbation expansion of the variational principle of energy in density-functional theory is demonstrated by calculating the static dipole polarizability α and second hyperpolarizability γ of the two-electron systems ${\mathrm{H}}^{\mathrm{-}}$, He, and ${\mathrm{Li}}^{+}$. Calculations are performed within both Hartree-Fock and density-functional theories. In the approach employed, energy change at each order (second and fourth in our case) is minimized so that no electric field needs to be applied explicitly. This makes the calculation very accurate. Significantly, Hartree-Fock results obtained by us, to our knowledge, are larger (and therefore closer to experiments) than those reported in the literature calculated by the finite field method, and also by other methods. © 1996 The American Physical Society.

An exact solution describing the quantum states of a hydrogen atom in a homogeneous magnetic field of arbitrary strength is obtained in the form of a power series in the radial variable with coefficients being polynomials in the sine of the polar angle. Energy levels and wave functions for the ground state and for several excited states are calculated exactly for the magnetic field varying in the range 0<B/(${\mathit{m}}^2$${\mathit{e}}^3$c/${\mathrm{ħ}}^3$)≤4000. © 1996 The American Physical Society.

Applying femtosecond pump-probe spectroscopy, we investigated via three-photon ionization (3PI) and high mass selection the vibrational dynamics of the potassium dimer’s electronic ${\mathit{A}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ state separately for two of its isotopoes, ${}_{}{}^{39,39}{}_{}{}^{}\mathrm{K}_2^{}{}_{}{}^{}$ and ${}_{}{}^{39,41}{}_{}{}^{}\mathrm{K}_2^{}{}_{}{}^{}$. The fast oscillation with ${\mathit{T}}_{\mathit{A}}$=500 fs, observed for both isotopes, reflects the wave-packet propagation prepared on the potential-energy surface of the A state. The long-time dynamics, however, of the isotopes is totally different. While for ${}_{}{}^{39,39}{}_{}{}^{}\mathrm{K}_2^{}{}_{}{}^{}$ a beat structure with ${\mathit{T}}_{\mathrm{BS}}$=10 ps is superimposed, for ${}_{}{}^{39,41}{}_{}{}^{}\mathrm{K}_2^{}{}_{}{}^{}$ a rather fast decay and revivals at 38 ps, 60 ps, and 82 ps could be resolved. A detailed Fourier analysis of the 200-ps scans with a resolution of 0.1 ${\mathrm{cm}}^{\mathrm{-}1}$ enables the identification of the excited vibrational levels of the A state in detail, including their energetic shifts due to spin-orbit coupling with the crossing ${\mathit{b}}^3$${\mathrm{\Pi }}_{\mathit{u}}$ state. Theoretical simulations of the pump-probe spectra on the basis of fully quantum-dynamical calculations reproduce well the experimental data. The reason for the slight differences can be identified as deviations between the real potential-energy surfaces and the ab initio data, used for the simulations and demonstrates the very high sensitivity of the femtosecond spectroscopy to investigate vibrational states and their perturbation. Furthermore, the theoretical investigations reveal the details of the ultrafast intersystem crossing process in real time. © 1996 The American Physical Society.