In Hartree-Fock theory, the exchange energy density can be expressed solely in terms of the first-order density matrix. Far from the nucleus of a closed-shell atom, idempotency of the density matrix yields the exchange energy density as the magnitude of the Coulomb energy $e^2$/r times the electron density ρ. Thus two lengths enter the asymptotic form in contrast to ${\rho }^{\mathrm{-}1/3}$ alone of local-density theory.

The near-threshold photoelectron spectrum in a resonant two-photon ionization process is investigated using a nonperturbative method. The hydrogen atom is represented by a realistic model including an infinite number of Rydberg states converging at the threshold. When the threshold is crossed a typical two-peak structure of the spectrum is modified by cutting off part of the spectrum which may include one or even two peaks.

In 1984 Aharonov and Casher proposed that a beam of neutral particles with magnetic dipole moments passing around opposite sides of a line charge will undergo a relative quantum phase shift. This is currently under experimental investigation. Aharonov and Casher claimed that the magnetic dipole particles should undergo the phase shift despite experiencing no classical force. They suggested that this new effect has a ‘‘duality’’ with the solenoid Aharonov-Bohm effect where charged particles passing around a magnetic solenoid experience a phase shift despite, it is claimed, experiencing no classical force. Here it is pointed out that a magnetic dipole particle passing a line charge does indeed experience a classical electromagnetic force in the usual electric-current model for a magnetic dipole. This force will produce a relative lag between dipoles passing on opposite sides of the line charge, and the classical lag then leads to a quantum phase shift in exact agreement with that calculated by Aharonov and Casher. Thus actually the proposed Aharonov-Casher effect has a transparent explanation as a classical lag effect. It is emphasized that the solenoid Aharonov-Bohm effect is currently the only phase-shift effect which cannot be explained in an obvious fashion as arising from a classical lag and it is again proposed that also this shift may actually involve a classical electromagnetic lag effect. A natural experimental consequence suggested by the lag point of view is the breakdown of the interference pattern when the lag becomes comparable to the wave-packet coherence length.

In recent predictions, metastable escape times $T_p$ over low (n-dimensional) barriers ΔΦ(μ) could show novel non-Arrhenius behavior, vanishing as a power of ΔΦ. Thus & as a control parameter μ approaches the spinodal limit ${\mu }_c$, where ΔΦ(μ=${\mu }_c$)=0. Monte Carlo simulations for the two-mode laser (n=4) are in excellent agreement with the predicted behavior of the mean first-passage time $T_p$. While the exponent prediction of ${\theta }_p$ is 2, the Monte Carlo simulations yield a value of ${\theta }_p$=2.007±0.008.

We discuss the thermodynamic phases and storage capacity of models which are extensions of the Hopfield-Little model of associative memory, generalized to allow for arbitrary polynomial Hamiltonians. The storage capacity increases as an exponential function of the highest power appearing in the polynomial Hamiltonian. We include the effects of replica symmetry breaking in our computations.

The process of laser-induced shock propagation was investigated for a number of double-layered plane targets with a one-dimensional Lagrangian hydrodynamic code using a realistic equation of state and experimentally reported laser absorption values. It was found that a suitably optimized layer of C${\mathrm{H}}_2$ on Pt can yield pressures in excess of 60 Mbar at its interface with a 1.06 μm, ${10}^{14}$ W/${\mathrm{cm}}^2$, 300-ps rise-time laser pulse. This should be the highest pressure that can be achieved in any single- or double-layered target with such a laser pulse. The scaling of this pressure with intensity is described by a power law having a higher exponent than usually found for any material. Suitable scaling is also investigated between the optimum thickness and peak pulse power. The results should help in designing experiments on any laser system.

The quasienergy spacing statistics of a particle in an infinite square well perturbed by a monochromatic external field is studied below and above nonlinear quantum resonance overlap. It is found that at small enough perturbations the quasienergies are accurately given by those obtained from a single resonance, integrable Hamiltonian. The quasienergy spacing distribution undergoes a transition from Poissonian toward Wigner-like behavior when quantum resonance zones overlap, indicating the destruction of a quantum local constant of motion.

Energy eigenvalues are obtained for the three-dimensional potential V(r)=(1/2[$r^2$+λ$r^2$/ (1+${\mathrm{gr}}^2$)], where λ and g are parameters, using the shifted-1/N-expansion method. Results are obtained for nine sets of $n_r$ and l values corresponding to n=0, 1, 2, 3, and 4. It is found that certain levels which are degenerate in the limit λ=0 do not remain so as λ increases. This splitting is studied as a function of g and of λ. It is also shown that with a negative λ, this potential gives a sequence for energy levels which is identical with that which occurs in the shell model of the nucleus.

This study concerns the determination of adiabatic electronic terms of $A^{\mathrm{*}}$-B systems where A is an atom whose spectral parameters are known from multichannel quantum-defect theory (MQDT) and B is a light rare-gas atom (He,Ne) in its ground state. The adiabatic terms are obtained as the roots of a transcendental equation for which the only required inputs are the MQDT parameters of A, the $e^{\mathrm{-}}$-B scattering s-wave phase shifts, and of course the internuclear distance R between the two atoms. The MQDT parameters of A are its eigenquantum defects and the unitary matrices relating the fragmentation channels to the short-range eigenchannels. It is found that for R (a.u.)≲2ν, ν being the effective principal quantum number relative to the highest ionization threshold involved in the MQDT analysis of A, the adiabatic spectra can be described by R-dependent Lu-Fano diagrams. The accuracy of this approximation increases as ν increases. Finally, some numerical results relative to the ${\mathrm{Ar}}^{\mathrm{*}}$-He system are presented and commented on.

Models are presented as examples in order to illustrate the previously proposed theory of measurement in quantum mechanics [R. Fukuda, Phys. Rev. A 35, 8 (1987)]. It is based on the specific structure of the Hilbert space of the macroscopic system. It is shown that after the interaction of an object with a detector we have to prepare the exponential of the extensive operators to recover the interference which is lost in the measuring process.

The frequency dependence of the hyperpolarizability (γ) of the nonrelativistic hydrogen atom is calculated for a range of third-order nonlinear optical processes using an expansion in Sturmian functions. It is shown that the quantitative relations between the various nonlinear optical processes are made much clearer when γ is treated as a function of an effective frequency ${\omega }_L$. The detailed, systematic exploration of the dispersion of γ of the hydrogen atom presented here should serve as a guide in the analysis and interpretation of experimental or theoretical results for less accessible systems.

To quantify the extent of validity of the molecular model of atoms with correlated electrons, we project well-converged configuration-interaction wave functions for doubly excited states of He and for bound states of alkaline-earth-metal atoms onto simple rotor-vibrator wave functions for the ‘‘linear triatomic molecule’’ e-core-e. The three independent vibrational frequencies and the equilibrium electron-nucleus separation are treated as parameters which are varied to maximize the overlap with the well-converged functions. For intrashell states, the overlaps with harmonic normal-mode functions are generally quite large, about 85–95 % for the alkaline-earth-metals, and the corresponding optimized parameters are in rough agreement with the energy-level separations. The overlaps are improved by using an anharmonic local-mode representation, particularly for intershell states (corresponding to excited stretching vibrations), though the optimized parameters appear to lose some of the consistency shown by those in the harmonic normal-mode representation. A comparison is made of plots of the conditional probability densities based on rotor-vibrator functions and on independent-particle functions with those based on accurate functions. This shows clearly the superiority of the molecular picture over the independent-particle picture as a zero-order model for intrashell states of two-electron atoms.

A relativistic virial theorem is used to construct a new optimization technique for the variational calculation of Dirac-Hartree-Fock energies in multielectron atomic systems. The method provides fast convergence and a natural criterion for the choice of the accuracy that should be required of the calculations.

We report the angle-dependent electron emission from the (2$s^2$${)\mathrm{}}^1$S, (2s2p${)\mathrm{}}^1$P, and (2$p^2$${)\mathrm{}}^1$D autoionizing states of helium, after excitation by 100-keV/amu ${\mathrm{Li}}^{+}$, ${\mathrm{Li}}^{2+}$, and 500-keV/amu ${\mathrm{He}}^{+}$, ${\mathrm{He}}^{2+}$, ${\mathrm{Li}}^{+}$, ${\mathrm{Li}}^{2+}$, and ${\mathrm{Li}}^{3+}$ ions. All of the peak profiles are strongly affected by the electron-ion interaction that occurs after ionization. A method that accounts for this post-collision interaction, and allows comparison with theoretical calculations, is presented, and some previously unexplained discrepancies between theoretical and experimental line profiles are resolved. The differently charged ions cause systematic changes in the observed line profiles. We report some projectile-charge-dependent emission intensities for the different peaks. Accurate energy differences between the excited states are reported.

The charge-exchange collision (at energies 80, 40, and 8 keV) between ${\mathrm{Ar}}^{8+}$ and He or ${\mathrm{H}}_2$ has been studied by vacuum ultraviolet spectroscopy (7.5–80 nm). Emission cross sections of the observed transitions have been measured. Absolute cross sections of the n and l projectile excited states formed by single-electron capture have been deduced. Comparison is made with theoretical prediction. Double-electron capture has also been observed and measured.

This paper reports measurements of absolute differential cross sections for elastic scattering of 0.5-, 1.5-, and 5.0-keV He atoms by Ne, Ar, Kr, and Xe at laboratory scattering angles between 0.05° and 0.5°. Comparisons are made between the measured differential cross sections and those calculated from various model potentials. These comparisons reveal the range of validity of potentials appearing in the literature and provide new information about the lower repulsive walls of the ground-state He–rare-gas interaction potentials.

The usual decomposition of the multichannel scattering matrix near an isolated, narrow resonance is given as a sum of a direct and resonant part. The direct part of the S matrix which describes the background scattering is regular and unitary. The resonant part features a pole at the complex resonance energy, and both its magnitude and phase change rapidly as the energy varies. Given the S matrix, it is often a cumbersome task to extract the resonance energy and partial widths from the usual decomposition. We propose a new decomposition (which is related to the usual one) that overcomes this difficulty. The new resonant part is a complete analog of the single-channel S matrix. Its magnitude is constant and its phase jumps by 2π as the energy passes through the resonance. The resonant time delays for each state-to-state transition are independent of the channel indices, and exhibit the same Lorentzian shape from which the resonance energy and total width are readily obtained. The square of the magnitude of the resonant S-matrix elements are the state-to-state transition probabilities of the resonant scattering and are expressed in terms of the channel partial widths. The applicability of the proposed decomposition is demonstrated in a coupled-channel study of multichannel resonances in H-CO collisions using a global ab initio potential-energy surface.

The electron-capture cross sections for ${\mathrm{H}}^{+}$ impact on H and ${\mathrm{H}}_2$ and the electron-loss cross sections for ${\mathrm{H}}^{\mathrm{-}}$ impact on H and ${\mathrm{H}}_2$ have been measured for projectile energies between 2.0 and 0.063 keV. Relative cross-section values for all these reactions were measured directly, and placed on an absolute scale by adopting a standard value of 6.95×${10}^{\mathrm{-}16}$ ${\mathrm{cm}}^2$ for the electron-capture cross section for ${\mathrm{H}}^{+}$+${\mathrm{H}}_2$ collisions at 2.0-keV ${\mathrm{H}}^{+}$ energy. A crossed-beam technique was used, and the reaction-product H atoms were measured by a secondary-electron-emission detector. The techniques used to make the measurements are described, and the results are compared with other experimental and theoretical data.

The electron-capture and electron-loss reactions for H impact on H and ${\mathrm{H}}_2$ have been examined for projectile energies between 2.0 and about 0.1 keV. Relative cross sections for these reactions were measured directly, and the data for H targets were placed on an absolute scale by normalizing to the available results for ${\mathrm{H}}_2$ targets. For the electron-capture (ion-pair formation) reaction, some new data are also reported here for ${\mathrm{H}}_2$ targets. The crossed-beam techniques used to accomplish the measurements are described, and the results are compared with other experimental and theoretical data where possible.

Rate constants for state changing in collisions of Rb(ns) Rydberg atoms (40≤n≤48) with HF molecules have been measured and have been calculated using a semiclassical approach. Agreement between the total rate constants measured experimentally and derived theoretically is very good. The results point to the near-resonant nature of n-changing collisions, but indicate that the rate constants for such reactions are less dependent on energy imbalance than suggested by calculations based on the impulse approximation.