The Casimir force between two dielectric slabs of finite thickness is calculated for the case of dissipative media. The medium is modeled as a continuous field of quantum harmonic oscillators interacting with the heat bath. The electromagnetic field inside and outside the cavity formed by the plates is found for the ground state of the coupled system, and its pressure is calculated. Two terms in the expression for the Casimir force are distinguished. One is the electromagnetic vacuum pressure, which is the only contribution in the case of lossless media. The other arises from the Langevin forces that appear together with the damping as the result of the interaction of atoms with the heat bath. It is shown that both contributions are necessary in order to arrive at a finite result.

The evolution of the quantum spectrum as the function of a control parameter can be mapped onto the molecular dynamics of a classical many-body system. This approach is used to study the parametric motion of energy levels in classically mostly regular and in mostly chaotic regimes. The parametric energy-level dynamics is described in terms of the velocity autocorrelation function and the friction kernel of a disordered many-body system. We show that the parametric dynamics is sensitively dependent on the underlying classical dynamics, and therefore provide new measures of quantum chaology. The transition from classically regular to chaotic motion manifests itself in the disappearance of parametric diffusion. Semiclassical arguments give analytic approximations for the spectrum of the velocity autocorrelation function, and these approximations are found to be consistent with numerical calculations for the vibronic motion of a triatomic molecule. We compare these autocorrelation functions with those found in gases, liquids, and glasses.

This paper examines momentum-space methods as a means of implementing a scattering-theoretic, long-time lemma on the extraction of sharp-energy S-matrix elements from a wave-packet description of collisions. In order to concentrate on the momentum space and computational aspects, the collision system studied is that of two particles; each has the mass of a nucleon. The formulation of the problem in momentum space avoids any spreading of the packets and allows for a straightforward analysis, which proceeds as follows. First, a time discretization is introduced, so that a conditionally stable, recursive, time-evolution scheme can be employed. The momentum dependence of the full wave packet is next expressed via an expansion in locally defined interpolating polynomials (here, piecewise quadratics), as in the finite-element method. Once the time evolution has progressed sufficiently, the S-matrix element S${\mathrm{̃}}_0$(q) can be extracted from the ratio of the qth momentum components of the full and free wave packets. It is essential here that the numerically propagated free wave packet be used in this ratio, since otherwise numerical errors induced in the full wave packet are not canceled, and ‖S${\mathrm{̃}}_0$(q)‖ can become as large as 2 or more. Wave packets with central momenta ${\mathit{q}}_0$ equal to 1, 2, and 4 ${\mathrm{fm}}^{\mathrm{-}1}$ (energies ranging from about 30 to 500 MeV) have been studied, and the behavior of the wave packets and S${\mathrm{̃}}_0$(q) for several time intervals, extraction times, numbers of mesh points, etc., have been explored. In general, results with errors of less than at most a few percent are easily obtainable.

For a system with canonical variables x and p, [x,p]=iħ, we associate with each density operator ρ an x coherence δx and a p coherence δp which specify, respectively, the characteristic distance and momentum range over which the underlying quantum-mechanical nature of the ensemble cannot be neglected. These coherences are less than or equal to the associated uncertainties δx≤Δx, δp≤Δp; so the ratios ${\mathit{c}}_{\mathit{x}}$≡δx/Δx, ${\mathit{c}}_{\mathit{p}}$≡δp/Δp give measures of the quantum character of the ensemble with respect to x and p. Examples are presented.

The metastable ${}_{}{}^4{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$ state of the ${\mathrm{Ne}}_2^{\mathrm{-}}$ anion is examined with the use of the numerical Hartree-Fock method. The results suggest that due to its similarity to the experimentally discovered ${}_{}{}^4{}_{}{}^{}\mathrm{\Pi }_{\mathit{g}}^{}{}_{}{}^{}$ state of ${\mathrm{He}}_2^{\mathrm{-}}$, this state should also be long lived.

The structure of the continuous spectrum of the muonic molecular ion tdμ has been investigated. We have calculated the energies, lifetimes, geometries, and fusion rates of several resonances having angular momentum J=0 in the neighborhood of the (tμ${)}_{2\mathit{S}}$ threshold. The significance of these states for muon-catalyzed fusion under high-temperature conditions is discussed.

Levy’s constrained-search procedure [Proc. Natl. Acad. Sci. U.S, North 76, 6062 (1979)] is employed to show how to determine Kohn-Sham and Hartree-Fock-Kohn-Sham orbitals and kinetic energies ${\mathit{T}}_{\mathit{s}}$ and ${\mathit{T}}_{\mathit{c}}$, for the two-electron, four-electron, and the general case starting from the electron density. Numerical results are presented for the species ${\mathrm{H}}^{\mathrm{-}}$ through ${\mathit{F}}^{7+}$ and the atom Be. The Pauli potential is also determined for Be. The small differences among Kohn-Sham, Hartree-Fock, and Hartree-Fock-Kohn-Sham orbitals suggest that determination of Kohn-Sham orbitals from the density in this way is an attractive procedure for getting an orbital description from an electron density.

A particular set of two-electron atomic resonances for the helium atom with zero total orbital angular momentum (S states) has been recently studied theoretically [K. Richter and D. Wintgen, J. Phys. B 24, L565 (1991)]. These resonances essentially have both electrons on the same side of the nucleus and the outer electron ‘‘frozen.’’ The present work suggests that the energies of these resonances correspond, when the degree of excitation of both electrons increases, to the energies of resonances associated with the Hamiltonian H=${\mathit{p}}^2$/2+p${\mathcal{’}}^2$/2-Z/r-Z/r’+1/‖‖r‖-‖r’‖‖ in a space where both particles have zero angular momentum (scrl=scrl’=0). Moreover, the energy of each of these resonances appears to be that of the lowest member of an almost unperturbed Rydberg series of resonances converging to a single ionization threshold of He. The analysis of the problem relies on the method of o(4,2) operator replacements generalized by the method of complex scaling.

Values of the magnetic shielding constant in the ground state of the hydrogen molecule are calculated using explicitly correlated Gaussian functions. The total shielding at equilibrium amounts to 26.73 ppm.

The second-order perturbation method for single-state multireference wave functions generated in complete-active-space self-consistent-field (CASSCF) calculations has been employed for computing electric dipole polarizabilities of different valence-electronic states of the first- (C,N,O,F) and second-row (Si,P,S,Cl) atoms. The results of calculations with polarized basis functions provide a uniform set of accurate polarizability data for those systems. Also, atomic quadrupole moment values obtained by using the CASSCF method are presented.

We searched for laser-induced 2${\mathit{S}}_{1/2}$-2${\mathit{P}}_{3/2}$ transitions in (${\mathrm{\mu }}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}\mathrm{He}$${)}^{+}$ ions at low pressure (4.1 kPa), where we determined a 2S lifetime of 1.014±0.121 μs from the simultaneously measured 2S→1S two-photon transitions. In contrast to a similar experiment in He gas of 40 bar (4×${10}^6$ Pa) reported by Carboni et al. [Nucl. Phys. A278, 381 (1977)], which was based on the questionable metastability of the 2S state at that pressure, we found no resonance effect at the wavelength λ=811.7 nm. We can reject this wavelength with a confidence level of less than 2×${10}^{\mathrm{-}3}$, and the interval 811.4≤λ≤812.0 nm with a greater than 95% probability.

The results of an extended series of high-precision variational calculations for all states of helium up to n=10 and L=7 (excluding S states above n=2) are presented. Convergence of the nonrelativistic eigenvalues ranges from five parts in ${10}^{15}$ for the 2P states to four parts in ${10}^{19}$ for the 10K states. Relativistic and quantum electrodynamic corrections of order ${\mathrm{\alpha }}^2$, ${\mathrm{\alpha }}^3$, ${\mathrm{\alpha }}^2$μ/M, ${\mathrm{\alpha }}^2$(μ/M${)}^2$, and ${\mathrm{\alpha }}^3$μ/M are included and the required matrix elements listed for each state. For the 1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{\mathit{J}}$ states, the lowest-order spin-dependent matrix elements of the Breit interaction are determined to an accuracy of three parts in ${10}^9$, which, together with higher-order corrections, would be sufficient to allow an improved measurement of the fine-structure constant. Methods of asymptotic analysis are extended to provide improved precision for the relativistic and relativistic-recoil corrections. A comparison with the variational results for the high-angular-momentum states shows that the ‘‘standard-atomic-theory’’ and ‘‘long-range-interaction’’ pictures discussed by Hessels et al. [Phys. Rev. Lett. 65, 2765 (1990)] come into agreement, thereby resolving what appeared to be a discrepancy. The comparison shows that the asymptotic expansions for the total energies are accurate to better than ±100 Hz for L>7, and results are presented for the 9L, 10L, and 10M states (i.e., angular momentum L=8 and 9). Significant discrepancies with experiment persist for transitions among the n=10 states, which cannot be easily accommodated by supposed higher-order corrections or additional terms. Finally, the asymptotic analysis indicates that a revision to the quantum-defect method is required for the analysis of high-precision data.

The molecular-orbital description of two-electron atoms [J. M. Feagin and J. S. Briggs, Phys. Rev. A 37, 4599 (1988)], derived from ${\mathrm{H}}_2^{+}$ by interchanging the roles of electrons and nuclei, is generalized to D dimensions. For ${\mathrm{H}}_2^{+}$ itself there exist myriad exact interdimensional degeneracies because D→D+2 is equivalent to m→m+1, augmenting by unity the projection of the electronic angular momentum on the internuclear axis. When the molecular orbitals (MO’s) are transcribed to treat two-electron motion, additional constraints limit the exact degeneracies to states in D=3 and 5, but many approximate degeneracies persist. Since the MO description emphasizes rotational properties of the two-electron atom, the link between dimension and orbital angular momentum is a pervasive feature. We use this link to classify groups of quasidegenerate doubly excited atomic energies and to explain striking similarities among certain pairs of hyperspherical or molecular-orbital two-electron potential curves.

Accurate hyperfine-structure parameters for the ground and first excited states of lithium are reported. Hyperfine parameters are calculated from multiconfiguration Hartree-Fock (MCHF) wave functions using a recently written hyperfine-structure program, being a part of the MCHF Atomic Structure Package. Convergence of the hyperfine-strucure parameters is studied as the active set of orbitals is increased. The relativistic, finite-nuclear-size, and finite-nuclear-mass-corrected values of the magnetic hyperfine-structure constants of the 2s ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ and 2p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2,3/2}$ states of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ were determiend to be ${\mathit{A}}_{1/2}$=401.70 MHz and ${\mathit{A}}_{1/2}$=45.94 MHz, ${\mathit{A}}_{3/2}$=3.098 MHz, respectively. The final values are compared with experiments and with the most reliable theoretical values obtained with other methods.

Kα (1${\mathit{s}}^{\mathrm{-}1\mathrm{-}}$2${\mathit{p}}^{\mathrm{-}1}$) transition energies for atoms in the range 31≤Z≤100 have been calculated using the Dirac-Fock model with self-consistent magnetic interaction and full relaxation. Complete retardation, hydrogenic radiative corrections (with finite nucleus effects), as well as screening corrections are included. Electrostatic and Breit correlation energies have been computed with relativistic many-body perturbation theory. Auger shifts and core-core contributions have also been added. Comparison of these theoretical results with a large body of experimental results shows that the agreement is well within theoretical and experimental uncertainties up to Z=83, but experiments for larger Z show a very large scatter, which remains to be explained.

We develop the hyperspherical coordinate method into a numerically reliable method competitive with other accurate ones. To this end, we present an efficient and accurate numerical scheme for setting up the hyperspherical channel functions which dictate the accuracy of the whole method. The diabatic-by-sector method is employed to integrate numerically the hyperspherical close-coupling equations. The two-dimensional matching procedure is implemented to impose the asymptotic boundary conditions in the independent-particle coordinates. The proposed scheme leads to accurate bound-state energies and resonance positions as well as accurate phase shifts and widths. The efficiency and accuracy of the method are tested on the He atom. For singly excited states, our results agree with experimental results to within five significant digits. For elastic phase shifts, ours agree with other accurate theoretical results to within a few milliradians. For doubly excited states of the N=2 and 3 manifolds, our level positions agree with recent theoretical results to within four to five significant digits, and with experiments to a similar degree of accuracy. Detailed comparisons of our resonance widths with other data are presented.

The elements of the statistical tensors describing the anisotropy of an ionic state are calculated for photoionization induced by linearly polarized light. Depending on the orbital angular momentum of the ionized subshell, there are some special photoelectron emission angles that correspond to selective population of a magnetic sublevel. We point out that, if only one magnetic substate is populated, then the elements of the statistical tensor depend only on a geometric factor that is independent of the orbital angular momentum of the photoelectron.

The circular polarization of x-ray lines emitted by heliumlike iron collisionally excited by a longitudinally polarized electron beam has been investigated theoretically. The required collision strengths for excitation of the different n=2 and 3 magnetic sublevels from the 1${\mathit{s}}^2$ ground level have been calculated by two different distorted-wave methods and compared with each other. The agreement is generally good. One of these methods is semirelativistic, and the other is fully relativistic with QED effects included in the atomic structure part of the calculations. A high degree of circular polarization is obtained for the magnetic dipole 1 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ and quadrupole 1 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$ lines, while the intercombination line 1 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ is found to be almost completely circularly polarized in the near-threshold region. In addition to being of intrinsic interest for atomic collision physics, the reported results might have useful applications in future diagnostics of high-temperature plasmas with a view to providing information on the possible polarization of suprathermal electron beams.

A three-state calculation of electron-impact excitation of formaldehyde to the ã ${}_{}{}^3{}_{}{}^{}$${\mathit{A}}_2$ and à ${}_{}{}^1{}_{}{}^{}$${\mathit{A}}_2$ states is carried out using the Schwinger multichannel variational method. The integral and differential cross sections so obtained agree fairly well with theoretical results obtained using the complex Kohn method. Though agreement between the calculated integral cross section and the single available experimental measurement is qualitative, similar conclusions regarding the excitation mechanism are reached. A generalization of the selection rule for (${\mathrm{\Sigma }}^{+}$⇆${\mathrm{\Sigma }}^{\mathrm{-}}$) electron-impact excitation of diatomic molecules is used to explain the shape of the differential cross sections for the ã ${}_{}{}^3{}_{}{}^{}$${\mathit{A}}_2$ and à ${}_{}{}^1{}_{}{}^{}$${\mathit{A}}_2$ excitations.

Using synchrotron-radiation-based angle-resolved photoelectron spectrometry, the Cl 3s3${\mathit{p}}^5$${(}^3$${\mathit{P}}_{2,1,0}^{\mathit{o}}$)np and 3s3${\mathit{p}}^5$${(}^1$${\mathit{P}}_1^{\mathit{o}}$)np autoionizing Rydberg series are studied by monitoring the relative partial photoionization cross sections and asymmetry parameters of the 3${\mathit{p}}^{\mathrm{-}1}$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,1,0}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2^{\mathit{e}}$, and ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0^{\mathit{e}}$ ionic states between 21.75 and 27.75 eV. The Rydberg series converging upon the 3${\mathit{s}}^{\mathrm{-}1}$ ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2^{\mathit{o}}$, ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{\mathrm{o}}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0^{\mathit{o}}$ thresholds are clearly resolved. Rydberg levels up to n=14 can be identified in the ${(}^3$${\mathit{P}}_{2,1,0}^{\mathit{o}}$)np series, while the ${(}^1$${\mathit{P}}_1^{\mathit{o}}$)np Rydberg series can be observed up to n=10.

The relative partial cross sections are placed on an absolute scale using previous data obtained with an electron spectroscopy modulation method. The present experimental results for the Cl ${(}^3$${\mathit{P}}_{2,1,0}^{\mathit{o}}$)np and ${(}^1$${\mathit{P}}_1^{\mathit{o}}$)np Rydberg series are compared with those of the Ar 3s3${\mathit{p}}^6$${(}^2$${\mathit{S}}_{1/2}^{\mathit{e}}$)np series, and with theoretical results of a nonrelativistic many-body perturbation theory calculation. The ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{2,1,0}^{\mathit{o}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ ionization thresholds obtained from the Rydberg series agree very well with the ionization limits calculated on the basis of the Cl ii spectrum, and with the ionization energies determined from a 3${\mathit{s}}^{\mathrm{-}1}$ photoelectron spectrum. Autoionization phenomena due to 3${\mathit{s}}^2$3${\mathit{p}}^5$→3${\mathit{s}}^2$3${\mathit{p}}^3$nln’l’ two-electron excitations are observed in the ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ resonance region.