The eigenvalues of the potentials ${\mathit{V}}_1$(r)=-a/r+br+${\mathit{cr}}^2$ and ${\mathit{V}}_2$(r)=μ${\mathit{r}}^2$+λ${\mathit{r}}^4$+η${\mathit{r}}^6$ are obtained in N-dimensional space by the infinite Hill determinant method for a wide range of values of the parameters. We discuss the explicit dependence of these two potentials in higher-dimensional space. By using the formalism of supersymmetric quantum mechanics, it is shown that exact solutions of these potentials exist when the parameters satisfy certain constraints.

In this paper, we study the multiphoton Jaynes-Cummings model (JCM) governed by the Milburn equation [G. J. Milburn, Phys. Rev. A 44, 5401 (1991); 47, 2415 (1993)], which models the decoherence of a quantum system as the quantum system evolves through intrinsic mechanisms beyond conventional quantum mechanics. We give an exact solution of this equation for the multiphoton Jaynes-Cummings Hamiltonian and apply it to investigate the influence of the intrinsic decoherence on nonclassical effects (atomic inversion, oscillations of the photon-number distribution, squeezing of the cavity field, and photon antibunching) in the JCM. It is shown that during the time evolution, the intrinsic decoherence in the atom-field interaction suppresses these nonclassical behaviors in the JCM.

The molecular Kohn-Sham (KS) exchange-correlation potential ${\mathit{v}}_{\mathrm{xc}}$ has been constructed for LiH from the correlated ab initio density ρ by means of the simple iterative procedure developed by van Leeuwen and Baerends [Phys. Rev. A 49, 2421 (1994)]. The corresponding KS energy characteristics, such as the kinetic energy of noninteracting particles ${\mathit{T}}_{\mathit{s}}$, kinetic part of the exchange-correlation energy ${\mathit{T}}_{\mathit{c}}$, and energy of the highest occupied molecular orbital ${\mathrm{\epsilon }}_{\mathit{N}}$, have been obtained with reasonable accuracy. A relation between the form of ${\mathit{v}}_{\mathrm{xc}}$ and the electronic structure of LiH has been discussed. Test calculations for the two-electron ${\mathrm{H}}_2$ molecule have shown the efficiency of the procedure.

We argue that a photon wave function can be introduced if one is willing to redefine, in what we feel is a physically meaningful way, what one wishes to mean by such a wave function. The generation of a photon wave function by a spontaneously emitting atom is discussed.

The relativistic nuclear recoil corrections to the energy levels of low-lying states of hydrogenlike and high-Z lithiumlike atoms in all orders in αZ are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low Z the results of the calculation are in good agreement with the αZ-expansion results. It is found that the nuclear recoil contribution, in addition to Salpeter’s contribution, to the Lamb shift (n=2) of hydrogen is -1.32(6) kHz. The total nuclear recoil correction to the energy of the (1s${)}^2$${\mathit{p}}_{1/2\mathrm{-}}$(1s${)}^2$2s transition in lithiumlike uranium constitutes -0.07 eV and is largely made up of QED contributions.

We have measured the parity-nonconserving (PNC) optical rotation near the 1.279-μm ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$${\to }^3$${\mathit{P}}_1$ magnetic-dipole absorption line in atomic lead vapor. We measure the quantity scrR≡Im(${\mathit{scrE}}_{\mathrm{PNC}}$/scrM), where scrM is the magnetic-dipole amplitude of the absorption line and ${\mathit{scrE}}_{\mathrm{PNC}}$ is the electric-dipole amplitude coupled into the same line by the PNC interaction within the lead atom. We find scrR to be (-9.86±0.04±0.11)×${10}^{\mathrm{-}8}$, where the first error is statistical and the second is systematic. The statistical errors are due to incompletely subtracted background fluctuations, and the systematic errors are caused by line-shape uncertainties and calibration error. Our value is consistent with the atomic PNC calculations for lead, which give scrR=(-10.7±0.8)×${10}^{\mathrm{-}8}$ for the standard electroweak model with ${\sin }^2$${\mathrm{\theta }}_{\mathit{W}}$=0.23 and no electroweak radiative corrections. Including radiative corrections yields the value S=-3±8 for the isospin-conserving electroweak parameter, with difficulties in the atomic theory of lead presently limiting the extent to which our result tests the standard model. This same technique can also be applied to thallium, where the atomic theory is currently accurate to 3%. By searching for a difference in scrR for the two hyperfine components of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$, we find the amplitude of the nuclear spin-dependent PNC rotation to be less than 2×${10}^{\mathrm{-}2}$ of the nuclear spin-independent rotation.

A variety of coherent states of the harmonic oscillator is considered. It is formed by a particular superposition of canonical coherent states. In the simplest case, these superpositions are eigenfunctions of the annihilation operator A=P(d/dx+x)/ √2 , where P is the parity operator. Such A arises naturally in the q→-1 limit for a symmetry operator of a specific self-similar potential obeying the q-Weyl algebra ${\mathit{AA}}^{\mathrm{°}}$-${\mathit{q}}^2$${\mathit{A}}^{\mathrm{°}}$A=1. Coherent states for this and other reflectionless potentials whose discrete spectra consist of N geometric series are analyzed. In the harmonic oscillator limit, the surviving part of these states takes the form of orthonormal superpositions of N canonical coherent states ‖${\mathrm{\epsilon }}^{\mathit{k}}$α〉, k=0,1,...,N-1, where ε is a primitive Nth root of unity, ${\mathrm{\epsilon }}^{\mathit{N}}$=1. A class of q-coherent states related to the bilateral q-hypergeometric series and Ramanujan type integrals is described. It includes an unusual set of coherent states of the free nonrelativistic particle, which is interpreted as a q-algebraic system without a discrete spectrum. A special degenerate form of the symmetry algebras of self-similar potentials is found to provide a natural q analog of the Floquet theory. Some properties of the factorization method, which is used throughout the paper, are discussed from the differential Galois theory point of view.

Time-resolved laser spectroscopy was used to measure natural radiative lifetimes of ten excited states of neutral bismuth. Four levels of the 6${\mathit{p}}^2$ns ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{1/2}$ sequence (n=7,8,9,10) and the 6${\mathit{p}}^2$7s ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}_{3/2,5/2}$ and 6${\mathit{p}}^2$nd ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{3/2;5/2}$ (n=6,7) levels were investigated. The results are compared with previous data when possible. Revised absolute transition probabilities for 26 lines are given. Several levels required vacuum-ultraviolet (vuv) excitation, which was achieved by stimulated anti-Stokes Raman shifting of frequency-tripled dye-laser radiation in high-pressure ${\mathrm{H}}_2$ gas.

Analytic properties of the ground-state energy of a two-electron atom as a function of λ=1/Z are studied. In addition to the previously known singular point of this function, ${\lambda }_{\mathit{s}}$≊1.097 660 79, we find a new singular point ${\lambda }_{\mathrm{\infty }}$=∞ in the λ complex plane. We show that the function E(λ) has a branch-point singularity of the type ${\lambda }^{\gamma }$ at this point, where the exponent γ=2.06±0.005. We find that the ansatz previously proposed to reproduce the asymptotic behavior of the large-order coefficients of the perturbation expansion [Baker et al., Phys. Rev. A 41, 1247 (1990)] can, with slight modification, reproduce the behavior of the exact ground-state energy of the two-electron atom around this singular point. We propose a representation of the exact ground-state energy of helium, possessing the required analytic properties.

Resonance line narrowing up to 1/2 of the natural linewidth has been observed for microwave magnetic-resonance transitions between Zeeman levels of ground-state muonium at a strong magnetic field of 1.7 T. The observed lines are in good agreement with predicted line shapes and are useful for a precision determination of Δν and ${\mathrm{\mu }}_{\mathrm{\mu }}$/${\mathrm{\mu }}_{\mathit{p}}$.

The frequencies of 22 rotational transitions in the four naturally occurring isotopic variants of lithium hydride have been measured to an unprecedented accuracy of a few parts in ${10}^8$ with a tunable far-infrared spectrometer. The values of the vibrational and rotational quantum numbers v and J involved range up to 2 and 12, respectively. The measurements have been fitted with already existing data on the vibration-rotation energy levels of lithium hydride in its ground ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ state to a single model based on the Dunham expansion. This model has been modified to take into account the Dunham and nonadiabatic corrections and their effects on the reduced mass dependence of the energy levels in the way first described by Watson [J. Mol. Spectrosc. 80, 411 (1980)]. The data are fitted to experimental accuracy to give an improved set of reduced Dunham parameters, ${\mathit{U}}_{\mathit{k}\mathit{l}}$, and an improved value for the Born-Oppenheimer equilibrium bond length for LiH, ${\mathit{r}}_{\mathit{e}}^{\mathrm{BO}}$=0.159 490 811(16) nm. The fit constitutes a stringent test of this type of model for the breakdown of the Born-Oppenheimer approximation.

In this paper, we present a unified approach to inverting molecular potential energy and dipole functions from time-dependent measurements. This algorithm combines the regularized solution of a Fredholm integral equation of the first kind containing the data with time-dependent wave-packet propagation. The result is a nonlinear, noniterative algorithm to recover the potential and dipole functions from the time-dependent data. The recovered regions of these functions correspond to those sampled by evolving wave packets associated with the laboratory data. Although the algorithm is designed to track temporal data, synthetic tracking data may be generated for inversion by the use of appropriate steady measurements.

The Schrödinger equation for the ground state of correlated two-electron atoms is treated by an accurate finite-element method (FEM) yielding energy eigenvalues of -2.903 724 377 021 a.u. for the helium atom and -0.527 751 016 532 a.u. for the hydrogen ion ${\mathrm{H}}^{\mathrm{-}}$. By means of an adaptive multilevel grid refinement the FEM energy eigenvalue is improved to a precision of 1×${10}^{\mathrm{-}11}$ a.u., which is comparable to results obtained with sophisticated global basis sets. The local and overall precision of the FEM wave function approximation is studied and discussed. Benchmark values for the expectation values 〈${\mathit{r}}^2$〉, 〈r〉, 〈1/r〉, and 〈1/${\mathit{r}}_{12}$〉 are presented.

The parameters describing the interference between allowed and collision-induced transitions in the far-infrared spectrum of HD-He and HD-Ar are computed following the formalism of Gao et al. [Phys. Rev. A 44, 7379 (1991)] and the calculational procedure of Gao et al. [Phys. Rev. A 46, 5781 (1992)]. The contribution from each component of the induced-dipole moment is identified. The interference between the induced-dipole component having the same symmetry as the allowed moment and the allowed moment itself has the largest single contribution to the intensity interference effect. The mixing of rotational levels by an anisotropic intermolecular interaction introduces other components into the interference mechanism. The overall effect is usually to decrease the magnitude of the interference and to permit line broadening and asymmetry to occur. This interaction is most effective in causing the anisotropic overlap-induced pair dipole moment ${\mathit{B}}_2$(21) to play a role in the interference mechanism. The effect of the isotropic overlap-induced dipole moment is usually negligible.

A key process in the muon-catalyzed fusion cycle is a low-energy collision of dμ or tμ with a ${\mathrm{D}}_2$ molecule that leads, at appropriate incident energies, to the formation of a resonant complex containng ddμ or dtμ. In this paper, a detailed description is given of a formal calculation in which elements of Feshbach’s treatment of resonances and Chan and Fraser’s coupled-scattering-equations approach to positronium formation in ${\mathit{e}}^{+}$H scattering in the region below the first target excitation threshold are used to obtain an expression for the cross section for resonant dtμ formation. The result is similar to the Breit-Wigner formula. The relationship of this expression to the expression used in some evaluations of this cross section is discussed.

Using a time-dependent formulation of Franck-Condon spectra, we analyze the spectra associated with the transitions into a saddle-point region of an unbound Born-Oppenheimer potential. We find a spectral peak at an energy near the barrier top, which we associate with the existence of a quasi-bound-state. We refer to this state as ‘‘barrier resonance.’’ Employing a quadratic approximation to the potential and the quantum dynamics of Gaussian wave packets, we develop a line-shape formula that accurately fits this spectral feature. This line-shape formula corresponds to an infinite set of complex energy poles rather than the usual single-pole approach used in the Breit-Wigner theory. We apply the line-shape formula to barrier resonances on the Eckart potential and in the H+${\mathrm{H}}_2$ chemical reaction.

Electronic spectra of ${\mathrm{Ca}}_2$, ${\mathrm{Cu}}_2$, and ${\mathrm{Ag}}_3$ have been studied in superfluid helium. The Σ-Σ transitions of ${\mathrm{Ca}}_2$ and ${\mathrm{Cu}}_2$ show vibrationally resolved absorption and emission bands close to those in free space. The emission has been observed only from the lowest vibrational states, reflecting rapid relaxation of the dimer vibration. Vibrational frequencies of the ground electronic states are slightly affected by the liquid. Anomalous spacings between the v′=0←v′′=0 and v′=1←v′′=0 absorption bands are discussed in terms of the coupling of dimer vibration and bubble bath modes.

The dynamics of an atomic wave packet in an electric field above the classical field ionization limit is studied in both the frequency and the time domain. We measure the photoionization yield of rubidium atoms in an electric field in the range 0.2–5 kV/cm as a function of the wavelength of the exciting laser. Fourier transforms of these spectra after multiplication with the spectrum of a short optical pulse allow us to make a direct comparison with time-resolved measurements performed by Broers et al. [Phys. Rev. A 49, 2498 (1994)]. The dynamics of electronic wave packets above the classical field ionization limit as a function of the excitation energy is studied in detail, showing angular-momentum recurrences of the wave packet to the core on a picosecond time scale. The observed lifetimes up to 50 ps depend on excitation energy and polarization of the laser light. We also transform the frequency spectra to scaled-energy spectra, i.e., an alternative way of representing the dynamics of Rydberg wave packets. The frequency spectra allow us to compare the time-resolved spectra and the scaled-energy spectra directly. We find that near the saddle point (ε=-1.9) radial and angular recurrences correspond to actions of S=0.77 and S=2.4, respectively. Just above the classical field ionization limit long-lived states are observed with lifetimes up to microseconds. These long decay times are measured in an alternative way: detection of the ionization yield as a function of time after the laser excitation.

Hyperspherical coordinates are used to study three-electron atomic systems. Within the adiabatic approximation, the Schrödinger equation for the three-electron systems is reduced to a set of partial differential equations of two hyperangles at each fixed hyper-radius. We restrict ourselves in the present paper to the configurations where the orbital angular momentum of each electron is zero. The adiabatic potential curves and the associated wave functions are obtained. We identify potential curves associated with singly, doubly, and triply excited states and analyze the nodal structure of the associated wave functions with respect to the two hyperangles.

The construction of global shape coordinates for the n-body problem is considered. Special attention is given to the three- and four-body problems. Quantities, including candidates for coordinates, are organized according to their transformation properties under so-called democracy transformations (orthogonal transformations of Jacobi vectors). Important submanifolds of shape space are identified and their topology studied, including the manifolds upon which shapes are coplanar or collinear, and the manifolds upon which the moment of inertia tensor is degenerate.