The quantum dynamics of the two-level system under a periodic external potential is mapped to the classical one of a charged particle moving in the harmonic-oscillator potential plus a magnetic field in a plane. The behavior of tunneling and localization is fully described by the radial trajectory of the particle. It is shown that localization may happen only if the radial trajectory is periodic. The possible period is an integral multiple of that of the external force. Three models are studied.

We present calculations for ${\mathrm{H}}_2^{+}$ photodissociation in intense short laser pulses where molecular rotation is fully included, resulting in the experimentally observed alignment of the photofragments. In addition, we show that by using a coherent superposition (phase-locked) of a fundamental radiation and its second harmonic, a strong asymmetry between the forwards and backwards proton distribution can be observed. Both the total dissociation probability and the asymmetry of the ion distribution are sensitive to the relative phase of the two colors and thus subject to coherent control.

Using the adiabatic superpromotion model of low-energy atomic collisions, a simple scaling relationship is derived for the ionization cross section of hydrogen atoms colliding with multiply charged ions. Detailed ionization-cross-section calculations for the systems H(1s)+${\mathrm{He}}^{2+}$, ${\mathrm{C}}^{6+}$, and ${\mathrm{O}}^{8+}$ have been performed and used to determine three numerical constants in the cross-section-scaling relationship. The scaled cross section represents well the available data for fully stripped ions with charge Z≥2 in the energy region below the cross-section maximum.

We report direct measurements of the ac Stark shifts of Xe Rydberg levels in high-intensity laser fields (up to 6 GW/${\mathrm{cm}}^2$), demonstrating the expected near-ponderomotive behavior. These measurements provide extensive unambiguous evidence for the validity of perturbative calculations of the nonresonant ac Stark shift at these intensities.

Using five-laser resonance excitation in combination with a method of sequential ionization by a pulsed and a constant electric field, we have observed the nearly pure spectra (the ion resonance background was greatly suppressed) for the highly excited double Rydberg states NLn’l (N≳40, N/n’≳0.5 and L,l<4) of ytterbium in which the mutual penetration of the two excited wave functions is remarkable. Analysis of the spectra (relative cross section for different L states) has revealed the importance of the ‘‘hybridization’’ in the excited electron orbits which arises from the correlation of the two electrons in such highly excited states.

This article discussed the melting of ‘‘crystals’’ of two laser-cooled ions in a Paul trap. It presents computer simulations which reproduce melting at some realistic trap parameters in a model which includes laser-ion interaction but no collisions with residual gas molecules, highlighting the importance of spontaneous-emission fluctuations. Crystal fragility at certain trap voltages coincides with low-order nonlinear resonances, an aspect not mentioned in earlier discussions of the system.

We consider the interaction of an intense laser field with an ensemble of electrons confined by a symmetric potential well, and show that, for times shorter than the dephasing time, the laser field can break the symmetry of the system regardless of its initial conditions, resulting in optical rectification and even-harmonic generation. In particular, we show that relatively moderate fields can give rise to significant even-harmonic generation, even if the system is initially in thermal equilibrium, with no need for pulse shaping, suggesting that the detection of symmetry-breaking effects may be experimentally accessible.

A four-port arrangement is shown to yield a direct measurement of the positive P distribution of Drummond and Gardiner [J. Phys. A 13, 2353 (1980)].

In this work we review some aspects of the semiclassical dipole impact approximation for isolated ion lines with a view to the questions on Z scaling raised by two recent experimental studies. Some theoretical and practical aspects of line-shape calculations are discussed. Detailed calculations are performed in the semiclassical (dipole) impact approximation for the Li isoelectronic 3P–3S line. Particular emphasis is given to inelasticity effects. In contrast to previous calculations, very good agreement is obtained for the lighter elements of the isoelectronic series. Ion dynamical corrections are also considered and are found to be negligible in the dipole approximation.

Optical isotope shifts have been measured in 11 lines of the neutral-tantalum spectrum. The tantalum atoms were introduced into a hollow cathode discharge, whose cathode wall was covered with 4 mg of a ${\mathrm{Ta}}_2$${\mathrm{O}}_5$ sample containing ${}_{}{}^{180}{}_{}{}^{}\mathrm{Ta}$ enriched to 4.1%. Using laser excitation with either optogalvanic or laser-induced fluorescence detection, the hyperfine constants of the levels involved and the shifts of the centers of gravity between ${}_{}{}^{180}{}_{}{}^{}\mathrm{Ta}$ and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ could be determined. The measurements show differences in the level isotope shifts within the terms ${}_{}{}^6{}_{}{}^{}\mathrm{D}$, z ${}_{}{}^6{}_{}{}^{}\mathrm{D}_{}^{\mathrm{o}}{}_{}{}^{}$, y ${}_{}{}^4{}_{}{}^{}\mathrm{D}_{}^{\mathrm{o}}{}_{}{}^{}$, and ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$: ΔT{5${\mathit{d}}^4$(a ${}_{}{}^5{}_{}{}^{}$D)6s ${}_{}{}^6{}_{}{}^{}\mathrm{D}_{3/2}^{}{}_{}{}^{}$–${5\mathrm{d}}^4$(a ${}_{}{}^5{}_{}{}^{}\mathrm{D}$)6s ${}_{}{}^6{}_{}{}^{}\mathrm{D}_{1/2}^{}{}_{}{}^{}$}=527(35) MHz, ΔT{5${\mathit{d}}^3$6s(a ${}_{}{}^5{}_{}{}^{}$F)6p ${}_{}{}^6{}_{}{}^{}\mathrm{D}_{3/2}^{\mathrm{o}}{}_{}{}^{}$–${5\mathrm{d}}^3$6s(a ${}_{}{}^5{}_{}{}^{}\mathrm{F}$)6p z ${}_{}{}^6{}_{}{}^{}\mathrm{D}_{1/2}^{\mathrm{o}}{}_{}{}^{}$} =355(35) MHz, ΔT{5${\mathit{d}}^3$6s(a ${}_{}{}^5{}_{}{}^{}$F)6p ${}_{}{}^4{}_{}{}^{}\mathrm{D}_{3/2}^{\mathrm{o}}{}_{}{}^{}$–${5\mathrm{d}}^3$6s(a ${}_{}{}^5{}_{}{}^{}\mathrm{F}$)6p y ${}_{}{}^4{}_{}{}^{}\mathrm{D}_{1/2}^{\mathrm{o}}{}_{}{}^{}$}=-591(30) MHz, and ΔT{5${\mathit{d}}^2$6${\mathit{s}}^2$(a ${}_{}{}^3{}_{}{}^{}$P)6p ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{3/2}^{\mathrm{o}}{}_{}{}^{}$–${5\mathrm{d}}^2$${6\mathrm{s}}^2$(a ${}_{}{}^3{}_{}{}^{}\mathrm{P}$)6p ${}_{}{}^4{}_{}{}^{}\mathrm{P}_{1/2}^{\mathrm{o}}{}_{}{}^{}$}=58(30) MHz, which are caused most probably by strong heretofore unknown perturbations.

Lifetimes in the 3${\mathit{d}}^{10}$np ${}_{}{}^2{}_{}{}^{}$P sequence in neutral copper were measured by time-resolved laser spectroscopy. Excitation from the ground state was performed with pulsed laser radiation in the vuv spectral region, generated by resonant sum-difference four-wave mixing in krypton gas. The life- times were evaluated from recorded optical transients. For the ${\mathit{np}}^2$${\mathit{P}}_{\mathit{J}}$ states we find the fol- lowing: τ(n=6,J=3/2)=5.2(8) ns, τ(6,1/2)=25.1(10) ns, τ(7,3/2)=15.0(12) ns, τ(7,1/2)=4.0(8) ns, τ(8,3/2)=31(2) ns, τ(8,1/2)=15.8(12) ns, τ(9,3/2)=123(6) ns, and τ(9,1/2)=51(6) ns. The data are compared with a recent multiconfiguration Hartree-Fock calculation.

The Born-Oppenheimer approximation is used as an exploratory tool to study bound states, quasibound states, and scattering resonances in muon (μ)–hydrogen (x)–hydrogen (y) molecular ions. Our purpose is to comment on the existence and nature of the narrow states reported in three-body calculations, for L=0 and 1, at approximately 55 eV above threshold and the family of states in the same partial waves reported about 1.9 keV above threshold. We first discuss the motivation for study of excited states beyond the well-known and well-studied bound states. Then we reproduce the energies and other properties of these well-known states to show that, despite the relatively large muon mass, the Born-Oppenheimer approximation gives a good, semiquantitative description containing all the essential physics. Born-Oppenheimer calculations of the s- and p-wave scattering of d-(dμ), d-(tμ), and t-(tμ) are compared with the accurate three-body results, again with general success. The places of disagreement are understood in terms of the differences in location of slightly bound (or unbound) states in the Born-Oppenheimer approximation compared to the accurate three-body calculations.

The analytic properties of the function ${\mathit{k}}^{2\mathit{L}+1\mathrm{}}$cotδ are used to illustrate the locating of bound states and resonance poles in the complex k or E plane from the scattering data and to deduce the expected widths of resonances of a given L value. The prominent L=3 resonance at 22 eV (Γ=1.4 eV) in d-(tμ) scattering provides a benchmark for the unsuccessful search within the Born-Oppenheimer approximation for the claimed narrow s-wave d-t-μ resonance at 54.35 eV (Γ=0.74 eV). Although absolute proof is obviously lacking (because of the approximate calculation), the Born-Oppenheimer results for the s-wave gerade scattering are entirely reasonable; the absence of a centrifugal barrier makes it implausible that there could be resonances at 50–60 eV with narrow widths. We argue that the threshold at 48 eV of the t+(dμ) channel is unlikely to have a major effect. The family of states at 1.9 keV and above are of a different nature. They are, as is already known, molecular states based on the 3d ${\mathrm{\sigma }}_{\mathit{g}}$ ‘‘electronic’’ potential-energy curve, which is asymptotically the energy of the x(yμ; n=2) system. Born-Oppenheimer calculations of binding energies, and properties depending dominantly on the wave functions in the classically allowed region, agree reasonably well with the accurate three-body computations for the d-t-μ system. Expected disagreement occurs in the probability density ${\mathrm{\rho }}_{\mathit{N}}$(0) for the nuclei to be at vanishing internuclear separation (relevant for the fusion rate), in which configuration mixing is more important in the classically forbidden region. Nonetheless, the reported values of ${\mathrm{\rho }}_{\mathit{N}}$(0), when compared to the average probability density in the classically allowed region of nuclear motion computed here, appear excessively large. The likelihood that this family of continuum resonances would play a significant role in molecular formation in the muonic cascade is discussed briefly.

The dielectric function and the absorption line shape of a gas of polarizable atoms are calculated using numerical simulations and analytical approximations. The theory of self-broadening is recast in the framework of disordered excitons. The shift, width, and asymmetry of the absorption line shape are calculated and compared with recent experiments on potassium gas.

We report observations of simultaneous electron excitation and electron capture in ion-atom collisions of 97-MeV ${\mathrm{Ca}}^{18+}$ and ${\mathrm{Ca}}^{19+}$ in an argon gas target. X-ray spectra at energies near 3.9 keV were collected using a high-resolution x-ray spectrometer. We have resolved transitions from doubly excited 1s2l2l’ and 1s2l3l’ states to singly excited 1${\mathit{s}}^2$2l’ and 1${\mathit{s}}^2$3l’ states in lithiumlike calcium. The observed transitions lie at energies close to the 1s2s-1s2p resonance transitions in heliumlike calcium. We compare the experimental wavelengths and intensities with relativistic Hartree-Fock calculations, and discuss the excitation mechanisms.

The x-ray-absorption near-edge structure of gas-phase ${\mathrm{H}}_2$S, hydrogen sulfide, and ${\mathrm{D}}_2$S, deuterium sulfide, at the sulfur ${\mathit{L}}_{2,3}$ ionization thresholds has been measured using synchrotron radiation with high-energy resolution from the SX700/II soft-x-ray monochromator at the Berliner Elektronenspeicherring-Gessellschaft für Synchrotronstrahlung m.b.H. Previously unobserved fine structure is resolved. The spectra of both molecules are characterized by multielectron excitations 8–14 eV above the ${\mathit{L}}_2$ threshold energy, broad valence-shell absorption features 5–8 eV below the ${\mathit{L}}_2$ edge, and many narrower Rydberg excitations 0–5 eV below the ${\mathit{L}}_2$ edge. Comparison of the ${\mathrm{H}}_2$S and ${\mathrm{D}}_2$S spectra allows the identification of transitions which include vibrational excitation, due to the isotopic dependence of vibrational energies. For the (2p${)}^{\mathrm{-}1}$ core-excited Rydberg states, a least-squares analysis was employed, which deconvoluted the core-level and excited-orbital splittings. Results show that the twofold degeneracy of the sulfur 2${\mathit{p}}_{3/2}$ core level is removed by the molecular field, with a resulting splitting of 115 meV for the higher-energy core-excited Rydberg states. The energies of the higher Rydberg states were well described by the Rydberg formula with the quantum defects ${\mathrm{\delta }}_{\mathit{p}}$=1.63 and ${\mathrm{\delta }}_{\mathit{d}}$=0.32. Fine structure was resolved in the transitions to the dissociative (2p${)}^{\mathrm{-}1}$ core-excited valence-shell states. The regular spacing and isotopic dependence of this structure clearly identifies it as a vibrational progression.

We investigate the stability of homonuclear diatomic molecules from ${\mathrm{H}}_2$ up to ${\mathrm{C}}_2$ and of the finite chains ${\mathrm{H}}_{\mathit{n}}$ (n≤5) and ${\mathrm{He}}_{\mathit{n}}$ (n≤4) immersed in very intense magnetic fields (B≊${10}^8$ T). The atomic and molecular total energies are calculated within the one-dimensional Hartree-Fock approximation, using a Lagrange basis set associated with a Cartesian mesh. The stability of the molecules decreases beyond ${\mathrm{Li}}_2$ although all the studied molecules are found stable. The energy per atom of H and He finite chains stabilizes already for the small chain sizes that we have investigated.

The Schrödinger equation for two-electron atoms is transformed into an alternative equation depending on a free dimensionless parameter β, according to the method of o(4,2) operator replacements. These operator replacements are well defined except for the case where both the orbital and spin momenta are zero, i.e., except for singlet S states. When β goes to positive infinity, the solutions of this present equation should correspond to the solutions of the Schrödinger equation. When β goes to negative infinity, the present equation becomes exactly solvable. These exact solutions are the zero-order solutions for a Rayleigh-Schrödinger perturbative expansion where the perturbation is the nondiagonal part of the replaced kinetic-energy operator. An essential property of this method is that the perturbative operator is bounded, and therefore the convergence radius of the series is nonzero. The method is purely nonvariational. A numerical application for the triplet S even-parity ground-state helium atom is performed.

An approximately relativistic theory of bound states which ensures Poincaré invariance of the atomic system to relative order (v/c${)}^2$ developed by one of us [K. J. Sebastian, Phys. Rev. A 23, 2810 (1981)] is used to derive the Zeeman interaction Hamiltonian for a two-body system. This Hamiltonian is correct to order α(Zα${)}^2$ and to all orders of ${\mathit{m}}_{\mathit{e}}$/${\mathit{m}}_{\mathit{N}}$ and includes contributions from previously neglected radiative and recoil corrections. Explicit analytic expressions for the ${\mathit{g}}_{\mathit{J}}$ and ${\mathit{g}}_{\mathit{I}}$ factors are given and verify the results of Grotch and Kashuba [Phys. Rev. A 7, 78 (1973)]. This interaction Hamiltonian in conjunction with the zero-field relativistic interaction correct to order α(Zα${)}^4$ is used to analyze the Zeeman structure of the n=1, 2, and 3 levels of hydrogen and positronium. In the case of hydrogen, corrections for the Lamb shift which include the most recent radiative recoil and pure recoil corrections have also been included to yield an extremely precise analysis for hydrogen in the ‖${\mathit{nFm}}_{\mathit{F}}$JL〉 representation. The Hamiltonian, g factors, and Zeeman splittings are compared with previously obtained results and experimental results. The results of these comparisons are discussed at length.

High-precision laser-resonance measurements accurate to ±0.5 MHz or better are reported for transitions among the 1s2s ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_{1–}$1s2p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_{\mathit{J}}$ hyperfine manifolds for each of J=0, 1, and 2 in both ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$. A detailed analysis of hyperfine structure is performed for both the S and P states, using newly calculated values for the magnetic dipole and electric quadrupole coupling constants, and the hyperfine shifts subtracted from the measurements. The resulting transition frequencies are then analyzed on three different levels. First, the isotope shifts in the fine-structure splittings are calculated from the relativistic reduced mass and recoil terms in the Breit interaction, and compared with experiment at the ±0.5-MHz level of accuracy. This comparison is particularly significant because J-independent theoretical uncertainties reduce through cancellation to the ±0.01-MHz level. Second, the isotope shifts in the full transition frequencies are used to deduce the difference in rms nuclear radii.

The result is ${\mathit{R}}_{\mathrm{rms}}$${(}^6$Li)-${\mathit{R}}_{\mathrm{rms}}$${(}^7$Li)=0.15±0.01 fm, in agreement with nuclear scattering data, but with substantially improved accuracy. Third, high-precision calculations of the low-order non-QED contributions to the transition frequencies are subtracted from the measurements to obtain the residual QED shifts. The isotope-averaged and spin-averaged effective shift for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ is 37 429.40±0.39 MHz, with an additional uncertainty of ±1.5 MHz due to finite nuclear size corrections. The accuracy of 11 parts per million is the best two-electron Lamb shift measurement in the literature, and is comparable to the accuracies achieved in hydrogen. Theoretical contributions to the two-electron Lamb shift are discussed, including terms of order (αZ${)}^4$ recently obtained by Chen, Cheng, and Johnson [Phys. Rev. A 47, 3692 (1993)], and the results used to extract a QED shift for the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ state. The result of 30 254±12 MHz is shown to be in good accord with theory (30 250±30 MHz) when two-electron corrections to the Bethe logarithm are taken into account by a 1/Z expansion method.

In order to test the validity of the LS-coupling approximation for light elements, the line-intensity ratios of the 3s-3p and 3p-3d multiplets in C ii through Fv and C ii through Ne vi, respectively, have been investigated experimentally with emission sources. Also, calculations with multiconfiguration Dirac-Fock wave functions have been performed. Within the errors of the experimental procedure, no significant violations of the LS-coupling approximation were found for the lines of the 3s-3p and 3p-3d multiplets in C ii through F v . However, in the case of Ne vi, small deviations of measured intensities from those obtained by applying the LS-coupling approximation were observed.