Isotope shifts in ${}_{}{}^{151,153}{}_{}{}^{}\mathrm{Eu}_{}^{+}{}_{}{}^{}$ have been measured for four optical transitions between the metastable levels 4${\mathit{f}}^7$${(}^8$S°)5${\mathit{d}}^9$D${\mathrm{°}}_{\mathit{J}}$ and the excited levels 4${\mathit{f}}^7$${(}^8$S${\mathrm{°}}_{7/2}$)6${\mathit{p}}_{3/2}$;J’ in a collinear laser and slow-ion-beam apparatus. A phenomenological interpretation and an ab initio calculation have been made and compared with experiment.

The third-order nonlinear-optical susceptibilities of 16 simple atoms and molecules (Ne, Ar, Kr, Xe, ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{CO}}_2$, ${\mathrm{CF}}_4$, ${\mathrm{SF}}_6$, ${\mathrm{CH}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_6$, ${\mathrm{C}}_3$${\mathrm{H}}_8$, n-${\mathrm{C}}_4$${\mathrm{H}}_{10}$, and ${\mathrm{C}}_4$${\mathrm{H}}_6$) have been measured in the gas phase at two near-infrared wavelengths using the technique of electric-field-induced second-harmonic generation (ESHG) with periodic phase matching and with He as the reference gas. These results are combined with previous ESHG data in the visible region to determine dispersion curves. The experimental estimate of the static hyperpolarizability γ for Ne, ${\gamma }_{\mathrm{Ne}}$=119±3 a.u., is in good agreement with the best ab initio calculations, but the experimental estimates of the static hyperpolarizabilities for Ar and ${\mathrm{H}}_2$, ${\gamma }_{\mathrm{Ar}}$=1167±20 a.u. and 〈${\gamma }_{\mathrm{H}2\mathrm{}}^{\mathit{e}}$〉=686±10 a.u., differ significantly from the best ab initio results.

We show that the quantum-mechanical time-reversal operator provides a satisfying formulation of the ‘‘generalized dilatation transformation’’ for forming scalar products with partial complex conjugation, and leads to a theoretically justified stationarity principle for finding resonances (i.e., metastable states) in atomic and molecular systems.

Experimental spin-polarization data for the Hg 6s Cooper minimum and dipole-transition amplitudes and phase-shift differences for photoionization of the Hg 5d and 6s shells (eight channels) in the photon-energy region from the ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}_{3/2}$ threshold up to 35 eV (kinetic energies from 0 to 20 eV) are presented and compared with new relativistic random-phase approximation calculations. The data were evaluated from an experimental data set, quantum mechanically ‘‘complete,’’ consisting of cross-section and photoelectron spin-polarization data. For the 5d subshells the results show strong interchannel coupling between the outgoing p and f continuum channels. The results for Hg 6s could be used for an independent determination of the photoelectron angular distribution parameter β in the Cooper-minimum region. This region is shown to be perturbed by numerous two-electron excitations, which might be a possible explanation for the controversy on its location.

Extensive multiconfigurational Hartree-Fock (MCHF) calculations on the ${}_{}{}^2{}_{}{}^{}$S ground state and the ${}_{}{}^2{}_{}{}^{}$P excited state of lithium are reported. MCHF problems involving full configuration-interaction calculations within up to 85 orbitals are solved numerically using the finite-element method. Systematic studies of the convergence of the hyperfine parameters with respect to the size of the active space are given. The Fermi contact term of Li${(}^2$S) has an accuracy of 0.07%. The Fermi contact, the orbital, the spin-dipolar, and the electric quadrupole terms of Li${(}^2$P) have an estimated inaccuracy of 0.7%, 0.13%, 0.15%, and 0.35%, respectively.

The structure of the reduced first-order density matrices in momentum space and ‘‘exchange-only’’ correlation factors for a few closed-shell atomic systems has been systematically investigated. These quantities are studied within the Hartree-Fock as well as the nonlocal-density-approximation regime. The suitably averaged contours have been plotted and some significant features are brought out. These quantities are seen to bear a gross resemblance to their respective position-space counterparts.

Accurate measurements, mostly to within 2%, of the total atomic cross section for the elastic scattering of 59.54-keV photons on atoms in the 13≤Z≤82 range were carried out at 60°, 90°, and 120° scattering angles. Very good agreement with other experimental data was observed, in particular, with those of Schumacher and Stoffregen [Z. Phys. A 283, 15 (1977)]. The comparison with the theoretical results given by Kissel and co-workers [Phys. Rev. A 22, 1979 (1980); Phys. Rep. 140, 75 (1986)] confirms the validity of their procedure within the value intervals explored.

We have obtained the partial and total widths for autoionization of the ${\mathrm{H}}^{\mathrm{-}}$ ${}_{}{}^1{}_{}{}^{}$S two-electron ionization ladder for n=3–7, which leads to the Wannier state at E=0. The theory starts from first principles by identifying and computing the appropriate localized, correlated wave functions on the real energy axis and then incorporating the effects of the multichannel continuum by solving state-specific, complex-eigenvalue non-Hermitian matrix equations. The outgoing channel-dependent Gamow orbitals are expanded in terms of Slater-type orbitals with coordinate complex scaling. The partial widths are obtained from an equation involving the complex mixing coefficients of the resonance wave function and the corresponding off-diagonal matrix element for each open channel. We find that by far the largest partial width is that which comes from the nearest threshold while within this hydrogenic threshold there is strong mixing of the angular momentum channels and a decay rate distribution which depends on the excitation energy.

Dielectronic data for state-specific F-like to Ne-like recombinations are obtained for elements between argon and krypton (and perhaps somewhat beyond). The data consist of energy levels, autoionization rates, radiative rates, and dielectronic-recombination branching ratios. Detailed calculations using a Hartree-Fock method that includes relativistic corrections, but no configuration interactions, were carried out for ${\mathrm{Ar}}^{9+}$, ${\mathrm{Ti}}^{13+}$, ${\mathrm{Fe}}^{17+}$, and Se ${}_{}{}^{25+}{}_{}{}^{}$. Three- and four-parameter fits were then made to these data enabling one to calculate dielectronic rates for all elements in the fourth row of the periodic table. These scaling relations provide checks on the accuracy of the numerical methods used to obtain the Ar, Ti, Fe, and Se data. Further checks are provided by comparisons made to other published work. The dielectronic-recombination rates presented in this paper are very important in the calculation of population inversions and x-ray laser gain within neonlike ionization stages.

We have observed the Ba n’${\mathit{p}}_{1/2}$np and n’${\mathit{p}}_{1/2}$nd double Rydberg series (n>60,n’<0.75n) using a five-laser excitation scheme. A single photon excites the n’${\mathit{p}}_{1/2}$nl levels from an initially populated Ba 8${\mathit{s}}_{1/2}$nl autoionizing state. If there were no correlation between the two valence electrons, we would observe only the n’pnp or n’pnd states. However, we observe strong excitation to n’snl and n’dnl states as well. We observe virtually no n’snl and n’dnl states for n’<0.4n. For n’>0.75n the Rydberg structure that is observed for the lower n’ levels disappears into an apparently unstructured continuum.

We present an alternative time-dependent method of calculating the S matrix in quantum systems governed by a Hamiltonian. In the first step one constructs a new Hamiltonian that describes the physics of scattering at energy E with a reduced number of degrees of freedom. Its matrix elements are computed with a Monte Carlo projector method. In the second step the scattering matrix is computed algebraically via diagonalization and exponentiation of the new Hamiltonian. Although we have in mind applications in many-body systems and quantum field theory, the method should be applicable and useful in such diverse areas as atomic and molecular physics, nuclear physics, high-energy physics and solid-state physics. As an illustration of the method, we compute s-wave scattering of two nucleons in a nonrelativistic potential model (Yamaguchi potential), for which the S matrix is known exactly.

A projection operator formalism is employed in considering the T operator for describing a scattering or reaction event in which a system evolves from one continuum channel into another continuum channel. The formalism is based upon projections of the Lippmann-Schwinger equations for T and an operator generalization of Gauss’s reduction for linear algebraic equations. A formal solution of the projected Lippmann-Schwinger equation is presented for the case in which the couplings involving the final-state continua satisfy a chosen separability condition. The simplifications that occur when the pole approximation is made on the final-state continua or on both the initial- and final-state continua are presented. The formalism is employed in considering the effects of an external dc electric field in photorecombination processes in a model atomic system which features two autoionizing states, two electron continua (one of which contains the initial state), and two photon continua (corresponding to radiatively stabilized atomic states). Particular attention is paid to the effects of the coupling between the two electron continua.

Detailed theoretical analyses are presented of the projectile-energy dependence as well as the target dependence of the electron-detachment collision processes, ${\mathrm{H}}^{\mathrm{-}}$+T→H(n=2)+${\mathrm{T}}^{\mathrm{*}}$+${\mathit{e}}^{\mathrm{-}}$. These analyses are illustrated by calculations of both projectile-frame and laboratory-frame doubly differential cross sections (DDCS’s) for 0.5-, 1.0-, and 1.5-MeV ${\mathrm{H}}^{\mathrm{-}}$ collisions with He targets and for 0.5-MeV ${\mathrm{H}}^{\mathrm{-}}$ collisions with Ne, Ar, Kr, and Xe targets; in addition, we present laboratory frame DDCS’s for 0.1-MeV ${\mathrm{H}}^{\mathrm{-}}$ collisions with Xe targets. Comparisons with available experimental data are given.

A two-potential approach is used to study the elastic scattering of electrons and positrons by lithium atoms in the intermediate-energy region. Within the framework of the two-potential method, the effect of close coupling is considered by including the closely lying 2p state in the distorted-wave representation of the total scattering wave function. Differential and integrated cross sections are calculated for the elastic electron and positron scattering. The differential spin asymmetry and ratio R of the triplet-to-singlet cross section are also calculated to study the effect of exchange for electron scattering. The results thus obtained are compared with available experimental data and other available theoretical calculations.

General principles of the asymptotic theory of adiabatically slow atomic collisions are reviewed. Special emphasis is placed on analytic properties of adiabatic potential energy curves for complex values of internuclear separation. The significance of the complex branch points and hidden avoided crossings for the dynamics of one-electron collisional systems is discussed. Adiabatic asymptotes of the cross sections for charge exchange, excitation, and ionization in slow ${\mathrm{He}}^{2+}$+H(1s) and ${\mathrm{H}}^{+}$+${\mathrm{He}}^{+}$(1s) collisions are calculated and compared with other theoretical and experimental data.

We propose an efficient method for reconstruction of the potential from scattering data. Starting from experimentally determined phase shifts and taking into consideration the incompleteness and inexactness of the input information, we construct iteratively a local potential that approximates the input phase shifts. The method is first tested on model examples and is then used for construction of a local effective potential describing the scattering of low-energy electrons by noble-gas atoms. Convergence of the method is usually very fast, and the reconstructed potential is close to the true one. A relation between the inverse-scattering problem and the Fourier analysis of experimental data is discussed.

A search for the ${\mathrm{Mg}}^{\mathrm{-}}$ ion detected via the 2${\mathit{p}}^6$3${\mathit{p}}^3$ ${}_{}{}^4{}_{}{}^{}$S→2${\mathit{p}}^6$3s3${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P transition is described. The ${\mathrm{Mg}}^{+}$→${\mathrm{Mg}}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}$S two-step charge-exchange process is investigated and compared with the recently observed ${\mathrm{Be}}^{+}$→${\mathrm{Be}}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}$S process. Analysis of the optical spectra shows that the cross section for producing the ${\mathrm{Be}}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}$S state by beam-foil or beam-gas collisions is much larger, a factor of 30 or more, than for producing ${\mathrm{Mg}}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}$S. The search has been concentrated in the 2860–2950-Å region that covers the two wavelengths 2921 and 2895 Å recently proposed theoretically for the above transition. None of the spectral lines observed within the spectral region studied exhibits the properties of a negative ion. While the possibility of observing the ${\mathrm{Mg}}^{\mathrm{-}}$ ${}_{}{}^4{}_{}{}^{}$S${\mathrm{-}}^4$P transition at 2921±4 Å [D. R. Beck, Phys. Rev. A 40, 2887 (1989)] can be excluded, the 2895±3 Å region [C. Froese Fischer, Phys. Rev. A 41, 3481 (1990)] is more complicated since it contains a so far unidentified spectral line. We can assign this line to the quintet spectrum of Mg i. This assignment is supported by four lines forming a closed loop, consistent with optical transitions between the 2${\mathit{p}}^5$3s3p4s and 2${\mathit{p}}^5$3s3${\mathit{p}}^2$ configurations, and by multiconfiguration Hartree-Fock calculations. The lack of experimental observations of the predicted ${\mathrm{Mg}}^{\mathrm{-}}$ ion is discussed.

Excitation and fluorescence spectra arising from bound-bound transitions between the E$0^{\mathrm{-}}$ and the A1, A$0^{\mathrm{-}}$, and B$0^{\mathrm{-}}$ states of the HgZn excimer were investigated using pump-and-probe methods of laser spectroscopy. Several previously unknown bands were recorded, interpreted, and analyzed, yielding vibrational constants, relative energies, and relative internuclear separations for the various states.

During a pump-and-probe spectroscopic study of the HgZn excimer, it was found that probing the Hg-Zn vapor cell with laser light in the 4200–4500-Å range resulted in the intense emission of Hg 4916-Å atomic fluorescence arising from the 8 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→6 ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ transition. This observation is ascribed to the predissociation of the HgZn F1 state through a curve crossing with the repulsive D$0^{\mathrm{-}}$ state, followed by pooling collisions of the resulting Hg 6 ${}_{}{}^3{}_{}{}^{}$P atoms, leading to the population of the 8 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ state. This interpretation is corroborated by the results of spectroscopic and time-evolution experiments.

The relative intensities of the vibrational components in the laser-induced fluorescence spectrum arising from a particular molecular vibronic state are usually independent of the exciting wavelength and thus do not depend on the lower vibronic state from which the excitation takes place. We have observed that although the intensity pattern in the fluorescence spectrum from the E$0^{\mathrm{-}}$(v’=0) level is independent of the excitation wavelength, the relative intensities of the bands in the fluorescence spectrum from the E$0^{\mathrm{-}}$(v’=1) level do depend on the wavelength of the exciting light. We have also observed that the vibrational intensity distribution in the excitation spectrum of the E$0^{\mathrm{-}}$(v’=1) level depends on the fluorescence wavelength at which it is monitored, whereas the intensity profile in the excitation spectrum of the E$0^{\mathrm{-}}$(v’=0) level is independent of the monitoring wavelength. These variations in the vibrational intensity patterns suggest that the intensities may arise from the sum of two Franck-Condon factors in some of the vibrational bands. This phenomenon is ascribed to the presence of a second upper state, the F$0^{\mathrm{-}}$ state, whose v’=0 level almost coincides with the v’=1 level of the E$0^{\mathrm{-}}$ state and which has substantial probabilities of transitions to the A1, A$0^{\mathrm{-}}$, and B$0^{\mathrm{-}}$ states.