An upper bound for the fat-fractal scaling exponent of area-preserving maps is calculated. The calculation consists of counting the number of islands of different sizes that occur near a Kolmogorov-Arnol’d-Moser surface. Approximate renormalization scaling results are used for the island sizes and numbers.

A semiclassical analog to the Abraham-Moses-Gel’fand-Levitan method for generating radial potentials with analytic sets of energy levels is presented. The algorithm begins with the selection of a model potential whose energy levels can be expressed as analytic functions of the corresponding quantum numbers. Then, a finite number of states is deleted from its spectrum, leaving all the others unchanged. Subsequently, the incomplete spectrum is analytically inverted using a generalized version of the Rydberg-Klein-Rees equations. The result is a family of potential functions that, when quantized, give rise to the incomplete spectra. Emphasis is placed on the application of this method to a Coulomb model potential. The simple l-dependent analytic functions obtained allow the straightforward calculation and systematic study of a number of members of this modified Coulomb-potential family. The connection between these modifications and atomic pseudopotentials is also discussed.

The mathematical content of the uncertainty principle is contained in special states akin to, and including, states of minimum uncertainty. Specific uncertainty relations are produced by averaging observables in these states. The approach is shown to give more flexible and complete expressions of indeterminacy than the familiar generalized Heisenberg inequality: statistical measures other than variances can be employed, the method is not limited to describing uncertainties in terms of products of statistical dispersions, and the resulting inequalities have the most stringent bounds attainable independent of the system state. Applications are then made to find uncertainty relations for position-momentum average displacements from the means, time-energy indeterminacy, and uncertainties in angular momentum components.

A recent recoil-corrected Dirac equation is completed by the introduction of hyperfine interactions, including anomalous magnetic-moment couplings. Numerical examples are presented for antiprotonic atoms.

The expression for the polarizability of a pair of centrosymmetric systems adsorbed on a dielectric or a metallic surface is given for the first time to our knowledge. Of course, if no surface is present our results can also be applied to the case of interactions between colliding molecules in vacuum. The use of the multipolar Hamiltonian leads to a complete expression of the hyperpolarizability which contains at the same time dispersive and inductive effects. This makes it possible to write down calculations in a very compact and simple form.

Relative cross sections for charge transfer and electron detachment in collisions of ${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{D}}^{\mathrm{-}}$ ions with Na and K atoms have been measured in the energy range from 2 to 300 eV. Measurements of the differential elastic cross sections for collisions of ${\mathrm{H}}^{\mathrm{-}}$ with Na are also reported for energies around 10 eV. A two-state perturbed-stationary-state calculation has been performed and compared with the experimental results and a previous calculation.

The pressure dependences of 2p-1s transitions in He-like and Li-like neon recoil ions produced in collisions with 1.4-MeV/amu Ar ions were studied for the purpose of assessing effects of polarization and nonstatistical population mechanisms on the relative intensities of prompt and metastable lines. A Johansson-type curved-crystal spectrometer was employed as an x-ray polarimeter by taking spectra with the plane of the focal circle oriented both parallel and perpendicular to the Ar-ion beam. The data indicate that the He-like ${}_{}{}^1{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{P}$ lines are only slightly polarized and that the intensity ratio I${(\mathrm{}}^1$P)/I${(\mathrm{}}^3$P) is not a linear function of pressure. Both of these results appear to be a direct consequence of serious contamination of the spectral region of interest by unresolved spectator-electron transitions.

Coincidence measurements between H, ${\mathrm{H}}^{+}$, and the Ly-α radiation from the decay of H(2p) resulting from the collision of low-keV ${\mathrm{H}}_2$${\mathrm{}}^{+}$ projectiles with a Ne target have been made. Our results show that the direct excitation of ${\mathrm{H}}_2$${\mathrm{}}^{+}$ with subsequent dissociation is a much more likely process than the electron charge transfer to (${\mathrm{H}}_2$${)}^{\mathrm{*}}$ followed by dissociation. The additional measurements of the polarization of the Ly-α radiation in coincidence with the scattered ${\mathrm{H}}^{+}$ show that σ states are more populated at ${\mathrm{H}}_2$${\mathrm{}}^{+}$ orientations perpendicular to the beam. Our findings are interpreted within the quasidiatomic description of ${\mathrm{H}}_2$-Ne molecular orbitals.

The $L_2$,3MM Auger electron spectra of atomic 3d transition-metal Ni have been studied for the first time to our knowledge both experimentally and theoretically. The electron-beam-excited $L_2$,3${\mathrm{M}}_4$,5${\mathrm{M}}_4$,5, $L_2$,3${\mathrm{M}}_2$,3${\mathrm{M}}_4$,5, and $L_2$,3${\mathrm{M}}_2$,3${\mathrm{M}}_2$,3 spectra show a very complicated spectral structure if compared with the corresponding spectra of Cu and Zn. The spectra have been analyzed by carrying out detailed comparisons between multiconfiguration calculations and experiment. It has been possible to identify the twofold structure of the $L_2$,3${\mathrm{M}}_4$,5${\mathrm{M}}_4$,5 spectrum to correspond to the 2$p^{\mathrm{-}1}$3$d^8$4$s^2$→3$d^6$4$s^2$ and 2$p^{\mathrm{-}1}$3$d^9$4s→3$d^7$4s transitions. The structure is found to be due to the thermal population of the levels of the two lowest-lying configurations in the ground state of the atom and not due to the configuration mixing.

One- and two-photon ionization cross sections for the negative hydrogen ion ${\mathrm{H}}^{\mathrm{-}}$ are evaluated by using a one-electron model where the effective intra-atomic potential energy is assumed to be of a very-short-range character and approximated by a ‘‘spherical δ shell.’’ The adjustment of the two parameters involved in the model potential so as to reproduce either the photodetachment energy or the behavior of the one-photon ionization cross section over a substantial range of frequencies beyond the ionization threshold leads to conjecture of a reasonable estimate of the two-photon ionization cross section over the proper range of frequencies of the ionizing field.

In view of the recent successful confinement of decelerated sodium atoms in a magnetostatic trap, it is of interest to evaluate possible trap-field configurations. Neutral atoms in a Zeeman sublevel whose energy increases with field can be confined by a field whose magnitude ‖B‖ increases with distance from the center. Because this same basic requirement applies also to traps for neutrons and for plasmas (in the guiding-center approximation), trap configurations developed previously for these purposes are of interest for neutral atoms. However, the desired properties differ considerably because of very different objectives and different behavior of very cold atoms as compared with hot plasmas. We characterize basic trap configurations using both the exact expressions for the field, and a multipole polynomial expansion that facilitates studies of symmetry properties and classical or quantum orbits. Polynomial terms for the field components are derived and coefficients obtained by comparison with Taylor-series expansions and by global fit. Contours of ‖B‖ for various trap configurations are also presented. Under certain restrictive conditions, ‖B‖, and hence the effective potential, can be made isotropic to second order.

The ${}_{}{}^1{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ shape resonance of ${\mathrm{H}}^{\mathrm{-}}$ has been studied in moderate motional electric fields by Doppler-tuning the photon energy absorbed by a 650-MeV ${\mathrm{H}}^{\mathrm{-}}$ beam crossed by the fourth-harmonic beam of a Nd:YAG laser (YAG denotes yttrium aluminum garnet). The resonance parameters are remarkably insensitive to electric fields in the range from 120 to 240 kV/cm. Our measurements reveal that the width of the shape resonance may decrease from its zero-field value, on average, by (3.3±0.9)% in this electric field regime. This observation contradicts the (naive) expectation that perturbation of the resonance by an electric field should promote more rapid decay, and hence greater width. Interpretations are given in terms of (a) Stark mixing with narrower singlet states and (b) tunneling through the potential barrier in hyperspherical coordinates.

The major purpose of the present paper is to find effective energy-dependent one-electron potentials for core excitations in atoms and solids in terms of the frequency-dependent density response of the system. In the case of the photoionization amplitude we demonstrate how all effects of many-electron interactions within the random phase approximation with exchange (RPAE) can be represented by an effective one-electron wave function or an effective, nonlocal, electron-photon interaction. We also demonstrate the usefulness of intermediate schemes with one-electron basis states of the Hartree-Fock average-of-configuration potentials ($V^{N\mathrm{-}1}$) or the local-density approximation (LDA) with which one calculates the density response within the RPA (no ‘‘exchange’’), and we make some comparisons with the time-dependent LDA. We also demonstrate how the form of an effective one-electron wave function depends on the choice of dipole-length or dipole-velocity operator. We finally express the RPAE photoionization amplitude in terms of an average amplitude with a Hartree-Fock ${}_{}{}^1{}_{}{}^{}\mathrm{P}$ wave function and an average dipole-length–dipole-velocity operator and a correction with a correlation wave function and a difference dipole-length–dipole-velocity operator.

The 4d→f transitions in Xe and Ba and the 4p→d transition in Kr are analyzed in terms of the effective wave functions and effective local potentials in an energy region where the response of the system is highly resonant and shows collective behavior. The effective potentials are obtained in the random-phase approximation with exchange, and the importance of relaxation is investigated. It is found that the energy dependence of the effective potential is necessary to describe the excitation spectrum reasonably well. The effects of external screening by adding and removing electrons (${\mathrm{Ba}}^{1\mathrm{-}}$-${\mathrm{Ba}}^{2+}$) are analyzed and the applicability of the atomiclike model for the 4d→f transitions in metallic Ba is discussed.

The Wei-Norman ordering technique is utilized to present a unified approach to the time ordering for SU(2), SU(1,1), and SU(3) coherence-preserving Hamiltonians. It is shown that the characteristic equations of the ordering method can be cast in the form of a generalized Bloch equation in an SU(2), SU(1,1), and SU(3) space. The laws of conservation, linked to the Casimir invariants of the algebra, are also directly derived from the Wei-Norman characteristic equations.

We study the ‘‘elastic’’ scattering of fast electrons by atomic hydrogen in the presence of a laser field. Our method takes into account the ‘‘dressing’’ of the target states by including the laser-atom interaction to first order, while the laser-projectile interaction is treated to all orders. This allows us to treat laser fields which, although weak compared to the atomic unit of field strength, can nevertheless be strong by laboratory standards. In the limit of weak fields our results reduce to those obtained recently by a perturbative approach (in the laser-projectile interaction) for all laser frequencies.

By using the reservoir theory and Dekker’s quantization procedure for a dissipation system, a set of new surface-dressed optical Bloch equations including the surface-induced frequency shift as well as the decay rate is derived to calculate the resonance fluorescence spectrum of an adatom near a bulk solid surface. A mediate layer composed of nonabsorbing dielectric is placed to separate the adatom and the bulk solid. The size and the dielectric effects of this layer are found to be as important as those effects from the bulk solid. These effects will be directly exhibited in the decay rates and the frequency shifts. The resonance fluorescence spectrum is discussed in different cases and is found to be strongly affected by the surfaces.

Photoionization in the 5d and 6s subshells of atomic mercury has been studied in the 17–40-eV photon-energy range using the 1-m aluminum Seya monochromator on the Tantalus storage ring. The angular distribution parameter β has been obtained for the 5$d_{3/2}$, 5$d_{5/2}$, and 6s photolines (up to ∼32 eV in the latter case). The 6s β’s have been observed to decrease by ∼0.4 units between the 5$d_{3/2}$ threshold (16.71 eV) and 17 eV (to a value less than 1), then increase to near 2 by hν=35 eV. Somewhat better agreement has been found with 5d Dirac-Fock calculations than with relativistic random-phase approximation (RRPA) results, while the 6s β’s are predicted very well by RRPA except for the position of the Cooper minimum at ∼17 eV.

Analysis of the x-ray emission spectra of Ti, V, Fe, and Co reveals the existence of new satellites in agreement with the recent results of nonrelativistic Hartree-Fock calculations. Theoretical and experimental values of the energy and relative intensity of these satellites are presented and discussed. Contrary to previous speculations, contributions to satellite spectra due to 2s spectator holes, although not appreciable, seem to be significant; they help explain certain features which may not be understood on the basis of (1s2p${)}^{\mathrm{-}1}$→(2p${)}^{\mathrm{-}2}$ transitions alone.

We have developed a new technique for determining Landé g factors of atoms by the measurement of hyperfine intervals as a function of an applied static magnetic field. This approach is widely applicable and has distinct advantages over previous methods. As an example, we have measured the $g_J$ factor of the 5$p^4$5d ${\mathrm{}}^4$${\mathrm{D}}_{7/2}$ level of Xe ii to be 1.420(14). The potential accuracy is considerably greater.