Inner-shell soft-x-ray absorption of formaldehyde, ${\mathrm{H}}_2$CO, in the region of the C K and O K absorption thresholds was studied with high energy resolution using synchrotron radiation from the SX700/II monochromator at BESSY. The absorption spectra were recorded via the total photocurrent yield. The C 1s–excitation spectrum is characterized by a dominant C 1${\mathit{s}}^{\mathrm{-}1}$ ${\mathrm{\pi }}^{\mathrm{*}}$ resonance and weaker transitions into Rydberg states, each exhibiting vibrational fine structure that is quantitatively analyzed in terms of the normal vibrational modes of ${\mathrm{H}}_2$CO. Isotopic effects on the vibrational modes were studied by taking analogous spectra of ${\mathrm{D}}_2$CO. A Franck-Condon analysis of the vibrationally split spectra yields equilibrium distances, molecular bond angles, and vibrational frequencies of C 1${\mathit{s}}^{\mathrm{-}1}$–excited formaldehyde, which show strong isotopic effects. In addition, the ground vibrational level of the lowest Rydberg state (C 1${\mathit{s}}^{\mathrm{-}1}$3s-${\mathit{a}}_1$) exhibits a pronounced shift to higher excitation energies upon replacement of H by D. This shift, as well as a considerable isotope-dependent line broadening, are presumably caused by perturbations of this state by valence orbitals. Analogous isotopic effects were observed for the O 1${\mathit{s}}^{\mathrm{-}1}$3s-${\mathit{a}}_1$ Rydberg state.

K-shell photoionization cross sections for Be were calculated by the R-matrix method in a close-coupling approximation using 16-, 17-, and 29-term target representations. Extensive configuration mixing was used to represent the target states so that their energies agreed closely with experiment. As a result the present ab initio calculation reproduces accurately the observed features of the photoelectron spectrum and allows its interpretation; it highlights the significance of direct and conjugate shakeup, especially at low energies, where conjugate shakeup has been found to be important. The calculated partial photoionization cross sections for the three major decay channels with an open K shell closely match recent experiments in magnitude and shape. Our representation of the ${\mathrm{Be}}^{+}$ target spans 9.8 Ry and is particularly suited for a discussion of highly excited states of Be.

An application of the coupled-channels optical method to energy-dependent phenomena, electron-hydrogen resonances for n=1 and 2, is given. The equivalent-local approximation is made for the optical potential. The calculation includes nine explicity coupled channels. The optical potential accounts for the target continuum. The good agreement with experiment shows the role played by the optical potential in the coupled-channels calculation. Some additional resonances have been found.

High-resolution x-ray photoabsorption measurements on Ar near its K edge are reported. A number of new two-electron KM features were detected. The three-electron ${\mathit{KM}}^2$ and the two-electron KL spectra were measured for the first time. The three-electron ${\mathit{KM}}^2$ and the two-electron KL spectra were measured. The previously unresolved three-electron ${\mathit{KM}}^2$ and the two-electron KL spectra were clearly resolved in this study. Identification of spectral features is discussed based on our Hartree-Fock and published Dirac-Fock [Dyall, J. Phys. B 16, 3137 (1983); Dyall and LaVilla, Phys. Rev. A 34, 5123 (1986)] energy-level calculations.

A study of the analytic behavior of different few-particle scattering amplitudes at low energies in two space dimensions is presented. Such a study is of use in modeling and understanding different few-particle processes at low energies. A detailed discussion of the energy and the momentum dependence of the partial-wave on-the-energy-shell and off-the-energy-shell two-particle t matrices is given. These t-matrix elements tend to zero as the energy and momentum variables tend to zero. The multiple-scattering series is used to show that the connected three-to-three amplitudes diverge in the low-energy-momentum limit. Unitarity relations are used to show that the connected two-to-three and one-to-three amplitudes have specific logarithmic singularities at the m-particle breakup threshold. The subenergy singularity in the two-to-three amplitudes is also studied, and comments are made on some applications of the present study in different problems of physical interest.

The algebraic eikonal approach to electron-molecule scattering, in which the coupling to both rotational and vibrational states of the molecule is taken into account to all orders in the dipole strength, is generalized to include more realistic interactions. Such interactions may be nonlinear functions of the generators of the dynamical algebra of the molecule. The approach is applied to electron scattering off LiF, where a realistic nonlinear dipole operator is used. A significant enhancement of the calculated inelastic vibrational cross section is observed.

The algebraic eikonal approach to electron-molecule scattering is applied to electron scattering off HF and HCl, for which rotational-vibrational excitation cross sections were recently measured. Calculations are done with realistic interactions that include improved dipole, quadrupole, and polarization interactions. Good agreement with the data is obtained in the vibrational elastic channels.

We studied the interaction of highly charged ions on metal surfaces leading to the emission of electrons from the projectile and from the target. The target electrons are due to potential emission, kinetic emission, and Auger-electron emission. In our electron spectra two types of target Auger electrons are distinguished. Electrons near 135 and 220 eV are ascribed to Pt ${\mathit{N}}_{45}$${\mathit{O}}_1$${\mathit{O}}_{23}$ and ${\mathit{N}}_{45}$${\mathit{N}}_{67}$V Auger transitions. They are caused by K-vacancy transfer into the Pt N shell and are only emitted under bombardment with ${\mathrm{N}}^{6+}$ and ${\mathrm{O}}^{7+}$. The other type of electrons near 40 and 60 eV are ascribed to Pt ${\mathit{O}}_{23}$VV and ${\mathit{N}}_{67}$VV Auger transitions. They are due to direct ionization and are emitted under bombardment with each projectile used. According to our analysis, the initial projectile K-shell vacancy survives the transport to and at least 8×${10}^{\mathrm{-}16}$ s within the target surface.

A computational method is described for obtaining inner-shell-vacancy states of three-electron atoms which combines a block-diagonalization procedure with generalized Feshbach projection operators applicable to systems with three or more electrons. Typically, the accuracy is about 1.5 parts per thousand (δE/E≊1.5×${10}^{\mathrm{-}3}$). The strength of the method is that it provides many energy levels for each Rydberg series. A quantum-defect analysis is then applied that identifies the members of each series and yields reliable quantum defects and series limits. The method is particularly important in symmetries for which multiple Rydberg series exist. The present work reports on ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{e}}$ states of three-electron systems with 3≤Z≤10, which are compared with other calculations. The energies of ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$ states of ${\mathrm{C}}^{3+}$ are also presented as an example requiring both the multielectron Feshbach projection operators and the quantum-defect analysis developed here. Four distinct Rydberg series are found for this case and their series limits obtained.

A variational Hamiltonian method for quantum field theory is applied to the problem of natural line shape. Within scalar quantum electrodynamics, coupled variational equations are derived for the scattering of photons from a scalar (pionic) atom. It is shown that the coupled equations have a continuous spectrum for all energies above the atomic ground state. Excited states of the atom appear as resonances in particular partial-wave cross sections. The line center and shape are derived from the behavior of the photon-atom scattering phase shifts.

We study recently proposed algebraic models [F. Iachello, Chem. Phys. Lett. 78, 581 (1981); F. Iachello and R. D. Levine, J. Chem. Phys. 77, 3046 (1982); F. Iachello, S. Oss, and R. Lemus, J. Mol. Spectrosc. 146, 56 (1991); F. Iachello and S. Oss, ibid. 149, 132 (1991)] for diatomic and linear polyatomic molecules in the mean-field approximation. In this approach, we recover the harmonic molecular spectra efficiently and accurately and, more importantly, we are able to explore the geometrical meaning of boson operators and to suggest boson Hamiltonians that have closer links to molecular geometries.

A solution of the dimensionless Thomas-Fermi equation is presented, which can be considered as a simple model for the ${\mathrm{C}}_{60}$ molecule. In the framework of this model, we derive estimates of the sphere radius ${\mathit{R}}_{\mathit{e}}$ at equilibrium, the total energy, and the scattering factor. The limitations of the model are discussed in relation to some experimental results and to some other approximations.

Using the concept of information entropy, it is shown that it is impossible to increase the phase-space density of atoms with time-dependent potentials or other time-dependent terms in the Hamiltonian, even if the motion is nonclassical.

The influence of center-of-mass corrections on transition probabilities in the hydrogen spectrum is studied in a homogeneous magnetic field with the help of canonical transformations. To a good approximation, only energy differences are modified but in an unexpected way for electric quadrupole transitions. Center-of-mass corrections mainly affect the lifetimes of the tightly bound states with m<0. Dipole transitions remain dominant for reduced fields γ up to at least 1000. Quadrupole transitions should dominate the lifetimes of even-parity m=0 states at higher fields.

We show how the so(2,1) Lie algebraic methods and symbolic computation can be used to obtain the energy expansion for a general parabolic state in both the two- (2D) and three-dimensional (3D) cases. It is shown by comparing the realizations of the so(2,1) generators that the resulting symbolic expressions for the energy corrections in the 3D case in terms of the parabolic quantum numbers also give the corresponding 2D expressions by a simple reinterpretation of the quantum numbers defining a parabolic state. The main 2D and 3D results reduce to algebraic expressions for the matrix elements of the operator V=${\mathit{X}}^2$=-1/2E${\xi }^2$, which suffice to provide polynomial expressions for the perturbative terms of any (n,${\mathit{n}}_1$,${\mathit{n}}_2$,m) level to any order j in the perturbation series.

A calculation of the collisional diffusion coefficient is made which estimates the effect of collisions in an optical trap. The theory is based on the method of Gordon and Ashkin [Phys. Rev. A 21, 1606 (1980)] and incorporates the equations derived by Smith and Burnett [J. Opt. Soc. Am. B 8, 1592 (1991)] to describe the interaction of two two-level atoms in a laser field. Results are obtained by using a nearest-neighbor model for the collisions and suggest a definite relationship between atomic density and collisional diffusion.

Based on the vanishing-damping continued-fraction method which I developed previously for the analysis of the resonance behavior of a two-level atom in a two-frequency field with equal intensities in the two field modes [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], I analyze here the related problem in which the two field intensities are unequal. Several analytical results are derived, namely, expressions for the lowest-order Bloch-Siegert shifts of all resonances, and an expression for the positions of the resonances in the limit of one strong and one weak field. It is shown that, in this limit, the resonances exhibit level crossings of the field-atom system.

We present an experimental study of the number and density of trapped atoms in a vapor-cell Zeeman optical trap. We have investigated how the number (and therefore the capture rate) and density change with the trapping laser’s beam diameter, intensity, and detuning and with the magnetic-field gradient of the trap. We have developed a quasi-one-dimensional numerical model that accurately predicts the number of trapped atoms for all conditions. We also have investigated chirping the laser frequency and trapping with broadband light, neither of which increase the number of trapped atoms.

A semiclassical analysis of the losses in an optical trap due to radiative collisions is presented. We use WKB theory to calculate the overlap between the ground- and excited-state wave functions. The results may be written as an absorption line shape and a survival on the excited state, with an excited-state velocity determined by energy conservation. In the region around resonance for the transition, the results reduce to those presented in previous analyses.

Laser-rf double-resonance spectroscopy of the hyperfine transition between F’’=0 and F’=1 in the metastable ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ was performed in 100-keV beam in the storage ring ASTRID. High efficiency of optical pumping was demonstrated for complex pumping schemes. A broadband (dc–6 GHz) rf device was designed and used for rf spectroscopy in the storage ring. The possibility of obtaining coherent rf signals (Ramsey fringes) from successive interactions with the same field was investigated. Important limitations for the coherences due to magnetic-field inhomogeneities were observed. These led to randomization of the atomic polarization during only one turn in the storage ring and completely prevented observation of Ramsey fringes. This situation is different from the case of fundamental particles in a storage ring, where the polarization may be preserved for many round-trips. Limits were put on the demands to beam quality, beam positioning, and magnetic-field quality to overcome the problem. The effects of the rf device on the external degrees of freedom of the ion beam were investigated. Its small aperture substantially reduced the beam lifetime, and at very low rf frequencies the electric field in the rf device was able to excite external transverse resonances in the beam.