The two-potential eikonal approximation proposed by Ishihara and Chen has been used to calculate the elastic differential scattering cross section of helium and lithium by electrons at intermediate energies. A significant improvement over the conventional Glauber cross section is achieved.

Accurate solutions of the four-electron Schrödinger nonrelativistic equation for nuclear charge $Z=3\mathrm{}$ reveal the existence of two core-excited bound states of ${\mathrm{Li}}^{-}$, which together with the ground state ${\mathrm{Li}}^{-}1s^{2}2s^2$ are found to be the only long-lived negative lithium ions. The metastable ${\mathrm{Li}}^{-}\left(1s2s2\mathrm{}{p}^2\right){}_{}{}^5{}_{}{}^{}P$ state is 504.5±2.0 meV below the (also metastable) $\mathrm{}\left(1s2s2p\right)\mathrm{}{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$ state of Li. Another bound state ${\mathrm{Li}}^{-}\left(1s2\mathrm{}{p}^3\right){}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}$, lies 291.0±2.0 meV below $\mathrm{Li}\left(1s2\mathrm{}{p}^2\right){}_{}{}^4{}_{}{}^{}P$ and it decays to the lower ${}_{}{}^5{}_{}{}^{}P$ state with $\tau =2.9\mathrm{}$ nsec, emitting uv photons of $\lambda =348.98\mathrm{}\pm 0.09$ nm. This is the first example of an electric dipole transition between bound states of atomic negative ions.

This paper states and proves Levinson's theorems for the classical scattering of two particles. The derivation is carried out by using time-delay theory. In both classical and quantum mechanics Levinson's theorems are shown to be the consequence of a common principle. This principle is the spectral property of time delay. Consider an arbitrary space region v. In quantum and classical mechanics a time-dependent scattering state traverses v in a definite time. The spectral property states that the sum of transit times for all orbits with total energy ε is proportional to the state density in region v. In classical mechanics it is established that this property can be derived from simple features of the time-evolution group.

Electron-impact ionization cross sections for highly ionized atoms in the hydrogen and lithium isoelectronic sequences have been computed in several variants of the Coulomb-Born and distorted-wave approximations. Electron exchange in the transition matrix element and Coulomb distortion of the partial waves were found to be important. The results are compared to recent crossed-beam experimental data and to other theoretical predictions.

Spectra of electrons ejected from doubly excited states of helium have been extensively measured at several observation angles for impact of lithium ions at energies lower than 5 keV. "Molecular-autoionization" spectra have been found at forward observation angles, and analyzed in terms of the Gerber-Niehaus theory with modification. The spectral shapes of atomic-autoionization peaks have been discussed in relation to both the Barker-Berry effect and the Doppler effect. Excitation cross sections of autoionizing states have been determined by a new method that uses simultaneous impact of ions and electrons.

The $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^3{}_{}{}^{}P$ electron-impact-excitation cross section for Li II is calculated in the distorted-wave approximation. Two forms of the distorted-wave method are examined; in the first form both the initial and final wave functions are distorted, while in the second form only the initial wave function is distorted. In both forms a partial-wave expansion of the scattered amplitude is made, and exchange is incorporated in a consistent manner. We also examine the effects of including more than one configuration in our target-state wave function. For incident energies greater than 90 eV, our distorted-wave calculations agree moderately well with recent experimental and theoretical results.

Time-resolved measurements of atomic observables are analyzed using a Liouville space formulation and a Hermitian unit tensor base. This approach makes it possible to distinguish cleanly the symmetries of a formation and/or excitation process completed by time $t=0\mathrm{}$, a time evolution under experimental control between $t=0\mathrm{}$ and $t=t$, and a measurement at $t=t$, even for hydrogenic observables. Each observable is labeled by a time-reversal quantum number, allowing exploration for the first time of the close relationship between time-reversal symmetry and the time evolution of atomic observables. The experimental reconstruction of atomic observables (at $t=0\mathrm{}$) from subsequent time-resolved measurements of the anisotropy and polarization of emitted electric dipole photons is discussed. Hydrogenic observables are stressed and the use of strong fields is included, thus generalizing Fano and Macek's approach.

Fully correlated Hylleraas-type electronic wave functions and a biased-selection Monte Carlo method have been used to find a rigorous upper bound to the Born-Oppenheimer potential between two helium atoms. The potential agrees with the experimental results of Burgmans, Farrar, and Lee (BFL) to within 1.4 Monte Carlo standard deviations for all nuclear separation distances calculated ($4.5-15.0a_B$). At the potential minimum of $5.6a_B$ this bound (- 7.10±0.30 Ry) is slightly below the BFL value of -6.70 Ry.

Strongly energy-dependent photoabsorption cross sections near excitation thresholds have been parametrized in terms of separate short- and long-range field contributions. The largest portion of this energy dependence results from standard parameters characterizing the long-range field effects; these parameters are known analytically for the most common outer fields, and can be calculated for others independently of the complicated short-range dynamics. The approach is illustrated in the Appendix by using a semiempirical fit to the total ${\mathrm{H}}^{-}$ photodetachment cross section to predict partial cross sections.

The influence of a strong atomic polarizability on photodetachment processes is isolated. In a model study of ${\mathrm{K}}^{-}$ photodetachment near the $4p_{\frac{1}{2}}$, $4p_{\frac{3}{2}}$ levels of K, the polarizability (${\alpha }_{4p}\simeq 600a_0^3$) is shown to cause a striking energy dependence of the parameters which determine the cross section. This study extends the effective range theory of O'Malley, Spruch, and Rosenberg to a broader energy range and to multichannel systems. An appendix provides a derivation of the polarization potential (and correction terms) starting from the electron-atom close-coupling equations, showing some new features.

A new technique for evaluating the critical exponent $\eta$, which governs the rate of decay of the pair-correlation function with distance at the critical temperature, is described. In this method, $\eta$ is obtained from plots of the reciprocal of the intensity as a function of the square of the scattering angle in the inner part of the small-angle scattering curve. The new procedure has the advantage of making use of the data at scattering angles at which the intensity is relatively high and thus is quite insensitive to effects which may distort the scattering curves. For argon, the value $\eta =0.03\mathrm{}\pm 0.02$ is obtained. The analysis of the scattering data also provides evidence for the need for corrections to the limiting scaling behavior which fluids exhibit very near the critical point.

The intensity distributions of rotational lines of the ${\mathrm{H}}_2^{+}$ photoelectron spectrum (Hei) were obtained using a high-resolution photoelectron spectrometer ($\Delta E=13\mathrm{}$ meV) and the deconvolution technique. The ratios of the intensity of the lines for the $(J^{\prime },J^{\prime \prime })=(0,0), \mathrm{}(2,2), \mathrm{and} \mathrm{}(3,3)\mathrm{}$ transitions to the intensity of the line for the $(J^{\prime },J^{\prime \prime })=(1,1)\mathrm{}$ transition were measured as a function of the vibrational quantum numbers ($v^{\prime }$) and found to be almost independent of $v^{\prime }$. It is observed that the ratio of the total intensity of the line with $\Delta J=2\mathrm{}$ to that with (1,1) decreases as $v^{\prime }$ becomes larger in agreement with the theoretical calculation. The rotational constants of the ground state of ${\mathrm{H}}_2^{+}$ obtained in the present experiment agree with previously reported data.

Measurements are reported for the Cs $nf-ng$ ($n=15-17\mathrm{}$) intervals by a microwave resonance technique. From the centers of gravity of the $n=15-17\mathrm{}$ $f-g$ intervals and previous measurements, values for the effective ${\mathrm{Cs}}^{+}$ dipole and quadrupole polarizabilities are determined. The observed inverted fine-structure intervals of the $f$ states are consistent with earlier measurements, and the $g$ fine-structure intervals are no larger than hydrogenic in magnitude.

The homogeneously broadened linewidth of OH due to collisions with water molecules was found to decrease with increasing rotational excitation, and tended to level off to a constant value. This observed dependence is a manifestation of the rotational distribution of the water molecule through rotational transitions in near resonance with those of the OH. The constant value at high rotational excitation reflects the nonresonant contributions to the homogeneous linewidth similar to those due to nonpolar molecules.

A precision measurement of the $1S$ Lamb shift of atomic hydrogen and deuterium, using high-resolution laser spectroscopy is reported. The $1S-2S$ transition was observed by Doppler-free two-photon spectroscopy, using a single-frequency cw dye laser near 4860 Å with a nitrogen-pumped pulsed dye amplifier and a lithium formate frequency doubler. The $n=2-4\mathrm{}$ Balmer-$\beta$ line was simultaneously recorded with the fundamental cw dye-laser output in a low-pressure glow discharge, using sensitive laser polarization spectroscopy. From a comparison of the two energy intervals a ground-state Lamb shift of 8151±30 MHz has been determined for hydrogen and 8177±30 MHz for deuterium, in agreement with theory. The same experiments yield a tenfold improved value of the $1S-2S$ isotope shift 670992.3±6.3 MHz and provide the first experimental confirmation of the relativistic nuclear recoil contribution to hydrogenic energy levels.

An electronic Hamiltonian appropriate for describing core-hole processes is derived and its properties are discussed. Based on this Hamiltonian a many-body theory is presented, and a useful linked-cluster theorem is proven. A distinction between relaxation and correlation terms can be made in each order of the perturbation expansion. Under certain well-defined conditions the core-ionization process can be visualized as a Franck-Condon transition between two multidimensional potential-energy surfaces in an abstract bosonic space. The corresponding approximation, the boson approximation, is discussed and applied to the water molecule.

Local approximations to interelectronic exchange are tested by comparing frozen-core relativistic Hartree-Fock calculations with relativistic model-potential results. The calculations are identical except in the treatment of exchange. Two new local approximations are suggested which appear significantly better than the usual Slater-type potential at reproducing effects of exchange between core and valence electrons of atoms. Results are tabulated for average radii and one-electron energies in Ag and Rb. Errors arising from the local approximation of exchange have been reduced on the average by a factor of about 5 with no increase in the complexity of the calculations.

General formulas of the angular distribution and spin polarization of photoelectrons are derived for arbitrarily polarized incident photons including all multipole effects of the photon fields. Dynamical parameters are given in terms of reduced matrix elements suitable for a general multichannel theory in both the relativistic and nonrelativistic formulations. Low-energy photoionization processes, where the electric-dipole approximation is valid, are dealt with in detail. Simple explicit formulas of the angular distribution and spin polarization of photoelectrons are given for closed-shell atoms. Applications of the present formulation using various relativistic multichannel theories are discussed briefly. A relativistic version of the $K$-matrix method, by which both closed- and open-shell atoms can be treated, is also given.