The coupled-cluster method is used to recursively organize the calculations for nondegenerate order-by-order many-body perturbation theory. Application to correlation energy with Hartree-Fock zeroth-order state is presented. Commutator algebra is efficiently handled with the contraction theorem. When compared to standard diagrammatic methods, considerable simplifications are found beyond third order.

With the aim of high-order calculations, a new recursive solution for the degenerate Rayleigh-Schrödinger perturbation-theory wave function and energy has been derived. The final formulas, ${\chi }_{\sigma }^{\mathrm{}\left(N\right)\mathrm{}}=R^{(-\sigma )}{\Sigma }_{k=0\mathrm{}}^{N-1\mathrm{}}{\overline{\mathcal{H}}}_{\sigma +1\mathrm{}}^{(\sigma +1+k)}{\chi }^{\mathrm{}(N-1-k)\mathrm{}}$ $E^{(N+\sigma )}=〈0\left|{\mathcal{H}}_{\sigma +1\mathrm{}}^{(N+\sigma )}\right|0\mathrm{}〉+〈0\left|{\Sigma }_{k=0\mathrm{}}^{N-2\mathrm{}}{\mathcal{H}}_{\sigma +1\mathrm{}}^{(\sigma +1+k)}\right|{\chi }^{\mathrm{}(N-1-k)\mathrm{}}〉$ which involve new Hamiltonian-related operators ${\mathcal{H}}_{\sigma }^{(\sigma +k)}$ and ${\overline{\mathcal{H}}}_{\sigma }^{(\sigma +k)}$, strongly resemble the standard nondegenerate recursive formulas. As an illustration, the perturbed energy coefficients for the $3s-3d_0$ states of hydrogen in the Zeeman effect have been calculated recursively through 87th order in the square of the magnetic field. Our treatment is compared with that of Hirschfelder and Certain [J. Chem. Phys. 60, 1118 (1974)], and some relative advantages of each are pointed out.

By stereographically projecting the four coordinates which transform the hydrogen atom into a four-dimensional harmonic oscillator into a six-dimensional space, the homomorphism between SO(4,2) and SU(2,2) is explicitly demonstrated.

The WKB approximation in parabolic coordinates is used to calculate electric-field-ionization rates from $L=0\mathrm{}$ states with quantum defects. The range of applied electric field and principal quantum number have been given for which the rate formula is valid. Previous studies of field ionization of shallow impurity levels with quantum defects in solid-state systems have shown this formula to be in agreement with experiments.

A method for obtaining triply-differential cross sections (TDCS) for electron-impact ionization of atomic hydrogen in the Glauber approximation is developed. The expression for the Glauber amplitude in the present case turns out to be a simple two-dimensional integral which can be accurately evaluated. The present procedure has an advantage over the conventional partial-wave technique in calculating TDCS in that the latter requires substantial computer time where many partial waves are involved. We present numerical results for electron-impact ionization of hydrogen atoms at incident energies of 100, 113.6, and 250 eV. A comparison is made of the present TDCS with the corresponding results of the first Born approximation and experiment.

The cross section for electron photodetachment from H${\mathrm{S}}^{-}$ has been measured using an ion cyclotron resonance (ICR) spectrometer with a tunable dye laser. A cubic spline routine is employed to remove random noise from the spectrum and allows the observation of rotational effects. The structure in the spectrum is explained in terms of a model which includes the interaction of the spin, orbital, and rotational angular momenta in HS. Comparison of the theoretically constructed photodetachment cross section predicted by this model with the experimental spectrum leads to an electron affinity for HS of 2.314±0.003 eV and an estimate of the rotational temperature of the H${\mathrm{S}}^{-}$ ions in the ICR cell.

The process of spontaneous electromagnetic radiation in the reaction $A^{+}+B\to A+B^{+}+\hslash \omega$ is studied. Here $A$ and $B$ are the same kind of atoms or atoms with small differences in ionization potentials (quasiresonant case). Differential cross section, energy spectrum of the emitted photons, and total intensity of electromagnetic radiation are determined for thermal velocities of relative motion. Results are applicable in a wide range of temperatures: $500\le T\le 50000$ K. It is shown that the radiation spectrum is very broad and the radiation intensity is considerable.

The quasiclassical phase shift is identified as the generator of the classical canonical $S$ transformation. This illuminates the connection between resonances and looping trajectories and the classical meaning of the time delay and Levinson's theorem. Finally the Coulomb phase shift is derived using for the time delay a free motion with a modified time dependence.

Observations are made of dipole-quadrupole laser-induced inelastic collisions occurring during the collision of two Ba atoms. Results for both stimulated-absorption and spontaneous-emission experiments using the same collisional configuration are reported for the first time. In both experiments the interaction maximizes at the $R=\infty$ wavelength and has a full-width-at-half-maximum linewidth of ∼8 ${\mathrm{cm}}^{-1\mathrm{}}$. These results bear on the study of the interatomic potentials for colliding atoms and permit the collisional energy transfer to states hitherto inaccessible to dipole-dipole collisions.

Single- and double-electron-capture cross sections have been measured for ${\mathrm{C}}^{q+}$ with initial charges $2\le q\le 6$ and for ${\mathrm{Ar}}^{q+}$ with initial charges $2\le q\le 12$ incident on molecular deuterium gas targets. The cross sections show little dependence on the incident-ion energy for the range studied $2q-10q$ keV. The single-electron-capture cross sections do not vary monotonically with the initial charge, but show an oscillation about a mean curve, reflecting the projectile electronic structure.

The cross sections for single and multiple ionization of uranium by electron impact for energies 7.5-500 eV have been measured using a modulated crossed-beam experiment. The absolute total ionization cross section was found by comparing the cross section for ionization to the cross section for associative ionization in the reaction U+${\mathrm{O}}_2$→U${\mathrm{O}}_2^{+}$+$e$. The total ion number cross section has a maximum value of (5.8±0.9)×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ occurring at an energy of about 50 eV. The single ionization cross section has a maximum of (4.80±1.24)×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at an energy of 27±5 eV. The cross sections for higher-order ionization have values at 500 eV that are 49%, 33%, and 17% that of single ionization for $n=2, 3, \mathrm{and} 4$, respectively. These ratios are significantly higher than those for other elements for which data are available.

The influence of the energy loss of slow projectiles during inelastic collisions on the inner-shell ionization cross sections is treated analytically. The result agrees with available experimental cross sections for $K$-shell ionization by protons. Residual trends in the data may gauge the quality of wave functions employed in calculations of Coulomb ionization cross sections.

$L$-subshell ionization cross sections for free xenon atoms have been measured by electron impact at incident electron energies from about one to three times the threshold energy. Ionization cross sections for the $L1$, $L2$, and $L3$ subshells were deduced from the measured yields of characteristic $L{\gamma }_{2,3,4,4^{\prime }}$, $L{\gamma }_1$, and $L{\alpha }_{1,2}$ x rays, using known values for the fluorescence yields $w_i$, transition probabilities ${\Gamma }_{\mathrm{ik}}$, and Coster-Kronig factors $f_{\mathrm{ik}}$. The cross sections have been made absolute by normalization on the simultaneously measured bremsstrahlung intensity, using known bremsstrahlung cross sections. For the incident electron energies investigated, the subshell ionization cross sections were always larger than recently published theoretical cross sections. However, only at the lower energies is this discrepancy larger than the experimental error bars (25% to 40%).

It is shown that the quantum-mechanical problem of charged-particle scattering by a point-dipole rotor has pathological behavior at and above the critical dipole moment wherein all partial-wave components of the solution become undefined. The total elastic and momentum-transfer cross sections diverge at the critical moment, and, at energies above thresholds, scattering in inelastic channels behaves similarly. Clarifications are made of some existing contradictions in the literature on the quantum mechanics of continuum states for dipolar systems.

We have measured the beam-foil collision-induced alignment of the $3p{}_{}{}^1{}_{}{}^{}P$, $3p{}_{}{}^3{}_{}{}^{}P$, $3d{}_{}{}^1{}_{}{}^{}D$, and $3d{}_{}{}^3{}_{}{}^{}D$ states of He i for ${\mathrm{He}}^{+}$ beam energies between 30 and 1300 keV. The alignment of all four states is found to vary with beam-current density as well as energy. The number of secondary electrons emitted per incident ion, $\gamma$, has also been measured as a function of foil temperature and beam energy between 400 and 1400 keV. The rate of change of both alignment and $\gamma$ with foil temperature exhibits a general correlation. The energy dependence of alignment may be understood in terms of simple impact-excitation collisions. We also discuss our results in terms of the Kupfer-Winter surface electric-field model. The interaction between atoms emerging from the foil and slow secondary electrons is considered.

We have measured the alignment of beam-foil collision-excited states of He I produced by bombarding carbon foils of various (1.3-110 μg/${\mathrm{cm}}^2$) areal densities with beams of ${\mathrm{He}}^{+}$ and He${\mathrm{H}}^{+}$. In addition, we have measured the total light yield of several transitions in He I, He II, and H as a function of foil thickness using beams of He${\mathrm{H}}^{+}$ ions. Experiments were done with He-foil exit energies of 125, 500, 550, and 650 keV. He I alignment decreases in all cases for the thinnest foils when molecular projectiles are used. Total light intensities generally increase with thin foils (small proton-He emergent internuclear separation), but a few decrease or are independent of foil thickness. We are able to explain several features of the alignment and intensity data in terms of the formation of quasimolecular He${\mathrm{H}}^{+}$ states at or near the foil surface. Alignment reduction results from incoherent Stark mixing of the He I excited states in the field of the close proton. A calculation of the rms emergent H-He internuclear separation as a function of foil thickness and beam energy is presented.

The two-state distortion approximation and a corresponding second Born approximation are employed to calculate the $2s$ excitation cross section of the projectile ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ in ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collision process, keeping the target atom unexcited for the incident energy ranging from 30 to 4000 keV. The distortion effect in the second Born calculation is taken into consideration in the present work by retaining the couplings between the initial and the final states in the infinite summation. The present results are compared with the existing theoretical and experimental cross sections. Our calculations give results in reasonably good agreement with the many-state close-coupling calculations of Bell and Kingston, but like the existing calculation, the present results are not in good agreement with the observed results.

The differential cross section for the excitation of the hydrogen atom to the $2s$ and $2p$ states are calculated by applying the Coulomb-projected-Born (CPB) method as proposed by Geltman. The results for the excitations of the hydrogen atom for the incident proton energies of 25, 50, 100, and 150 keV and for the scattering angles $\theta$ varying from 0 to 1.5 (in ${10}^{-3\mathrm{}}$ rad c.m.) obtained by the present CPB approach are compared with the experimental observations and other existing theoretical calculations. At the incident energy 100 keV the present CPB results, except at large scattering angles, are found to be in good agreement with the observed results and are as reliable as the calculated results obtained by applying the many-state close-coupling (CC) approximation. For 50 keV and for scattering angles varying from 0.4 to 1.0 (in ${10}^{-3\mathrm{}}$ rad c.m.) the present CPB results agree with the observed data and are as reliable as the CC and the Glauber results, however with the decrease of scattering angle ($\theta \le 0.4$ in ${10}^{-3\mathrm{}}$ rad c.m.) the results obtained by the CPB method become less reliable compared to the CC or the Glauber results. At 25 keV the present CPB results for the differential cross sections underestimate the observed values throughout the angular region considered except at the large angles, where $\theta \ge 0.5$ in ${10}^{-3\mathrm{}}$ rad c.m. On the other hand, the Glauber results at this energy give quite good agreement throughout the angular region, whereas the Born results grossly overestimate the observed differential cross sections.

The use of Siegert boundary conditions in a direct solution of the Dyson equation for poles of the one-particle Green's function corresponding to resonances of the ($N\pm 1$)-particle systems is discussed and the pertinent complex pseudoeigenvalue problem is formulated as an implicit matrix eigenvalue equation. Thus the calculational setup is very similar to the methods employed in calculating atomic and molecular ionization potentials. Particular emphasis is laid upon the asymptotic expansion of the diverging Siegert orbital.

The present calculation is the first application of a Green's-function approach to resonance states based upon the direct use of Siegert boundary conditions. Consequently, the emphasis is on methodological aspects rather than the description of a great number of resonances. Of particular interest is the treatment of inner-shell vacancies and their satellites as resonance states. We have evaluated the energies and widths of one electron scattering resonance and three Auger-type resonances all of ${}_{}{}^2{}_{}{}^{}S$ symmetry.