Starting from a quantum-mechanical description of the total system consisting of an electron and two nuclei, the semiclassical equation for the transition amplitude between electronic adiabatic basis states is derived for the case of the Rutherford scattering. This method is then generalized to include the effect of nuclear elastic and inelastic collisions. The total transition amplitude for a reaction in which both the electron and nuclei are excited is expressed as products of three factors summed over the intermediate atomic states. Of these three factors, the first and the third are the semiclassical atomic transition amplitudes before and after the nuclear collision, respectively, and the second is the $S$-matrix element for the nuclear collision.

A theory of electron detachment in slow collisions of negative ions with atoms is developed. The theory is based on assumptions that are similar to, but more general than, the assumptions made in earlier papers: The motion of the nuclei is described semiclassically, the electronic wave function is expanded in a partially diabatic basis that includes a discrete state and a continuum, and certain couplings are assumed to be small. With such assumptions the Schrödinger equation is reduced to a nondenumerably infinite set of coupled differential equations, and then to a single integro-differential equation (an equation with "memory"). It is shown that the solution depends upon two functions, the energy gap $\Delta \mathrm{}\left(t\right)\mathrm{}$ between the discrete state and the continuum, and a propagator $\mathcal{G}(t,t^{\prime })$. General properties of the propagator are given and it is calculated for a very simple model. Formal properties of the integro-differential equation are also investigated.

Early experiments on collisional detachment of electrons from negative ions were interpreted in terms of a "local" or "static" complex potential. In the preceding paper we developed a more general close-coupling framework for describing such collisions. In this theory, the amplitude for finding the electron in the bound state $C_{-1\mathrm{}}\mathrm{}\left(t\right)\mathrm{}$ satisfies an integro-differential equation. We define an "exact" or "dynamical" complex potential $\mathcal{E}\mathrm{}\left(t\right)\mathrm{}$ such that $C_{-1\mathrm{}}\mathrm{}\left(t\right)\mathrm{}\equiv \exp \left[-i \int {t_0}^t\frac{\mathcal{E}\left(t^{\prime }\right)d{t}^{\prime }}{\hslash }\right]$. An integral equation for $\mathcal{E}\mathrm{}\left(t\right)\mathrm{}$ is derived and solved. It is found that in slow collisions, the dynamical complex potential oscillates about the static complex potential. Approximate formulas for $\mathcal{E}\mathrm{}\left(t\right)\mathrm{}$ are given.

A numerical method is developed to search the complex momentum plane for the poles of the multichannel $T$ matrix. No resonance or continuum wave functions are calculated and no complex basis functions are required. The appropriate Green's function is constructed and used to enforce the asymptotic behavior. Results are obtained for a three-state model problem and compared with results from other techniques.

Absolute cross sections for simultaneous double ionization and excitation of Ba by electron impact have been measured in a crossed-beam experiment. The lines investigated are at 74.3, 58.7, and 55.5 nm. The vacuum-ultraviolet system was calibrated using a single-ionization chamber. Absolute cross sections were derived by comparison with the known excitation function of the Ba I resonance line at 553.5 nm.

Cross sections have been calculated for electron transfer into the $1s$, $2s$, and $2p$ states and for excitation into the $2s$ and $2p$ states in collisions between 1.5—15-keV protons and hydrogen atoms The triple-center, coupled-state method of Anderson, Antal, and McElroy has been used: Bound atomic states are centered on each nucleus and on a third center (the center of charge) in order to simulate the molecular character of slow collisions. Convergence of cross sections (and molecular potential-energy curves) with respect to the size of the basis has been studied; the present basis includes up to 36 states (16 gerade, 20 ungerade states). The $1s$ capture cross section is estimated to be converged, and the $2p$ and $2s$ cross sections are estimated to be converged to about 10% and 20%, respectively. Dips are observed in the $2s$ and $2p$ excitation cross sections at about 10 keV and in the $2p$ capture cross section at about 5 keV. Results have been compared with atomic-state, pseudostate, and molecular-state results, as well as with experimental results. The results agree fairly closely with the related AO+ pseudostate results of Fritsch and Lin at the lowest calculated energy, although there are differences at higher energies. There are differences from some of the many experimental results, but overall there is agreement within the experimental error limits.

We report the results of a series of experiments investigating the nature of very-highly-excited states of fast ions emerging from thin foils. The yields of electrons produced by field ionization of these atoms are compared for different projectiles and beam energies. Various field arrangements were used. The consequences for related studies of fast-ion beams penetrating solids are discussed.

An adiabatic quantal theory of spectral line shapes in collision-induced absorption and emission is presented which incorporates the induced translation-rotation and translation-vibration spectra. The generalization to account for the anisotropy of the scattering potential is given. Calculations are carried out of the collision-induced absorption spectra of He in collisions with ${\mathrm{H}}_2$ with ab initio electric dipole functions and realistic potentials. The anisotropy of the interaction potential is small and is not included in the calculations. The predicted spectra are in satisfactory agreement with experimental data though some deviations occur which may be significant. The rotational line shapes have exponential wings and are not Lorentzian. The connection between the quantal and classical theories is written out explicitly for the isotropic overlap induction.

A light ion, incident on a heavy atom with a speed $v\gg \frac{e^2}{\hslash }$, may capture an outer electron as follows: The ion first hits the electron and knocks the electron out of the atom with a speed $v$. The ion then scatters elastically, through an angle $\theta$, from the target nucleus so as to finally move in the same direction, and with the same speed, as the emergent electron. Kinematics require that $\theta \approx 60$°. This process is analyzed both classically and semiclassically, and it is shown that the angular distribution has a sharp peak about $\theta =60\mathrm{}$°.

We measure the charge transfer cross section for protons in potassium and sodium with the final state being $\mathrm{H}\mathrm{}\left(2s\right)+A^{+}$. Using a crossed-beam experimental method we look at this cross section as a function of proton beam energy from 500 to 2500 eV. Our results for potassium agree with previous experiments and theories in showing two main peaks in the cross section: one of (3.9 ± 1.5)× ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at a proton beam energy of 800 eV, and another of (2.8± 1.1)× ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at a proton beam energy of 2.5 keV. Our results for sodium show a steadily rising cross section with a value of (7.3± 2.5)× ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at a proton beam energy of 2.5 keV in agreement with the prediction of Kubach and Sidis; we do not find the maximum at 700 eV reported by Nagata that agrees with the theory of Kimura, Olson, and Pascale.

The thermal cross sections for inelastic transfer of excited rubidium atoms from the $n{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ to the $n{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ fine-structure state caused by fine-structure-changing collisions with ground-state rubidium atoms have been measured by selective stepwise excitation of the rubidium atoms and observation of the resulting fluorescence. The cross sections (in units of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$) for $n$ being 5-9 are 2.9±0.6, 6.9±1.4, 11.5±2.3, 17.1±3.0, and 26.0±5.0, respectively. The fine-structure-changing cross sections are of the order of the geometrical cross sections and increase slightly less than ${\left(n^{*}\right)}^4$ for the low-lying $n{}_{}{}^2{}_{}{}^{}D$ states studied.

A time-dependent local-density theory of the photoemission spectra and polarizabilities of finite systems is extended from atoms to molecules. The theory is implemented in a single-center formulation and is applied to ${\mathrm{N}}_2$ and ${\mathrm{C}}_2$${\mathrm{H}}_2$. The partial photoemission cross sections and asymmetry parameters for the $1{\pi }_g$ and $3{\sigma }_g$ levels are presented as well as the optical-frequency polarizabilities; agreement with experiment is generally, but not uniformly, excellent.

Electron excitation cross sections have been measured for the following two Rydberg series of ${\mathrm{H}}_2$: ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{} 1s\sigma \mathrm{np}\sigma$ ($B$, $B^{\prime }$, and $B^{\prime \prime }$, states with principal quantum numbers $n=2, 3, \mathrm{and} 4$, respectively) and ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{} 1s\sigma \mathrm{np}\pi$ ($C$, $D$, and $D^{\prime }$ states with principal quantum numbers $n=2, 3, \mathrm{and} 4$, respectively) over the energy range from threshold to 350 eV. The cross sections for these six states account for all (>99%) of the vacuum-ultraviolet emission (78-170 nm) of the singlet states of ${\mathrm{H}}_2$. The estimated total direct-excitation cross sections for these six states at 100 eV in decreasing value are (4.02±0.60)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ (3.86±0.60)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $C{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, (0.76±0.11)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $D{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, (0.76±0.11)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $B^{\prime } {}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, (0.30±0.06)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $D^{\prime }{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and (0.23±0.05)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $B^{\prime \prime }{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and, additionally, (0.43±0.10)×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for $E$,$F{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ which populates the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state through radiative cascade transitions. We estimate the predissociation (autoionization is weak) and emission yields of the vibrational levels of the $D$, $D^{\prime }$, and $B^{\prime \prime }$ states whose band systems exhibit strong "breaking off in emission" for wavelengths below 85 nm. Furthermore, we report the first direct measurement of the dissociative excitation cross section for production of Lyman-$\beta$ of (8.9±3.0)×${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ at 100 eV. In particular, it is shown that the high-lying Rydberg states ($n=3\mathrm{} \mathrm{and} 4$) make a substantial contribution to the observed emission below 110 nm while above 110 nm the Lyman bands ($B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) and Werner bands ($C{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$), the first members of the Rydberg series, dominate the spectrum. As a result of these measurements and spectroscopic models the ultraviolet (UV) spectrum from ${\mathrm{H}}_2$ by electron impact can serve as an intensity calibration standard from 80 to 170 nm.

The radiometric force (photothermal) on a sphere is investigated theoretically in the surface-mode region ($-1>\epsilon >-2\mathrm{}$). Closed-form expressions obtained for this force in the transition regime ($K_n\sim 1$) reveal a quasi-double-resonant character, with contributions from both dipole and quadrupole surface modes. Full Mie calculations verify these asymptotic expressions and extend the range of the calculations to an optical size (the ratio of the circumference to the wavelength) near 1. Applications of the theory to surface plasmons in Ag and surface phonons in SiC show that excitation of the quadrupole mode causes a reversal in the radiometric force with a factor-of-${10}^4$ increase in magnitude. The overall force (radiometric plus radiation pressure) is evaluated, and photophoretic spectra are presented.

High-resolution spectra of the Ly-${\alpha }_1$ and Ly-${\alpha }_2$ lines of hydrogenlike titanium, Ti XXII, and the associated dielectronic satellites which are due to transitions $1snl-2pnl$ with $n\ge 2$, have been observed from tokamak discharges with auxiliary ion-cyclotron heating with central electron temperatures of 2 keV and central electron densities of 8× ${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$ on the Princeton Large Torus (PLT). The data have been used for a detailed comparison with theoretical predictions based on the $Z$-expansion method and on the multiconfiguration Thomas-Fermi—potential wave-function method (SUPERSTRUCTURE code). The predictions from the $Z$-expansion method are in excellent agreement with the observed spectral data except for minor discrepancies between the theoretical and experimental wavelengths of 0.0003 Å for the $n=2\mathrm{}$ satellites and of 0.0001 Å for the separation of the Ly-${\alpha }_1$ and Ly-${\alpha }_2$ lines. The latter discrepancy is, however, removed if the Lamb shift and relativistic effects of order ${\alpha }^4$ are taken into account. Very good agreement with the experimental wavelengths is also obtained for the results from SUPERSTRUCTURE though somewhat larger and systematic discrepancies (≃0.0009 Å) exist. The observed spectra have been used for diagnosis of the central ion and electron temperatures of the PLT discharges and for a measurement of the total dielectronic recombination rate coefficient of Ti XXII. The measured rate coefficient is in good agreement with the predictions from both the detailed calculations and Burgess's general formula.

Continuum states and bound states of the hydrogen atom in a strong magnetic field are studied for field strengths somewhat smaller than $B_0=2.35\mathrm{}\times {10}^9$ G, and for azimuthal quantum numbers up to $\left|m\right|=2\mathrm{}$. At field strengths for which the third Landau excited state in a given $m^{\pi }$ subspace with positive $z$ parity $\pi$ lies close to the ionization threshold, the width of this state is orders of magnitude smaller than might be expected from the widths of the two lower-lying Landau excited states in the respective $m^{+}$ subspace.

Using an $\mathrm{LSJ}$ coupling scheme and a configuration-interaction wave function, the relativistic energies, fine structures, and transition wavelengths of the $1s2p2p{}_{}{}^4{}_{}{}^{}P$ and $1s2s2p{}_{}{}^4{}_{}{}^{}P$ states are studied. The relativistic correction, Breit-Pauli operator, and mass-polarization correction are calculated for ions from Li I through F VII and for Mg X. Excellent agreement with experimental data is obtained in most cases. For example, the calculated transition wavelengths of Be II, B III, and C IV are 2324.96, 1701.77, and 1344.22 Å, respectively. It is to be compared with the corresponding experimental data of 2324.6, 1701.4, and 1344.2 Å. However, a few questions are raised concerning some part of the experimental data. For the fine structure of Mg X, a 5% error appears in the present calculation. The validity and limitation of the present method is also discussed.

The problem of achieving population inversion adiabatically in an $N$-level system using one or more laser fields whose detunings and/or amplitudes are continuously varied is studied analytically and numerically. The $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ coherence vector picture is shown to suggest unexpected inversion procedures and also to give a generalized interpretation of adiabatic following. It is shown that the ($N^2-1\mathrm{}$)-dimensional $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ space contains an ($N-1\mathrm{}$)--dimensional steady-state subspace $\mathit{\Gamma }\mathrm{}\left(t\right)\mathrm{}$ whose orthonormal basis vectors ${\overrightarrow{\Gamma }}_1,\dots , {\overrightarrow{\Gamma }}_{N-1\mathrm{}}$ are given explicitly in terms of the Hamiltonian matrix elements. The motion of the system can be interpreted as a "generalized precession" of $\overrightarrow{\mathrm{S}}$ about $\mathit{\Gamma }$. Multilevel adiabatic following occurs when the angle $\chi \mathrm{}\left(t\right)\mathrm{}$ between the coherence vector $\overrightarrow{\mathrm{S}}$ and its projection onto $\mathit{\Gamma }$ is very small. The multiple dimension of $\mathit{\Gamma }$ is shown to provide a variety of paths for adiabatic inversion. The adiabatic solution is obtained by solving $N-1\mathrm{}$ simple equations for the directional cosines of $\overrightarrow{\mathrm{S}}$ on ${\overrightarrow{\Gamma }}_i$. The adiabatic solution and time scale and the state taken up by the atomic variable are discussed analytically and numerically for a three-level system.

In the context of two-body bound-state systems subjected to a plane-wave electromagnetic field, it is shown that high field intensity introduces a distinction between long-wavelength approximation and electric dipole approximation. This distinction is gauge dependent, since it is absent in Coulomb gauge, whereas in "completed" gauges of Göppert-Mayer type the presence of high field intensity makes electric quadrupole and magnetic dipole terms of importance equal to electric dipole at long wavelengths. Another consequence of high field intensity is that multipole expansions lose their utility in view of the equivalent importance of a number of low-order multipole terms and the appearance of large-magnitude terms which defy multipole categorization. This loss of the multipole expansion is gauge independent. Also gauge independent is another related consequence of high field intensity, which is the intimate coupling of center-of-mass and relative coordinate motions in a two-body system.

Angular distributions of bremsstrahlung emission are calculated for various energy and angular distributions of hot electrons incident on a laser-irradiated plastic target. These theoretical results are used to interpret experimental data of x-ray continuum emission from a C${\mathrm{O}}_2$-laser-produced plasma. It is shown that at low irradiance ($I_L\le 5\times {10}^{12}$ W/${\mathrm{cm}}^2$) the incident electrons are normal to the target surface but that at higher irradiance, the incident electrons' angular distribution (spatially integrated over the target surface) is semi-isotropic. The influence of the directional distribution of hot electrons on axial energy transport is also studied by comparing calculated continum x-ray spectra as well as energy-deposition profiles with experimental results.