The problem of long-range dipole coupling of an electron to a rotating polar symmetric top molecule is investigated using a basis proposed by Engelking for near-threshold photodetachment of negative ions. Angular momentum coupling invariants are identified for the new basis and illustrate the fundamental difference of this approach from the usual fixed-nuclei approximation at higher energies. The dipole channels are found to have an intrinsic SO(4) Lie-group symmetry which simplifies the interpretation of computed channel structure. Application of second-order perturbation theory leads to estimates of the new channel invariant, which predict a leading-order threshold scaling law $\sigma \simeq k^x$, with $x<\mathrm{}1\mathrm{}$ for a molecular dipole moment $\mu <{\left[\frac{3J(J+1\mathrm{})\mathrm{}}{8K^2}\right]}^{\frac{1}{2}}$. In cases where the total angular momentum of the system is equal to the angular momentum of the molecule ($J$), the dipole coupling becomes identical to that predicted for $S$-wave doubly excited states of two-electron atoms.

The effect of $K$, $\Lambda$, or $\Omega$ doubling on the threshold scaling is examined for molecular photodetachment. Anomalous power-law scaling, observed for molecules possessing internal angular momentum about the dipole axis, is found to break down on an energy scale comparable to that of the rotational doubling that quenches this internal angular momentum. The case of OH in $J=\frac{1}{2}$, $\Omega =\frac{1}{2}$ is examined by explicit calculation.

Differential cross sections $\frac{d^2\sigma }{d{E}_{e}d{\Omega }_e}$ of the $\delta$-electron emission from superheavy quasiatoms formed during heavy-ion collision of the systems Br on Pb and Br on U were measured for beam energies of 3.88 and 4.66 MeV/u. These cross sections were compared with the available theoretical results. Binding-energy differences of $K$- and $L$-shell electrons of the quasiatoms are extracted from the differential cross sections and compared with theoretical values. The measured angular distribution of $\delta$ electrons emitted from the collision system I on Pb at a beam energy of 4.0 MeV/u shows a clear isotropic behavior.

Ionization cross sections, differential in the energy of secondary electrons, are presented for high-energy electrons incident on helium, neon, and argon. The results are based on Bethe's theory for inelastic scattering of fast charged particles using photoabsorption data and proton-impact differential ionization cross sections to determine the coefficients of this asymptotic expansion of the first Born approximation. The model cross sections are compared with experimental data for primary-electron energies between 100 and 5000 eV.

$K$-shell ionization probabilities $P_K$ in 0.6-2-MeV $p+\mathrm{Cu}$, $p+\mathrm{Mo}$, and $p+\mathrm{Ag}$ and 0.92-2.56-MeV/amu O+Cu, O+Zr, O+Ag, and O+Pb collisions were measured at scattering angles $\theta$ between 9° and 125°. Large-solid-angle, plastic-scintillator detectors were used to detect scattered particles. The measured ionization probabilities were fitted to the expression $P_K\left(\theta \right)=A(1+Bcos\theta )$. Factors affecting values of $B$ in various theories of $K$-shell ionization are discussed. The measured $B$ values are compared with two models: an atomic model which approximates the electronic wave functions with atomic united-atom wave functions centered on the heavier nucleus and a molecular model which uses atomic wave functions of varying charge and center, optimized by minimizing the electronic energies. The present data agree best with the atomic model for proton collisions and the molecular model for oxygen collisions.

Charge-transfer cross sections for ${\mathrm{He}}^{2+}$ and ${\mathrm{Li}}^{3+}$ colliding with H, He, Li, Be, B, C, Ne, Na, Mg, Ar, K, Ca, and Cs have been calculated using the Landau-Zener model over the velocity range ${10}^7$-${10}^8$ cm/sec. In these collisions, electron capture occurs predominantly into excited states of the product ion, ${\mathrm{He}}^{2+}$ or ${\mathrm{Li}}^{2+}$. Laser-gain calculations have also been made for consideration of a possible short-wavelength laser.

Experimental cross sections are reported for single-electron capture by protons, ${\mathrm{He}}^{+}$ and ${\mathrm{He}}^{2+}$ ions from lithium at projectile energies between 0.257 and 8.2 keV. For proton projectiles the results are in agreement with recent theoretical predictions from both molecular- and atomic-orbital expansions, as well as with older data. For ${\mathrm{He}}^{2+}$ projectiles the results are in agreement with recent atomic- and molecular-orbital expansion results, but some disagreement is found with earlier experimental and theoretical results.

Experimental cross sections have been measured for single-electron capture from Li by Ne, Ar, Kr, and Xe ions in charge states ($q$) between 2 and 10 and at projectile energies between $100q$ and $1000q$ eV. The cross sections are found to depend on the incident charge state but are nearly independent of both the projectile species and energy. Good agreement between the experimental results and those of absorbing sphere and classical barrier models is found.

The resonant charge-transfer reaction of protons on highly excited hydrogen atoms is considered by taking into account both the tunneling (under-barrier) and the over-barrier (classically allowed) electron transitions. It is demonstrated that in a wide range of variation of the reduced velocity $\tilde{v}=vn$, the classical transition mechanism is predominant. Cross-section calculations for principal quantum numbers $n$ between 10 and 50 are presented. The results for $45\le n\le 50$ are compared with the available experimental data and with other theoretical calculations.

Schwinger's variational principle is applied to low-energy electron—hydrogenlike-ion collisions in the static-exchange approximation. Wave functions, phase shifts, and quantum defects for energies near ionization thresholds are obtained. All of the integrals, including the integrals involving Coulomb Green's functions, are evaluated in closed form. When a few Slater-type trial functions are used, good agreement with the results of direct numerical integration of close-coupling equations is achieved.

We propose a new method to solve the multistate coupled equation. It overcomes the fatal defect of divergence which conventional perturbation theory has when the interaction is not small. We apply it successfully to laser-induced transition processes and obtain a total-cross-section formula.

The projection-operator formalism of Feshbach defines a separation of the $T$ matrix into a smooth background term and a resonant $T$ matrix which may vary rapidly with energy. The resonance is characterized by an unperturbed energy ${\epsilon }_d$, a width function $\Gamma \mathrm{}\left(E\right)\mathrm{}$, and a level-shift function $\Delta \mathrm{}\left(E\right)\mathrm{}$. Such a separation of the fixed-nuclei electron-molecule scattering $T$ matrix is of considerable practical relevance for the treatment of nuclear dynamics in resonant electron-molecule scattering. We present an explicit realization of the projection-operator formalism for electron-molecule scattering within the framework of the many-body optical-potential approach. In contrast to the approach of Hazi [J. Phys. B 11, L259 (1978)] which is based on the use of Stieltjes moment techniques to compute $\Gamma \mathrm{}\left(E\right)\mathrm{}$, we obtain explicitly the background $T$ matrix as well as the information on the angular distribution of the resonant scattering. The performance of the method is illustrated for the well-known 2.3-eV shape resonance in electron scattering from the nitrogen molecule. The two-particle-hole Tamm-Dancoff approximation (2ph-TDA) is adopted for the optical potential and the Schwinger variational principle is used to solve the background scattering problem. The resulting resonance parameters ${\epsilon }_d$, $\Gamma \mathrm{}\left(E\right)\mathrm{}$, $\Delta \mathrm{}\left(E\right)\mathrm{}$, and the resonant eigenphase sum are in excellent agreement with results obtained previously by Hazi using different computational methods.

We have calculated an ab initio nonadiabatic polarization potential for the $e-{\mathrm{H}}_2$ system using a procedure that is based on the variational method. The importance of various multipole contributions to this potential has been investigated and the dipole approximation found to be accurate for this system. When used in scattering calculations with accurate representations of the static and exchange components of the interaction potential, the new polarization potential is found to yield total integrated $e-{\mathrm{H}}_2$ cross sections that are in very good agreement with results of recent measurements and of optical-potential calculations.

Analytic solutions to two-state collision problems are obtained for systems in which the interaction matrix element of the Hamiltonian displays an exponential variation with time. When the difference in the diagonal matrix elements is either constant or governed by the same exponential function, exact analytic solutions can be found. When it is in the form of a constant plus an exponential term, the case of practical importance, an approximate solution is obtained based upon these exact solutions. The solution is used to calculate cross sections for fine-structure transitions in atomic collisions (Na-He, F-Xe, F-${\mathrm{H}}^{+}$).

The adiabatic-nuclei (AN) theory of nuclear excitation in molecules is critically examined for low-energy $e-{\mathrm{H}}_2$ collisions in the context of the rigid-rotor approximation. Theoretical concerns relevant to near-threshold scattering processes, where the AN theory is expected to be invalid, are discussed for rotational and vibrational excitation. A quantitative assessment of the AN theory for rotation and of an energy-modified approximation to this theory is obtained by comparison of approximate cross sections to results from laboratory-frame close-coupling calculations. The breakdown of the AN theory for rotation is found to be more severe at energies a few times threshold than was anticipated by rough qualitative arguments made heretofore.

Kinetic theory has recently been used to describe the spin dynamics associated with the stopping process encountered by highly energetic muons as they thermalize in a single-component gas. The result is a pair of rate equations that describe the dynamics encountered by the diamagnetic and paramagnetic muon species. This dynamical system has motion generated by the hyperfine interaction of the paramagnetic muon species (muonium) and by rates which are products of time-dependent rate constants for the electron-capture and -loss processes with the number density of the moderating gas. These rates are positive by definition. Using a finite-width-step-function approximation to the time dependence of the rates, analytic solutions of these equations are obtained and related to the muon spin polarization of the diamagnetic and paramagnetic species. Line shapes are obtained for the amplitudes of these polarizations as a function of the length of the charge exchange regime $t_c$. This time duration is inversely proportional to the number density of the moderating gas. The line shapes have two general features, namely, (i) they are constants when the duration of the charge exchange region is short (high-number densities), and (ii) they have resonances for long durations (low-number densities). Also, in general, the amplitudes of the "singlet" (muonium hyperfine frequency) term and the "triplet" (muonium Larmor frequency) term are not equal. Fits to the available experimental noble-gas data are presented using the rate constants and the time duration of the charge exchange region as parameters. The theoretical predictions suggest further experimental studies be made, in particular, to see whether the resonances are experimentally resolvable or not.

A theory describing the radiative decay of an autoionizing state under strong pumping by a coherent field is developed. The theory systematically takes into account the radiative decay of the unperturbed continuum. The problem at hand corresponds to the case of strongly coupled bound states decaying to electron and photon continua with the two continua also weakly coupled to each other. A master equation describing the time evolution of the atomic system is derived, and its exact solution under arbitrary initial conditions is given. The effect of radiative decay on the Fano profiles and photoelectron spectra is analyzed in detail. The time development of the system is also examined. The radiative decay of the autoionizing state and the unperturbed continuum changes the spectra in a significant way. The characteristics of the spectra are correlated with the dressed states (with complex energies) of the system. The changes in the structure of the dressed states as a function of the system parameters such as the spontaneous-emission rate and laser intensity are discussed in detail.

The fluorescence produced by an autoionizing state under strong pumping by a coherent laser field is considered. It is shown how the spectrum of emitted photons and the total number of photons are related to the two-time and single-time atomic expectation values, and explicit expressions are derived for them. Numerical results for the time development of the number of photons ejected are presented for finite times and in the long-time limit. The photon spectra are shown to exhibit ac Stark splitting of the states involved. The spectrum is a doublet for transitions to a stable final state and a triplet for transitions connected back to the initial, strongly driven state. The decay of an autoionizing state in the absence of a laser driving field is considered, and the square of the Fano $q$ value is interpreted as the ratio of two decay rates.

When excited by a microwave discharge, pairs of gaseous oxygen molecules radiate strong luminescence and display bimolecular oscillatory transitions. At low pressures the intensities of both processes have an unusual density dependence, increasing with decreasing density, indicating molecular competition between radiative and nonradiative decay schemes. The data provide the first direct observation of a weakly bound ${\mathrm{O}}_2$-${\mathrm{O}}_2$ structure.

High-resolution two-photon resonant three-photon spectroscopy was applied to investigate the 3 $\mathrm{snf}$ Rydberg series of Mg. Hyperfine-induced level shifts were detected for the ${}_{}{}^{1,3}{}_{}{}^{}F$ states of the odd isotope ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$. From these measurements the hyperfine coupling constant $a_{3s}$ of the ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}_{}^{+}{}_{}{}^{}$-ion ground state was derived.