Time-of-flight techniques have been used to investigate the electron-impact dissociation of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ in order to determine the effect of isotopic mass variation in the target molecule on the dissociative excitation process. At incident electron energies near 100 eV, the time-of-flight spectrum produced from each molecule was found to consist of atoms in the metastable $2s$ state and in high-lying, long-lived Rydberg levels. The individual time-of-flight distributions, kinetic-energy spectra, and relative differential cross sections for these two species resulting from each molecule have been measured. In several instances these results were found to vary significantly between the three isotopic forms. In particular, the kinetic-energy spectrum of the Rydberg atoms produced from dissociative excitation of ${\mathrm{H}}_2$ was notably dissimilar in shape from the corresponding distributions produced from HD and ${\mathrm{D}}_2$. Also the $2s$ and Rydberg production cross sections differed between the three molecules, being less in both cases for HD and ${\mathrm{D}}_2$ than for ${\mathrm{H}}_2$. In the dissociation of the heteronuclear HD molecule, it was found that the ratio of fast $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms to $\mathrm{D}\mathrm{}\left(2s\right)\mathrm{}$ atoms was about 1 to 1, while the same ratio comparing the Rydberg atoms was nearly 2 to 1. These differences indicate the influence of the mass variation on the position of the Franck-Condon region in the production of $2s$ atoms and on the competition between autoionization and dissociation in the formation of Rydberg fragments.

In a previous paper, the quantum number $k\equiv n+l$ was considered as an energy-ordering quantum number for the excited states of the alkali-metal atoms and the singly ionized alkaline-earth atoms. It was shown that the energy levels of the valence electron in these cases of a single electron outside a core of closed shells are energy ordered according to the values of $k$ and, moreover, within each $k$ group, there is a definite constant sequence of $l$ values for each atom or ion as the electronic energy is increased; this sequence has been called the "$l$ pattern." In the present work, these considerations are extended to 33 additional spectra of atoms and their isoelectronic ions, which possess a single ($n_{0}s$ or $n_{0}p$) electron or two electrons [${\left(n_{0}s\right)}^2$] outside of closed shells in their ground states. An additional 852 energy levels are investigated which exhibit $k$ ordering with very few exceptions. In addition, these spectra possess constant $l$ patterns, which are generally independen of $k$. Thus the statistics in favor of the $k$ ordering and the $l$ patterns now comprise a total of 1155 levels (including the 303 levels previously investigated). Also discussed are the regions of validity of $k$ ordering and hydrogenic ordering as a function of the atomic number $Z$ and the degree of ionization $Z-N$.

The magnetic susceptibility to second order in the magnetic field is calculated for the molecules ${\mathrm{H}}_2$, HF, and BH. The finite perturbation method and basis sets of gauge-invariant Gaussian functions are used.

Three-body and four-body contributions to the third-order diagrammatic perturbative energy expansion are evaluated for the electronic energy, using both the standard self-consistent-field potential $V^N$ and a modified potential $V^{N-1\mathrm{}}$ to determine the unoccupied states. The [$\frac{2}{1}$] Padé approximants to the energy are constructed and first-order perturbative wave functions are inserted into the Rayleigh quotient to yield rigorous upper bounds for the energy. The results indicate that the standard $V^N$ potential generates a more suitable virtual orbital basis for the calculations.

The dipolar and quadrupolar hyperfine coupling constants, $A$ and $B$, respectively, and the atomic $g_J$ factor have been measured for the ${}_{}{}^4{}_{}{}^{}S_{\frac{3}{2}}^{}{}_{}{}^{}$ ground state of atomic nitrogen 14. An atomic hydrogen maser oscillating at the $\Delta M_F=-1\mathrm{}$ transition in a magnetic field ranging from 0.008 to 8 G was used as a detector of transitions in both hydrogen and nitrogen. The magnetic field was calibrated by the hydrogen Zeeman transition frequency. Values of the constants were found to be $A=10450\mathrm{}929.12\left(10\right)\mathrm{}$ Hz, $B=1.27\mathrm{}\left(10\right)\mathrm{}$ Hz, and $g_J=2.002\mathrm{}134652\left(64\right)\mathrm{}$. These results are compared to current theoretical results and other experimental measurements.

The static dipole polarizability of helium atoms in the metastable $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ states has been determined by measuring the deflection of a beam of excited helium atoms that is caused by an inhomogeneous electric field of known properties. The necessary velocity distribution information is obtained from time-of-flight measurements, and a resonance quenching technique made it possible to distinguish the singlet and triplet components of the beam. The results, $\alpha \left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\right)=(44.6\mathrm{}\pm 3)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^3$ and $\alpha \left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)=(108\mathrm{}\pm 13)\times {10}^{-24\mathrm{}}$ ${\mathrm{cm}}^3$, agree with the theoretical value that has been used to calibrate earlier polarizability measurements of the alkali metals and the heavier noble gases.

Calculations of the electronic stopping power for low-velocity ($v<\mathrm{}{Z}_1^{\frac{2}{3}}{v}_0, v_0=\frac{e^2}{\hslash }$) heavy ions, based upon three models, are performed for two systems for which experimental data are available: 800-keV ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{+}{}_{}{}^{}$ ions incident on amorphous solid targets from carbon to tellurium and 100-keV ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ ions incident on amorphous targets from carbon to selenium. The results of the models are compared with each other and with the experimental data. The models are found to offer qualitatively better fits to the oscillatory experimental data than the smooth curves of the Lindhard-Scharff theory, with a particular modification of the Firsov theory favored for predictive calculations. All the models, as implemented here, required a parameter to be determined by fitting the calculated curves to the experimental points.

Ab initio calculations of radiative charge-transfer rate coefficients are described for ${\mathrm{C}}^{++}$, ${\mathrm{C}}^{+++}$, and ${\mathrm{N}}^{++}$ ions in collision with atomic hydrogen at temperatures up to ${10}^5$ K. The rate coefficients increase slowly with increasing temperature and attain values between 2 × ${10}^{-14\mathrm{}}$ and 6 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$${\sec }^{-1\mathrm{}}$ at ${10}^4$ K.

Cross sections, differential in emission energy and angle, have been measured for the ejection of electrons in collisions of ${\mathrm{H}}^{+}$ with argon gas targets. Incident-proton energies studied were from 5 keV to 1.5 MeV and electron emission angles ranged from 10° to 160°. Integration of the double-differential cross sections over emission angle and energy yield results in good agreement with direct measurement of total ionization cross sections. The electron distributions are compared to two plane-wave Born-approximation calculations, one using Hartree-Slater wave functions and the other using Hartree-Fock wave functions in the $3p-\epsilon d$ channel.

A Monte Carlo method is described for simulating the trajectories and annihilation of positrons in matter. The technique is applied to the calculation of annihilation spectra of slow positrons in helium gas at several temperatures and with various assumed distributions for the initial positron momenta. The results obtained are essentially independent of the initial momentum distribution and are in excellent agreement with the available experimental and theoretical data. Advantages of the Monte Carlo formulation for treating a wide range of problems in positron annihilation are discussed.

Measurements of total x-ray production cross sections for ${\mathrm{Ar}}^{+}$ -Ar and ${\mathrm{Cl}}^{+}$ -Ar collisions for incident energies between 200 keV and 1.5 MeV are reported. For ${\mathrm{Cl}}^{+}$ -Ar collisions, separate argon and chlorine x-ray production cross sections are extracted. The cross sections exhibit steep increases as bombarding energy is increased. Using existing measurements of Auger cross sections, values for the mean fluorescence yields as a function of bombarding energy are deduced. The increases in the x-ray production cross sections are shown to be due primarily to changes in the mean fluorescence yields. A qualitative explanation for the observations is proposed.

Classical trajectory calculations have been used to predict the charge-transfer and impact-ionization cross sections for collisions of $A^{+q}$+H in the velocity range of (2-7) × ${10}^8$ cm/sec. The calculations employ a three-dimensional Monte Carlo approach that uses a classical description of the H atom and the Coulomb forces among all particles to obtain the cross sections. The positive ions studied include fully stripped $A^{+q}$, with $q=1-8, 10, 14, 18, 26, \mathrm{and} 36$, and partially stripped ${\mathrm{B}}^{+q}$, ${\mathrm{C}}^{+q}$, ${\mathrm{N}}^{+q}$, and ${\mathrm{O}}^{+q}$, with $q\ge 3$. The total electron-loss cross sections (sum of charge exchange and impact ionization) vary only slightly with velocity for the higher charge states and reach a value of 2 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ for ${\mathrm{Kr}}^{+36\mathrm{}}$ + H collisions. The importance of impact ionization relative to charge transfer is found to decrease with increasing $q$ in the velocity range studied. Transition probabilities versus impact parameters are presented for the ${\mathrm{H}}^{+}$ + H and ${\mathrm{Ar}}^{+18\mathrm{}}$ + H reactions. The calculations are in reasonable agreement with experimentally measured cross sections for the ${\mathrm{H}}^{+}$, ${\mathrm{C}}^{+q}$, ${\mathrm{N}}^{+q}$, and ${\mathrm{O}}^{q+}$+H systems.

Ab initio quantum calculations are presented for the ${\mathrm{H}}^{+}$-${\mathrm{H}}_2$ system at several collision energies. The correct close-coupling (CC) equations are solved within the energy-corrected rigid-rotor (ECRR) approximation for the target molecule, and inelastic integral and differential cross sections between low rotational levels are thus obtained. The relevant adiabatic potential hypersurface given by self-consistent-field, configuration-interaction computed points was used here by expanding around the center of mass a general analytic expression recently suggested by Giese and Gentry. The energy dependence of the various transitions is examined and numerical convergence effects discussed. The nature of the molecular interaction with proton projectiles is discussed from the viewpoint of its direct bearing on the behavior of the various cross sections.

Triple-differential cross sections for electron-impact ionization of helium are calculated in the distorted-wave approximation. A general distorted-wave formalism for ionization is presented for two coordinate systems—one with the $z$ axis parallel to the direction of the incident electron and one with the $z$ axis parallel to the momentum-transfer direction. Cross sections in the scattering plane are compared with experimental results and with other theoretical calculations. Cross sections out of the scattering plane are presented and spatial symmetries are discussed.

Cross sections and polarization of impact radiation have been calculated for the excitation of ${\mathrm{Be}}^{+}\mathrm{}\left(2s\right)\mathrm{}$ and ${\mathrm{Mg}}^{+}\mathrm{}\left(3s\right)\mathrm{}$ ions in collisions with ground-state He and Ne atom targets in the energy range $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=0.5-100\mathrm{}$ keV. Each ion-atom pair has been treated as a quasi-one-electron three-particle system consisting of the valence electron of the ion, the closed-shell ion core, and the closed-shell rare-gas atom. The interactions among these three have been represented by model potentials. Charge transfer and excitation of the rare-gas target atoms are neglected. We have obtained three- and seven-state (in the case of ${\mathrm{Mg}}^{+}$) close-coupling solutions to the impact-parameter equations, assuming a rectilinear trajectory for the motion of the two heavy particles. Comparisons are made of theoretical predictions based on two Bottcher-type model potentials ($V_{B1\mathrm{}}$ and $V_{B2\mathrm{}}$) and the simple Hartree-Fock frozen-core potential ($V_{\mathrm{HF}}$) for the electron-rare-gas interaction. The predictions based on $V_{\mathrm{HF}}$ agree better with experimental results than do those based on $V_{B1\mathrm{}}$ or $V_{B2\mathrm{}}$, especially in the case of ${\mathrm{Be}}^{+}$-${\mathrm{Mg}}^{+}$-He collisions.

Observations are reported of the autoionizing transitions $2s^{2}2p^6-2s2\mathrm{}{p}^6\mathrm{np}$ in neonlike Mg iii and Al iv and the similar transitions $3s^{2}3p^6-3s3\mathrm{}{p}^6\mathrm{np}$ in argonlike ions Ca iii, Sciv, Tiv, Vvi, Crvii, and Feix. These transitions are present in high-voltage spark spectra as absorption lines of varying width and shape. Both $\mathrm{LS}$-allowed and intercombination lines are present. Effective quantum numbers of the upper levels are given, with estimates of the Fano profile parameter $q$. The probable plasma configuration which produces these absorption lines is discussed.

An experiment is analyzed in which an atomic beam in a collinear, counterstreaming laser beam is deflected by an inhomogeneous dc electric field. The force acting on the translational motion of the atom is found. This describes a modification of the deflection due to the laser. The atom tends to decouple itself from the laser, but a method is suggested for a continuous recoupling. This can result in a large difference in the scattering between atoms coupled to the laser and atoms uncoupled. The applicability to isotope separation is pointed out.

The relativistic electric dipole oscillator strengths in length and velocity forms are calculated for a number of elements in the argon sequence. The transitions studied are $3p^6-3\mathrm{}{p}^5\mathrm{nd}$ $(n=3, 4)$ and $3p^6-3\mathrm{}{p}^{5}4s$. The ground state includes correlation due to the configuration $3p^{4}3d^2$ in computing $p-d$ transitions. Relativistic effects on line strengths are found to be important in the $\Delta n\ne 0$ transitions even at low $Z$. The origin of these large relativistic effects for low $Z$ in the $3p^6-3\mathrm{}{p}^{5}4l$ transitions are discussed.

Gauge properties of electromagnetic and matter fields in atomic theories are discussed. It is shown that the equality of oscillator strengths in length and velocity forms and the sum rule in the random-phase approximation are direct consequences of preserving gauge invariance in its transition amplitude. The Hartree-Fock Hamiltonian is shown to violate gauge invariance, and hence produces unequal oscillator strengths for length and velocity forms.

We present the detailed result of a calculation on two- and three-photon ionization of hydrogen and lithium based on a recently proposed calculational method. Our calculation has demonstrated that this method is capable of retaining the numerical advantages enjoyed by most of the existing calculational methods and, at the same time, circumventing their limitations. In particular, we have concentrated our discussion on the relative contribution from the resonant and nonresonant intermediate states.