An interpolation between the quadrupole and extreme relativistic electron-electron brems-strahlung contribution to the emission rate and spectra from a Maxwell-Boltzmann electron gas is carried out. These results are then added to the "exact" electron-ion results already in the literature to give the total emission for the temperature region $1 \mathrm{keV}\le k{T}_e\lesssim 0.3 \mathrm{MeV}$. It is found that quadrupole corrections are sufficient until the temperatures reach $k{T}_e\simeq 100$ keV. At higher temperatures all multipoles must be included in order to describe the emission accurately.

Self-induced transparency has been studied in detail experimentally for a simple two-level atomic absorption. A Hg II laser pulse is used at resonance with the $D_1$ line of Rb. This system eliminates many previous experimental problems such as nonuniform wave fronts and degenerate off-resonant absorbers. Nonlinear transmission, pulse delays, pulse breakup, peak amplification, incoherent-decay effects, off-resonance effects, and focusing effects have been observed. Quantitative comparison with theory is obtained by computer solutions which include the incoherent decay and optical-pulse shapes of the Hg-Rb system. Good agreement is obtained with the theory of McCall and Hahn. Pulse compression by an order of magnitude is obtained by focusing in the resonant absorber. The theory predicting preferred pulse widths and velocities proposed by Davidovich and Eberly is discussed and found inappropriate for the Hg-Rb and other similar systems.

A computation of the probability per unit path per photon for an arbitrary number of photons to be emitted or absorbed by an electron passing through the field of an ion is presented. The results provide a qualitative estimate of the conditions for the onset of nonlinear processes.

A method is presented to remedy the defects of the projection-operator technique for calculating electron resonances in scattering from many-electron targets. Specifically it is shown that if the projection operator (i.e., idempotent) $Q$ is replaced by a quasi-projection operator $\hat{Q}$ such that $\lim \hat{Q}\Psi =0\mathrm{}$ as any ${\mathcal{r}}_i\to \infty$, then the spectrum of $\hat{Q}H\hat{Q}$ is discrete, and can be made to be in essentially a unique correspondence with resonance energies. Relaxation of the idempotency requirement allows us to define two forms of $\hat{Q}$ operator. The simpler of the two forms is tested on $e$-H and $e$-${\mathrm{He}}^{+}$ systems; the two lowest resonant energies differ by less than 0.01 eV from rigorous $\mathrm{QHQ}$ results. For many-electron targets it is further argued that replacement of the exact target eigenfunction (${\varphi }_0$) by reasonable approximations (${\tilde{\varphi }}_0$) in constructing $\hat{Q}$ will affect neither the discreteness of the spectrum $\hat{Q}H\hat{Q}$ nor the proximity of its eigenvalues to the resonant energies. Calculations of ${\mathrm{He}}^{-}$ using two different (open and closed shell) ${\varphi }_0\text{'}\mathrm{s}$ and an angle-independent total wave function as well as a configuration-interaction wave function containing up to 40 configurations are carried out. The difference between open- and closed-shell ground-states results is about 0.02 eV, and the latter yields $E_{\mathrm{res}}\left({}_{}{}^2{}_{}{}^{}S\right)=19.363\mathrm{}$ eV plus a width $\Gamma =0.014\mathrm{}$ eV. No other resonances are found below the first excited ($2{}_{}{}^3{}_{}{}^{}S$) He threshold.

A transmission experiment is used to observe structure in the total electron-impact cross section for He, Ne, Ar, Kr, and Xe below the respective ionization potentials, and also in the region of autoionizing states. The positions of the resonances are tabulated and compared with the results of other investigators. In both neon and argon, relatively large isolated resonances exist near the edge of the Rydberg series involving inner-shell autoionizing states, i.e., near 47.5 and 29 eV, respectively.

The $L>\mathrm{}0\mathrm{}$ phase shifts ${\delta }_L$ for low-energy scattering by a van der Waals ${\mathcal{r}}^{-6\mathrm{}}$ potential are calculated using the two-potential formula of scattering theory. We calculate ${tan\delta }_L$ up to and including the $k^{2L+5}\ln k$ term. We compare our results with those obtained using the Born approximation.

Absolute cross sections are reported here for the ionization of K atoms having laboratory energies in the range 20-1000 eV when interacting with ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and CO molecules. The range of energies covered, $E$, and the corresponding cross sections ${\sigma }_{01}$ for each of the four target species are as follows: for ${\mathrm{O}}_2$, $20<E<\mathrm{}1000\mathrm{}$ eV, $8\times {10}^{-19\mathrm{}}<{\sigma }_{01}<1.1\mathrm{}\times {10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$; for ${\mathrm{N}}_2$, $50<E<\mathrm{}1000\mathrm{}$ eV, $2.5\times {10}^{-19\mathrm{}}<{\sigma }_{01}<4\mathrm{}\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$; for CO, $100<E<\mathrm{}1000\mathrm{}$ eV, $2\times {10}^{-19\mathrm{}}<{\sigma }_{01}<2.3\mathrm{}\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$; for ${\mathrm{H}}_2$, $150<E<\mathrm{}1000\mathrm{}$ eV, $6\times {10}^{-20\mathrm{}}<{\sigma }_{01}<8\mathrm{}\times {10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$.

A study has been made of the charge-transfer processes whereby neutral atoms of hydrogen are formed in the $3s$, $3p$, and $3d$ states as a result of the impact of protons on targets of helium and argon. Impact energies range from 75 to 400 keV. The experimental procedures involve the quantitative measurement of the Balmer-$\alpha$ radiation emitted by the spontaneous decay of atoms in these three states. The contributions of the three different states are separated by a time-of-flight technique that utilizes the different lifetimes of these states. The cross sections decrease rapidly with increasing energy and are greatest for the state of lowest angular-momentum quantum number. For a helium target, comparisons are made with a Born-approximation prediction; there is a marked discrepancy between theory and experiment for the $3p$ level but good agreement for the $3s$ and $3d$ levels.

An experimental study is made of the cross sections for forming fast hydrogen atoms in the $3s$, $3p$, and $3d$ states by charge-transfer neutralizations of ${\mathrm{H}}^{+}$ as it traverses molecular targets. The formation of excited hydrogen is detected by a quantitative measurement of collisionally induced Balmer-$\alpha$ emission; the contributions from the $3s$, $3p$, and $3d$ levels are separated by a method that utilizes the different lifetime of the excited states. Proton-impact energies range from 75 to 700 keV; targets include ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, NO, ${\mathrm{O}}_2$, CO, C${\mathrm{O}}_2$, C${\mathrm{H}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_6$, and ${\mathrm{C}}_3$${\mathrm{H}}_3$. Cross sections decrease rapidly with impact energy; the $3s$ cross section was always largest followed by the $3p$ and $3d$. There was no convincing evidence for a general additive rule whereby cross sections could be assigned to the individual constituent atoms of the molecule and then used to predict cross sections for complex molecules.

The collisional dissociation of 75- to 700-keV ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$ by impact on targets of He is studied. The formation of excited hydrogen is detected by quantitative measurement of collisionally induced Balmer-$\alpha$ emission; the contributions from $3s$, $3p$, and $3d$ levels are separated by a method that utilizes the different lifetime of the excited states. Cross sections are almost the same for each of the $3s$, $3p$, and $3d$ states; they vary slowly with projectile energy.

The exponential repulsion between atoms, molecules, and ions with closed-shell structure arising from the Pauli exclusion principle is examined in the light of a distortion model. The repulsion energy arises mainly from the distortion of the two atoms, each of which is constrained by the presence of the other to terminate at an intermediate surface, which is often approximately planar. The location of this surface is determined by minimizing the total distortion energy, with the result that the restoring forces in each atom are equal and opposite. There results a new combining rule for these repulsive potentials, allowing the potential for $\mathrm{AB}$ to be deduced from those for $A_2$ and $B_2$, which reduces in some special cases to the previously assumed geometric-mean rule. A further consequence is a relationship between the instantaneous collisional dipole moments in a family of asymmetric collisions such as HeNe, NeAr, and ArHe, provided that they are all measured at equal values of the collision force.

By using relativistic Hartree-Fock equations which automatically take the spin-orbit interaction into account, we calculate the single-particle states for photoejected electrons from heavy alkali-metal atoms. We derive an expression for the perturbation function $x$. Our results are in fair agreement with the experiments, but more accurate calculations including electron correlations are desirable.

A general procedure is formulated by which the hierarchy of many-particle scattering equations of the Faddeev types can be reduced systematically to matrix equations of lower dimensions. As illustrations, such reduced sets are derived explicitly for the three-particle system by rearranging different components of the total Green's function. The resulting equations iterate with connected kernels only in the explicit channels. Using the reduction method, the connection between the various versions of scattering equations derived earlier have been exhibited. The effect of implicit channels may be taken into account noniteratively using the channel projection operators. It is also shown that an arbitrary set of distortion potentials may be introduced for the purpose of minimizing the coupling between the rearrangement channels, thus improving the convergence of the multiple-scattering series.

Measurements are reported of the cross sections for photodissociation of ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ at 21 wavelengths ranging from 2472 to 13 613 Å. The measurements are compared with theory using normalized Franck-Condon factors for the vibrational populations of the ions. Deviations are found, which are interpreted as a failure of this latter approximation. A least-squares analysis of the data yields vibrational-state populations different from simple Franck-Condon factors and alleged to be those characteristic of high-energy electron-impact ionization of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. Interpretation of the data using a mechanism requiring that a fraction of the ions formed by electron impact be generated via the autoionization channel can qualitatively lead to the observations of this experiment. However, such an explanation would require about $\frac{2}{3}$ of all ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$ to be formed via autoionization—a seemingly unrealistic requirement. Interpretation of the data in terms of a variation with internuclear separation of the electronic matrix element involved in the electron-impact ionization process shows that a matrix element varying as $Q_e\left(\mathcal{r}\right)=1+0.56\mathrm{}{({\mathcal{r}}_{\mathrm{a}.\mathrm{u}.\mathrm{}}-0.99)}^2$ can lead to the experimentally deduced populations of both ${\mathrm{H}}_2^{+}$ and ${\mathrm{D}}_2^{+}$. This latter interpretation is favored, though one cannot rule out the former or some combination of the two. The data and interpretation are consistent with other related experiments.

The contribution of the ${\mathrm{N}}_2\left(E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$ state to the total metastable excitation function of ${\mathrm{N}}_2$ was assessed on the basis of previous time-of-flight studies of metastable nitrogen molecules. As a result, the cross section for electron-impact excitation of the ${\mathrm{N}}_2\left(E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$ state was determined in the domain of the resonance from threshold (11.87 eV) to an energy of about 13 eV. The maximum value of the cross section was found to be about 7×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at an energy of 12.2 eV. The measurement was made absolute by using the previously determined yield of the metastable detector, the lifetime of the $E$ state and eliminating the energy spread in the electron beam from the primary data. The half-width (full width at half-maximum) of the resonance like excitation function near threshold was found to be about 0.4 eV. No substantial evidence was obtained from the present data for the presence of the nonresonant part of the excitation function for the $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state.

Relativistic calculations of the elastic differential cross sections for mercury at 46, 79, and 100 keV are performed using a Liberman (Hartree-Fock-Slater) potential. Various approximations for the exchange of incident and atomic electrons are considered. These calculations explain previous discrepancies between theory and experiment at higher angles.

The thermal-average cross section $\lambda$ for shifts of the ground-atomic-state hydrogen hyperfine transitions caused by electron spin-exchange collisions between radiating hydrogen atoms has been measured at 308°K by two related techniques using atomic-hydrogen masers. The result is $\lambda =+(4.1\mathrm{}\pm 1.0)\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ and is consistent with calculations relating the hydrogen interaction potentials to the atomic-hydrogen-maser oscillation frequency to within this 70% confidence limit.

The total cross section for ${\mathrm{Li}}^{+}$-Li symmetric charge transfer is considered theoretically by an impact-parameter method using a suitable atomic wave function. This cross section exhibits oscillations and is in qualitative agreement with experimental measurements and other theoretical results based on a simplified two-state theory.

Absolute cross sections have been measured for the production of hydrogen atoms in the metastable $2s$ state by fast (20- to 120-keV) ground-state hydrogen-atom impact on He, Ne, Ar, and ${\mathrm{N}}_2$. The shape of the excitation curve for impact on He is not reproduced by the Bornwave calculation of Levy although the theory curve intersects the experimental curve near the two energy extremes. The scaled Born curves of Levy lie below the experimental curves for impact on Ne and Ar, although there is a general agreement near 20 keV for both gases. Experimental values for the cross sections for production of the $2s$ and the $2p$ states by hydrogen-atom impact on the four gases are presented in the range of 1-120 keV by combining and weighting the data of Birely and McNeal with the present data where they overlap.

The effect of the hyperfine interaction on collisional relaxation among Zeeman sublevels is evaluated for a $J=\frac{3}{2}$ state coupled to nuclear spins of $\frac{3}{2}$, $\frac{5}{2}$, and $\frac{7}{2}$. Standard depolarization experiments, performed on atoms with hyperfine structure, are discussed in terms of relaxation-probability matrices parametrized in terms of the relative collisional-transition probabilities for a nuclear-spin-zero atom. Experimental results involving $D_2$ optical pumping of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ are shown to support the approximation of nuclear decoupling in collisional relaxation. The cross sections for electronic collisional relaxation, assuming a van der Waals model for the collisional interaction, are, in units of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$, 1.19 (${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$-He), 1.09 (${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$-Ne), 2.44 (${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$-Ar), 1.13 (${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$-He), 1.03 (${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$-Ne), and 2.26 (${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$-Ar).