Analytical expressions for the forward elastic-scattering amplitudes for electrons and positrons scattered by hydrogen and helium atoms are developed. The expressions are employed to recalculate total cross sections in the intermediate-energy range (50-1000 eV). The present values are consistently lower than those obtained by the eikonal-Born series (EBS) method and are in better agreement with the experimental data.

The vibrational distribution of the $B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state of ${\mathrm{N}}_2^{+}$ produced in collisions of ${\mathrm{He}}^{+}$ and ${\mathrm{N}}_2\left(X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$ is calculated using a simple moving-wave-packet model. The results agree very well with the experimental data over the entire accessible range of ${\mathrm{He}}^{+}$ velocity (${10}^5$ - ${10}^8$ cm/sec).

Variation of the ratio of partial photoionization cross sections $R=\frac{\sigma \left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)}{\sigma \left({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)}$ and the asymmetry parameter $\beta$ have been determined in the region of the $4s4p^{6}5p$ resonances in krypton and $5s5p^{6}6p$ resonances in xenon. In both cases these resonances are affected by the interaction with a configuration involving two excited outer $p$ electrons. This admixture influences the number of resonances present, and the value of $\beta$ and $R$. Large variations in $\beta$ and $R$ are observed in the region of these resonances.

The recombination of atomic hydrogen to form ${\mathrm{H}}_2$ in its electronic ground state $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ via a Raman light-scattering process is considered. A rate coefficient is obtained in two approximations. For wavelengths of light much above that of Lyman $\alpha$, the polarizability theory is used to compute a recombination rate coefficient, which amounts to ≅ ${10}^{-39\mathrm{}}$ ${\mathrm{cm}}^6$/s at a wavelength of $\lambda =2000\mathrm{}$ Å and features a $\frac{1}{{\lambda }^4}$ dependence. For wavelengths approaching that of Lyman-$\alpha$ a sum over states, suitably truncated, is used. For wavelengths from 1220 to 1600 Å, where resonance behavior occurs, values for the rate coefficient of ≅ ${10}^{-34\mathrm{}}$ ${\mathrm{cm}}^6$/s and greater are obtained nearly independent of temperature (100- 10 000 K).

The $3d^8-3\mathrm{}{d}^{7}4p$ transitions in Zn V have been studied using spectrograms obtained on 2-, 3-, and 6.60-m grazing incidence spectrographs. The source used was a low-inductance-triggered spark. All levels of the $3d^8$ configuration and 93 of 110 levels of the $3d^{7}4p$ configuration have been established. The energy parameters obtained from least-squares-fit calculations and Hartree-Fock calculations in the Ni III-to-Ge VII isoelectronic sequence are compared. Two-hundred and sixty-six (266) lines have been classified in the region 260-385 Å.

The degree of polarization of a target ion excited by (inner-shell) photoionization is shown to depend on only two parameters in Dill's angular-momentum-transfer formalism. The measured alignment of ${\mathrm{Cd}}^{+}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2},\frac{3}{2}}^{}{}_{}{}^{}$ is corrected for unresolved hyperfine structure, showing that anisotropic electron-ion interactions are substantially stronger than previously thought.

The problem of resonance Rayleigh scattering by an atom in an intense laser beam, whose bare spectrum consists of one discrete fundamental state and an excited continuum of states, is studied with the use of the density-matrix formalism. Evolution equations for the density-matrix elements are solved, leading to the determination of the populations of the atom in the discrete state $|g〉$ in the presence of $n$ laser photons, and to the calculation of the dipole-moment correlation function. The importance of cascade effects is discussed. The emitted spectrum is calculated and its dependence on the intensity of the laser beam and on the frequency of the incident photons is studied.

Photoionization cross sections for the $4d^{10}$ subshells of Ba and ${\mathrm{Ba}}^{2+}$ have been calculated in the Hartree-Fock approximation with and without inclusion of relaxation effects. Use has also been made of the geometric mean between length and velocity results. The present calculations are compared with previous calculations and with results of experiments.

Resonantly enhanced multiphoton ionization (MPI) and third-harmonic generation (THG) have been concurrently studied in the rare gases, xenon, krypton, and argon. The disappearance with increasing pressure of the MPI signals resonant with the three-photon allowed $6s$, $5s$, and $4s$ states, respectively, of the rare gases is linked to the appearance of THG. Conversely, THG is shown to be partially quenched at certain wavelengths by one- and two-photon absorption leading to ionization.

Stark broadening of $6s-6p$ and $5d-6p$ singly ionized xenon lines is measured as a function of electron density $6\le N_e\le 18\times {10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in a gas-driven shock tube. Doppler and resonance broadening, and radiative trapping, are negligible at $10.2\le T\le 12.4\times {10}^3$ K and $2\le N_{\mathrm{Xe}}\le 8\times {10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Results are compared with theoretical predictions and with trends in the broadening of ions in the homologous structure sequences: Ne II, Ar II, Kr II, Xe II and Mg II, Ca II, Sr II, Ba II.

Discontinuities resulting from the simultaneous creation of two electronic vacancies in the $L$ atomic shells of praseodymium and samarium were observed in the x-ray absorption spectra of these elements. These discontinuities were identified as being the results of the double excitations ($2s^{-1\mathrm{}}+2\mathrm{}{p}_{\frac{1}{2}}^{-1\mathrm{}}$), ($2s^{-1\mathrm{}}+2\mathrm{}{p}_{\frac{3}{2}}^{-1\mathrm{}}$), and ($2p_{\frac{1}{2}}^{-1\mathrm{}}+2\mathrm{}{p}_{\frac{3}{2}}^{-1\mathrm{}}$), and their measured energies were found to be in good agreement with the results of relativistic Hartree-Fock-Slater calculations. The magnitude of these discontinuities, although difficult to determine, is about fifty times smaller than the magnitude of the discontinuity at the $L_3$-absorption edge of the element.

Wave functions of doubly excited states ${}_{}{}^2{}_{}{}^{}S$, ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}P$, ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}D$ of the $n=2\mathrm{}$ shell of ${\mathrm{He}}^{-}$ are studied in hypersherical coordinates. The interaction between the outer electron pair and the ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ open-shell core is treated by imposing boundary conditions at the core's surface and by spin recoupling. Adiabatic potential curves and the corresponding eigenvectors are studied as functions of the hyperradius $R$. Complex effects of channel couplings are analyzed, particularly for the ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ states. Resonant "free-free" radiative transitions ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ and ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}\to {}_{}{}^4{}_{}{}^{}P$ are calculated and analyzed into contributions from the dipole operator at different $R$.

Theoretical curves for the Goos-Hänchen shift of a well-collimated beam of polarized radiation at an interface where the reflecting medium possesses nonzero extinction are presented. Under certain circumstances the beam shift can be negative and several wavelengths in magnitude.

We analyze the excitation by an electromagnetic wave of a two-level molecule (or atom) within a rarefied gas. This process differs from the excitation of an isolated molecule because there is significant interaction between the molecule and the surrounding gas particles as they are all polarized by the electromagnetic wave. These interactions lead to corrections to the recoil and Doppler shifts of the molecule's transition frequency. We propose an experiment using saturation spectroscopy to observe sodium molecular transitions near the atomic $D$ lines which could easily detect the correction to the first-order Doppler shift caused by the interaction between the sodium molecules and the surrounding atomic vapor.

The absolute cross section of atomic lithium has been measured in the spectral range from 175 to 110 Å thus extending previous work to shorter wavelengths. Good agreement is found with theoretical predictions. The autoionizing-resonant-structure excitation between 176 and 160 Å has been measured and line-profile parameters obtained for several of the resonances. The resonant structure for core excitation associated with $N=3\mathrm{}$ and $N=4\mathrm{}$ principal quantum numbers is found to bear a close relationship to the analogous excitations in helium. A new classification of the resonant structure is given and comparisons made with theoretical results. A discussion of the total oscillator strength for $K$-shell excitation in lithium is given and the results obtained from the present and previous work are compared with the Thomas-Reiche-Kuhn sum-rule value.

The fluorescence emitted by atoms whose excited states have Zeeman structure is studied for the case of excitation by partially coherent optical sources whose amplitudes are weakly modulated at a low frequency $\Omega$. The temporal fluctuations in lasers are taken into account exactly by using the phase-diffusion model of the laser. Analytical results for the modulated fluorescence are presented for the case of weak fields. It is shown that the shape of the fluorescent signal is extremely sensitive to the bandwidth of the field; for example, one gets resonances at a Larmor frequency equal to $\mathcal{s}=\frac{\pm \Omega }{2}(0,\pm \Omega )$ for broadband (monochromatic) fields. Various limiting cases are treated, and in the limit of very broadband fields, results reduce to those of Corney and Series. The fluorescence is studied both as a function of the modulation frequency and as a function of the magnetic field. Numerical studies of the modulated Hanle signals in intense fields reveal resonant structures in the modulation-frequency scan at $\Omega =0,\pm {\alpha }_0$, $\pm 2{\alpha }_0({\alpha }_0^2={\mathcal{s}}^2+2\mathrm{}{\alpha }^2)$ due to the dynamical Stark splitting of the various energy levels, with the strength of the resonances depending on the direction of detection.

A graphical procedure is presented for evaluating each term in the equation satisfied by the first-order transition matrix for an arbitrary (open-shell) atom. For those terms involving the interaction of excited virtual pairs of electrons with the ionic core, we introduce the approximation that there is no exchange of orbital or spin angular momentum with the ionic core. This approximation is shown to lead to the random-phase approximation (RPA) equations in the closed-shell-atom case; we use it to define the RPA for open-shell atoms. The single equation satisfied by the first-order transition matrix is used to obtain a set of $N+N^{\prime }$ coupled differential equations for $N$ final-state radial functions and $N^{\prime }$ initial-state radial functions, which together, completely determine the first-order transition matrix for an atomic system having $N$ final-state channels. (The relation of $N^{\prime }$ to $N$ depends on the particular atom studied). The $N+N^{\prime }$ differential equations are shown to reduce to familiar forms in the following cases: (1) When initial-state correlations are ignored, one obtains the close-coupling equations and (2) when closed-shell atoms are considered, $N=N^{\prime }$ and one obtains the $2N$ coupled differential equations of the Chang-Fano version of the RPA. Finally, our RPA first-order transition matrix is used to evaluate the matrix element of the electric-dipole operator for an arbitrary (open-shell) atom. These RPA electric-dipole transition matrix elements may be used to calculate nonrelativistically all experimentally observable quantities resulting from a single-electron atomic photoabsorption process.

The structure of the hydrogen Balmer-alpha line emission profiles from three types of neutral-beam-injector ion-source plasmas [filling pressure ∼10 mTorr, electron density ∼(1-2)×${10}^{12}$ ${\mathrm{cm}}^{-3\mathrm{}}$, electron temperature ∼2-4 eV] is studied with the aid of a simple model for the neutral-particle balance and ${\mathrm{H}}_{\alpha }$ emission. This model includes molecular and atomic reactions, wall interactions, and nonthermal electrons. A large fraction of the ${\mathrm{H}}_{\alpha }$ is produced by dissociative excitation of ${\mathrm{H}}_2$ and dissociative recombination of ${\mathrm{H}}_2^{+}$, while the remainder is produced by excitation of H atoms, most of which have energies that are close to the characteristic ${\mathrm{H}}_2$ dissociation energies. The ${\mathrm{H}}_{\alpha }$ linewidth is thus insensitive to the discharge operating conditions and equals ∼0.27 Å when only slow (∼0.3 eV) dissociatively excited atoms are present or ∼0.35 Å when fast (> 1 eV) atoms, apparently also produced in dissociation reactions, are present as well.

A theory of the motion of photons in physical space is presented. Operators representing the photon density and the photon current density are defined in terms of a pair of vector field operators in much the same way as the energy density and the Poynting vector are defined in terms of the electric and magnetic fields. For polychromatic light, this theory predicts an ideal photon-counting rate which differs from that of the usual theory of photoelectron counting.

We use the eight-dimensional coherence vector $\overrightarrow{\mathrm{S}}$, recently introduced for three-level quantum systems, to derive three independent nonlinear constants of motion. Two of these were known previously, but not known to be related, and the third is new.