The profiles of He I 4471- and 4921 - Å lines and their forbidden components have been calculated for $N_e=6\mathrm{}\times {10}^{15}e$ ${\mathrm{cm}}^{-3\mathrm{}}$ and $T_e=2\mathrm{}\times {10}^4$ °K in the presence of a 70-kG magnetic field, with the aid of an extended formulation of the impact theory. In both cases, the lines exhibit important modifications, which are not shown by isolated or completely degenerate lines in similar situations.

The contribution of the hyperfine contact interaction in the iron atom has been calculated by many-body theory. Terms involving one and two Coulomb interactions have been included, and our result for the contact constant is -4.55 MHz as compared with the experimental result of -5.1 MHz obtained by Childs and Goodman. Inclusion of an approximate relativistic correction changes the calculated value to -4.87 MHz. An estimate of higher-order terms gives a theoretical result -5.35 MHz or -5.72 MHz when the relativistic correction factor is included.

The spin-optimized self-consistent-field (SOSCF) function, a product of one-electron spatial orbitals multiplied by a spin function optimized in the relevant ($S,M_S$) space, is calculated for $\mathrm{B}\left({}_{}{}^2{}_{}{}^{}P\right)$ and $\mathrm{C}\left({}_{}{}^3{}_{}{}^{}P\right)$. The energy reduction relative to restricted Hartree-Fock values is considerable and includes most of the "radial correlation energy." The hfs constants are calculated and found to be in very good agreement with experiment, where experimental values are known. The use of partial spaces for the spin-function variation is considered. The spatial orbitals are described, and as observed previously for other atoms, they possess no radial nodes.

Relaxation experiments performed on alkali atoms polarized in their ground state by optical pumping in the presence of a rare gas have been previously reported and interpreted. It was shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. The previous theoretical analysis, restricted to the longitudinal relaxation, is extended here to relaxation processes involving the transverse components of the electronic polarization and hyperfine "coherences" (elements of the density matrix between different hyperfine states). The effects resulting from the action of a rf field are also examined. The main results of this work, among others, are (a) the prediction of a Zeeman transition-line pressure shift, in some circumstances larger by several orders of magnitude than the one calculated by Herman, and having a very peculiar variation with the rare-gas pressure; (b) a quantitative explanation of the anomalous pressure dependence of the hyperfine transition linewidth discovered by Bender and Cohen; (c) a proposal of a method of detection of rf transitions between states of the alkali—rare-gas molecules by their effect on the relaxation process.

A treatment of molecular excited states in the second-quantization formalism, using the dual-space operator technique, is given. The open-shell configurations give degenerate multiplets which are easily described in what we call the occupation-branching-number representation. Equivalent monoelectronic and bielectronic operators are defined and a diagrammatic technique is developed. The method is at present restricted to molecules with Abelian symmetry groups. A linked-cluster theorem is finally proved.

From observations of the kinetic-energy distribution of protons and deuterons at corresponding forward and backward angles with respect to the electron-beam direction, the forward momentum imparted to the dissociating ${\mathrm{H}}_2$ (${\mathrm{D}}_2$) molecule by the incident electron has been determined for electron energies up to 300 eV. The momentum transfer along the beam was found to remain nearly constant at all energies above threshold, although above 100 eV the values obtained for ${\mathrm{D}}_2$ were systematically higher than the values for ${\mathrm{H}}_2$. When corrected to the center-of-mass system, the angular distribution of ${\mathrm{H}}^{+}$ (${\mathrm{D}}^{+}$) near threshold was found to contain a large isotropic component and an anisotropic component which deviates, in a manner suggested by Zare, from the ${cos}^2\Theta$ dependence predicted from a simple dipole Born approximation.

The electron excitation functions of some fifty states from the $2p^5\mathrm{ns}$, $2p^5\mathrm{np}$, and $2p^5\mathrm{nd}$ configurations have been measured by the optical method. Corrections due to cascade from the upper levels are important only for the $\mathrm{np}$ states and typically amount to 50% of the total population. The scheme of characterizing the excitation behaviors of helium by the quantum numbers $L$ and $S$ of the states can be carried over to neon if one expresses the wave functions of the excited states of neon in terms of the $\mathrm{LS}$ eigenfunctions. For example, all the optically allowed states exhibit very broad excitation functions and large cross sections, and the purely triplet states have narrow excitation functions. For the other states, the wave functions are expressible as linear combinations of those of triplet states and dipole-forbidden singlet states; hence, the excitation functions have intermediate widths. From group-theoretical arguments, we have shown that within a configuration $2p^5\mathrm{nl}$, the states with odd values of $J+l$ have larger excitation cross sections than the ones with even values. This theoretical rule has been well confirmed by our experimental data. In addition, we have deduced theoretically that $Q(J=0\mathrm{})>Q(J=2\mathrm{})\mathrm{}$ for the $\mathrm{np}$ states, and $Q(J=1\mathrm{})>Q(J=3\mathrm{})\mathrm{}$ for $\mathrm{nd}$; and in a more restricted way, that $Q(J=1\mathrm{})>Q(J=3\mathrm{})\mathrm{}$ for $\mathrm{np}$ and $Q(J=2\mathrm{})>Q(J=0,4\mathrm{})\mathrm{}$ for $\mathrm{nd}$. These relations are in good agreement with experiment with only a few exceptions. Most of the qualitative and semiquantitative features of the experimental data can be understood from generalization of the results of helium and by simple theoretical considerations. The excitation cross sections of the states with odd values of $J+l$ have been calculated by the Born approximation using atomic wave functions constructed by the Hartree-Fock-Slater orbitals, together with a semiempirical treatment of the intermediate vector coupling. The agreement between the theoretical and experimental values is generally satisfactory. The even-($J+l$) states are strongly influenced by indirect coupling; thus, no attempt was made to compare the experimental data of these states with the Born-approximation calculations.

Absolute differential cross sections for the production of electrons by collisions of neon ions with a neon-gas target and argon ions with an argon-gas target were measured. The cross sections were doubly differential in angle and energy of the ejected electrons. The energy range of the primary ions was 50 to 300 keV. Electrons that were produced by the ion-atom collisions were analyzed in angle and energy, counted, and, from a knowledge of the other parameters of the apparatus, an absolute cross section was determined. The experimental results show some structure in the electron-energy spectra superimposed on a continuous background. This is consistent with the predictions of the Fano-Lichten electron-promotion model. Calculations based on the results of the Russek statistical model are compared with experiment.

Cross sections for the emission of Auger electrons from excited atoms and ions produced in symmetric ${\mathrm{Ar}}^{+}$-Ar and ${\mathrm{Ne}}^{+}$-Ne collisions have been measured at ion energies from 50 to 300 keV. A simple model is proposed to explain the dependence of the cross section on the impact energy; the predicted results agree well with the experiment. Also, the argon x-ray data of Saris and Onderdelinden are compared with the model and with the results of this experiment.

A consistent set of total cross sections for electron impact excitation of the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$, $W{}_{}{}^3{}_{}{}^{}\Delta _u^{}{}_{}{}^{}$, $B^{\prime }{}_{}{}^3{}_{}{}^{}\Sigma _u^{-}{}_{}{}^{}$, $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, and $D{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ triplet states of molecular nitrogen from the $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state has been calculated quantum mechanically for incident electron energies from threshold to 80 eV. The Ochkur-Rudge exchange scattering and Franck-Condon approximations were employed to obtain these cross sections. Minimum and double-minimum basis-set LCAO-MO wave functions centered on the nuclei were used, and the multicenter terms in the scattering amplitude were evaluated using a $\zeta$-function expansion. Rotationally averaged cross sections were calculated for excitation from $v^{\prime \prime }=0\mathrm{}$ to individual $v^{\prime }$ levels of the excited electronic states. The calculated total cross section for excitation of the $B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state is in good agreement with that deduced from recent experimental data for the process. The cross section for excitation of the $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state agrees well with one pair of experimental measurements and is a factor of 2 larger than another pair of measurements and about a factor of 4 larger than a fifth experimental determination and the previous calculations. The calculated cross section for excitation of the $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state is a good deal larger than previous theoretical and experimental estimates. However, a comparison with recent experimental differential cross-section data indicates that the theoretical $A{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ total cross section is correct for incident energies greater than about 35 eV. The relative magnitude of these excitation cross sections leads to interesting predictions concerning ${\mathrm{N}}_2$ processes in the upper atmosphere.

The close-coupling approximation is used to calculate integral and differential cross sections for pure vibrational excitation $\sigma (v=0\mathrm{}\to 1, \Delta j=0)$ and $\sigma (v=0\mathrm{}\to 2, \Delta j=0)$, and for simultaneous rotational-vibrational excitation $\sigma (v=0\mathrm{}\to 1, \Delta j=2)$ of ${\mathrm{H}}_2$ by slow-electron impact. Static-field and electron-exchange effects, long-range quadrupole, and an effective polarization potential are included in the $e-{\mathrm{H}}_2$ interaction. Pure vibrational cross sections are found to depend on the initial rotational state $j$ of the molecule, but the total vibrational cross section is almost independent of $j$. Cross sections are compared with experiments for energies $E\le 10$ eV. For $2<E<\mathrm{}5\mathrm{}$ eV, $\sigma (v=0\mathrm{}\to 1,\Delta j=0)$ and $\sigma (v=0\mathrm{}\to 1,j=1\to 3)$ are 50% larger than experimental values while agreement is better in the remaining energy regions. For $1<E<\mathrm{}3\mathrm{}$ eV, $\sigma (v=0\mathrm{}\to 2,\Delta j=0)$ is in good agreement with experiment but is understimated for $E>\mathrm{}3\mathrm{}$ eV. Differential scattering cross sections for vibrational excitation are found to be dominated by the polarization potential at low angles, and by the short-range potential at large angles.

Calculations of the dissociative-recombination rate for diatomic molecular ions and electrons are reported for various arrangements of the potential-energy curves. The temperature variation is shown to be different for the two possible heating mechanisms: selective electron heating or total gas heating. An attempt is made to correlate the afterglow and shock-tube measurements of the recombination rate for nitric oxide and neon. This attempt fails, and this suggests the need for further studies.

Delayed-coincidence techniques have provided measurements of the distributions in values of $Q$, the energy transferred to inelastic processes, during ${\mathrm{O}}^{+}$ + Ne collisions at 50-200 keV. The average values $\overline{Q}$ of the $Q$ distributions remain almost constant as a function of $r_0$, the distance of closest approach of the colliding particles. For fixed $r_0$, the $\overline{Q}$ values vary slowly with bombarding energy and lie, for example, approximately 40 eV higher at 100 keV than at 50 keV. The flatness of the $\overline{Q}\left(r_0\right)$ functions is reflected in a similar independence of $r_0$ found in measurements of the average charges of the particles after collision. These results indicate that the collisions produce excitations only among $L$-shell electrons. However, some data describing the widths of certain $Q$ distributions indicate that $K$-shell excitations may occur infrequently among collisions that produce ${\mathrm{O}}^{+4\mathrm{}}$ ions. Supplementing the data for inelastic energy transfers are determinations of average ionic charge states after collision, measurements of angular distributions of scattering cross sections, and calculations of inelastic energy-loss cross sections deduced from the $\overline{Q}$ data.

The semiclassical impact-parameter treatment of the electron excitation of atoms yields a set of coupled first-order linear differential equations, which have been solved by previous authors in first-order perturbation theory. The present results utilize an approximate solution of the full set of coupled equations, employing the dipole approximation of Seaton. Results are described applying this method to electron excitation of hydrogen, coupling together the ($n,l,m$) states through $n=3\mathrm{}$, and these results are compared with those of quantum-mechanical close-coupling calculations. The agreement indicates the general utility of this method.

Absolute cross sections for single- and multiple-electron capture and loss by fast aluminum ions in collisions with ${\mathrm{N}}_2$ gas molecules have been measured. Data were taken at nine projectile energies between 0.4 and 4.0 MeV, for several incident charge states at each energy. Cross sections were determined from the initial behavior of charge-fraction growth curves under thin-target conditions.

The $v=0\mathrm{}\to 1$ vibrational cross section for ${\mathrm{H}}_2$ derived from swarm experiments is shown to be a good approximation to the sum of the cross sections for vibrational transitions that take place with and without simultaneous rotational excitation of the molecule. Experiments are described that prove that this summed cross section does not depend on whether the ${\mathrm{H}}_2$ molecules are in the $J=0\mathrm{}$ or the $J=1\mathrm{}$ rotational state, in agreement with a recent theoretical calculation. Reasons are given for the disagreement between the two published swarm-derived vibrational cross sections. However, the discrepancies between the threshold behavior of the cross sections determined by the swarm measurements, beam experiments, and theory have not yet been explained.

Secondary electrons in the energy range 150-210 eV produced by 125-300-keV ${\mathrm{H}}^{+}$ and $\mathrm{H}_2^{}{}_{}{}^{+}$ impacts on argon gas are measured as a function of their energy and angle of emission. Discrete line spectra are due to Auger transitions from ${\mathrm{L}}_2$ and ${\mathrm{L}}_3$ vacancy states as well as satellite transitions from multivacancy states. The widths, energies, and branching ratios of the ${\mathrm{L}}_2$ and ${\mathrm{L}}_3$ vacancy states are presented. Widths of these states are appreciably greater than those obtained with electron impact excitation. This can be attributed to the recoil velocities of the target atom and to the presence of the proton in the vicinity of the emitting atom. The angular distribution of Auger electrons is found to be nearly isotropic, in marked contrast to electrons in the continum spectrum. The cross sections for the production of ${\mathrm{L}}_{2,3}$ and ${\mathrm{L}}_3$ vacancy states are determined as a function of impact energy.

Attention is called to the remarkable agreement between a recent experiment and the Gerjuoy-Stein theory based on the Born approximation for the rotational excitation of ${\mathrm{H}}_2$ near threshold. The comparison is conducted through partial-wave analysis and application of the Wigner threshold law.

Absolute measurements are reported here of the total cross section ${\sigma }_{10}$ for charge transfer of ${\mathrm{He}}^{+}$, ${\mathrm{Ne}}^{+}$, ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, and ${\mathrm{Xe}}^{+}$ in ${\mathrm{N}}_2$ in the energy range from 10 to 100 keV. These measurements were obtained with ions produced in both an rf ion source and an electron-impact ion source. Differences are observed in the measured cross sections obtained with the different sources, except for ${\mathrm{Ne}}^{+}$. These differences are attributed to metastable ions produced in the rf source. (Note: ${\mathrm{Ne}}^{+}$ has no known metastable states.) The largest difference occurs with ${\mathrm{Xe}}^{+}$ ions, where the ratio of the two measurements is 1.5 at a velocity of 2×${10}^7$ cm/sec. In addition, a peak in the ${\mathrm{Xe}}^{+}$ cross sections obtained with the rf ion source is not present in data taken with the electron-impact source. It is believed that the peak is caused by the near resonant charge transfer which can occur between metastable ${\mathrm{Xe}}^{+}$ and dissociative ionization of ${\mathrm{N}}_2$ or with excitation of $\mathrm{N}_2^{}{}_{}{}^{+}$ to the $C{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state.

Earlier work on the hyperfine pressure shift (HPS) of hydrogen atoms in a helium atmosphere is generalized and extended to include the entire rare-gas series from helium to xenon. Such an analysis allows a more complete understanding of the relative importance of short-range and long-range contributions to the HPS data over the rare-gas series. The temperature variation of the hyperfine constant has also been analyzed in some detail, and comparison is made with available experimental data on H-He and H-Ar systems. The over-all nature of agreement between theory and experiment indicates the need for incorporation of short-range correlation effects for the lighter rare-gas systems such as H-He and H-Ne, while for the heavier rare gases a careful treatment of the intermediate range is essential.