Accurate values of the mobility of positive- and negative-charge carriers in liquid helium are presented. The measurements were carried out at the vapor pressure, over a temperature range of $0.28°\mathrm{K}<T<\mathrm{}5.18\mathrm{}°\mathrm{K}$ for negative-charge and $0.37°\mathrm{K}<T<\mathrm{}5.18\mathrm{}°\mathrm{K}$ for positive-charge carriers. A detailed description is given of the experimental techniques and of possible sources of error.

The experimental study of polarization in a Zeeman laser with strong $x-y$-type anisotropies makes evident the rotations of the electric field vector greater than the limiting value of $\frac{1}{4}\pi$ which is fixed by the self-consistent theory. The results are in agreement with the vectorial theory based on the resonance condition, which is necessary for the representation of such a type of quantum oscillator with nonreciprocal effects (including anisotropies). The self-consistent theory appears to provide a limit which becomes valid only for very weak anisotropies. Only the polarization of the so-called "Lamb's vector" can be described by the self-consistent theory and its rotation effectively attains $\frac{1}{4}\pi$ whatever the value of the anisotropy.

The rotation of the plane of polarization during the propagation of a pulse undergoing self-induced transparency is reinvestigated. The rotation per unit length, which is constant along the pulse, is shown to be exactly equal to the linear result obtained far out on the trailing edge of the hyperbolic-secant pulse. If the two circular components have their center frequencies shifted with respect to each other, it is pointed out that the rotation will not be stationary in the laboratory frame, but will propagate with a characteristic velocity. The existence of such propagation of a plane of polarization could be useful to test experimentally the existence of frequency pulling.

Linear polarizabilities for inert gases at ruby-laser frequencies have been evaluated. Contributions from continuum and single-electron-jump processes have been explicitly obtained. The calculated values are in reasonable agreement with the experimental values.

The frequency distributions of the He ii lines at 256, 304, 1085, 1216, 1640, 3203, and 4686 Å, broadened by the local fields of both ions and electrons in a plasma, are calculated in the classical-path approximation. The calculations for the electron broadening are based on an impact theory which accounts for perturbations to both upper and lower levels of the radiating ion. The theory allows (approximately) for the level splitting caused by the fields of the (perturbing) ions, finite duration of the collisions, screening of the electron fields, and includes (approximately) the effects of inelastic collisions. The effect of perturbations by singly charged ions is calculated in the quasistatic linear Stark-effect approximation using Hooper's microfield distribution functions. Comparison to previous calculations shows fair agreement with some increase in linewidth. Comparison with experimental results is less conclusive. Fair agreement is found with some results while others reveal a discrepancy of as much as a factor of 2 in the line wings.

The hyperfine structure of eleven optical transitions in the molecules ${\mathrm{I}}_2^{127}$ and ${\mathrm{I}}_2^{129}$ was resolved by the technique of laser-saturated absorption. All the absorption lines correspond to transitions between the ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\mathrm{}\left(X\right)\mathrm{}$ and the ${}_{}{}^3{}_{}{}^{}\Pi _{0u}^{+}{}_{}{}^{}\mathrm{}\left(B\right)\mathrm{}$ electronic states, but the rotational and vibrational quantum numbers varied widely. Two distinct types of hyperfine interaction were observed: (i) a nuclear electric quadrupole coupling which changed little among the lines investigated, and (ii) a magnetic spin-rotation interaction which varied strongly with the vibrational energy in the electronically excited state. The origin of the latter effect is discussed.

The hyperfine structure (hfs) of the $3d^{8}4s^2{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$ metastable atomic state of ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$ has been measured by the atomic-beam magnetic-resonance technique. Isotopic enrichment of the normally 1% abundant ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$ was necessary to achieve adequate intensity. The results, when combined with earlier hfs measurements of the ${}_{}{}^3{}_{}{}^{}F_{4,3}^{}{}_{}{}^{}$ states of ${}_{}{}^{61}{}_{}{}^{}\mathrm{Ni}$, allow a comparison with predictions of Bauche-Arnoult's recent theoretical treatment of the effects of configuration interaction on hfs. Good agreement is found. Similar experimental results for the Hund-rule terms of other $3d^{N}4s^2$ atoms are tabulated. The electron spin density at the nucleus, as determined from the experimental hfs results, is compared with recent unrestricted-Hartree-Fock calculations.

In the Brueckner-Goldstone many-body perturbation theory as applied to atomic calculations, the origin of important higher-order diagrams is associated with the inflexibility of the single basis set upon which the perturbation expansion is normally based. We show that in calculating each diagram one may employ more than one basis set simultaneously. The use of multiple basis sets is identical to the exact inclusion of a large class of important higher-order terms. We give illustrated examples to show where this technique will be of practical importance. This possibility is expected to improve the accuracy and to extend the range of applicability of the Brueckner-Goldstone many-body perturbation-theory approach.

A calculation is carried out within the framework of the Brueckner-Goldstone many-body perturbation approach for the photoionization of helium. In particular, we have utilized a newly developed technique of multiple basis sets to circumvent the difficulty of evaluating the singular integrals which appear in the important final-state correlation. This technique also enables us to achieve considerable calculational simplicity, reducing the final evaluation to only two diagrams. Our result agrees well with the accurate experimental data of Samson.

Positions of the lowest ${}_{}{}^{1,3}{}_{}{}^{}D_{}^e{}_{}{}^{}$ autonization states of He and ${\mathrm{H}}^{-}$ below the $n=2\mathrm{}$ level of ${\mathrm{He}}^{+}$ and H have been calculated variationally using Feshbach's $Q$-operator formalism. The trial wave function is of the Hylleraas type with appropriate angular momentum factors. The widths and the shifts of the states have also been calculated. The shifts are found to be positive for all the states calculated here. The results with 112 terms for most states are lower than any previously calculated. The calculated lowest autoionization states of He and ${\mathrm{H}}^{-}$ (relative to the ground states of He and H, respectively) are 59.902 and 10.1185 eV, in good agreement with the observed values of 59.9 and 10.13 ± 0.015 eV.

The cross sections for positronium-negative-ion formation by double electron capture in molecular hydrogen are calculated by the Born approximation for incident positron energies ranging between 45 and 500 eV. The maximum of the cross section occurs at about 60 eV and thereafter the cross section decreases rapidly with an increase in incident energy.

A general expression is found for the Green's function of a two-level system interacting with a classical monochromatic field of arbitrary frequency and intensity. The Green's function is first used to calculate the transition probability from the lower to the upper state as a function of the frequency and intensity of the field and a comparison of the results is made with experiment. It is then used to study the problem of scattering. It is found that the spectrum of the scattered radiation consists of a line at the frequency of the field (Rayleigh line) and two satellites symmetrically displaced from the Rayleigh line by an amount depending both on the intensity and frequency of the field. In addition there are emissions at three, five, etc., times the frequency of the field, and accompanying satellites. The cross sections for the production of the Rayleigh line and its satellites, and for the third-harmonic line and its satellites have been calculated for a range of values of the frequency and intensity of the incident field.

The lifetime, coherence narrowing, and collision broadening of the $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ excited state of atomic thallium has been studied by the technique of zero-field level-crossing spectroscopy. The lifetime of the $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state is determined to be 7.55 (0.08) nsec. The full coherence-narrowing effect gave a branching ratio, from $F=0\mathrm{}$ of $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ to the ground state, of 43%. The cross section for thallium-thallium resonance-broadening collisions is ${\sigma }_{\mathrm{T}\mathrm{l}-\mathrm{T}\mathrm{l}}=\frac{5.38\left(0.49\right)\mathrm{}\times {10}^{-8\mathrm{}}}{\overline{v}}$ ${\mathrm{cm}}^2$. The effect of 426-torr helium on the thallium lifetime, coherence narrowing, and resonance broadening was also investigated. From the low-thallium-density region the cross section for helium depolarization of the thallium $7{}_{}{}^2{}_{}{}^{}S$ state is ${\sigma }_{\mathrm{T}\mathrm{l}-\mathrm{H}\mathrm{e}}\cong \frac{7\times {10}^{-13\mathrm{}}}{\overline{v}}$ ${\mathrm{cm}}^2$. There is also indication of a buildup of population in the metastable $6{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ thallium state. From the data, the cross section for the process $\mathrm{Tl}\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)\to \mathrm{Tl}\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\right)$ by helium collisions is $\sigma \simeq 1\times {10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$. The Tl branching ratio in the presence of helium is 39%. It was also found that the thallium-thallium resonance-broadening cross section is ${\sigma }_{\mathrm{T}\mathrm{l}-\mathrm{T}\mathrm{l}}=\frac{4.04\mathrm{}\left(0.32\right)\mathrm{}\times {10}^{-8\mathrm{}}}{\overline{v}}$ ${\mathrm{cm}}^2$ in the presence of 426 torr of helium. In the presence of 113 torr of He, the resonance-broadening cross section was found to be ${\sigma }_{\mathrm{T}\mathrm{l}-\mathrm{T}\mathrm{l}}=\frac{5.22\mathrm{}\left(0.13\right)\mathrm{}\times {10}^{-8\mathrm{}}}{\overline{v}}$ ${\mathrm{cm}}^2$. In the case of Ar as the buffer gas, ${\sigma }_{\mathrm{T}\mathrm{l}-\mathrm{A}\mathrm{r}}=\frac{8\times {10}^{-13\mathrm{}}}{\overline{v}}$ ${\mathrm{cm}}^2$.

The experimental results for the self-broadening of pure Tl of the previous paper are shown to be in good agreement with the theory of resonant collisions, taking into account the effects of the hyperfine structure. Wall collisions are nearly negligible in that case. The decrease of the self-broadening observed with the addition of a foreign gas is explained in terms of three-body collisions (Tl-He collisions occurring during a Tl*-Tl collision) which broaden the optical transitions of Tl and decrease the resonance effect in the transfer of excitation between Tl atoms. The quantitative agreement obtained with the experimental results shows that these three-body collisions must be responsible for the major part of the observed reduction in self-broadening.

Fano's theory of photoabsorption by ${\mathrm{H}}_2$ near the ionization threshold is extended to yield photoelectron angular distributions above as well as between the ionization thresholds for alternative rotational states of the ${\mathrm{H}}_2^{+}$ ion. In accordance with recent measurements, the angular distribution of direct photoionization is quite different depending on whether or not the ionization is accompanied by a rotational transition. In the autoionization range between rotational thresholds the angular distribution oscillates along each Rydberg line of the rotational autoionization spectrum, resulting in Beutler-Fano resonance profiles which depend strongly on angle of observation. The results are compared with available experimental data. Angular distributions provide very sensitive tests of the theory. The calculation may serve as a basis for extensions to electronic and vibrational autoionization processes.

Laboratory-frame and body-frame treatments are combined using the $l$-uncoupling transformation which had served to interpret the absorption spectrum of ${\mathrm{H}}_2$. Application of a phase-amplitude procedure converts the Schrödinger equation to a Volterra-type integral form, which reduces to a Born-like approximation when the long-range interactions are weak. Attention is directed to features of low-energy collisions that must be considered by a realistic theory. This paper develops a formalism that can take advantage of different simplifying factors in different ranges of the electron-molecule distance. Detailed developments and applications are deferred.