Lambert's proof that the inclusion of nuclear spin does not alter the equation of motion for the electronic polarization is shown to be valid only when the hyperfine interaction is negligible. Usually the hyperfine frequency is much greater than the frequency of spin-exchange collisions; then the effect of the hyperfine interaction between collisions invalidates Lambert's proof. In general, spin exchange with a second depolarized species relaxes the electronic polarization as the sum of two exponentials, as shown by Gibbs and Grossetête.

A two-parameter analytic potential for electrons in atoms, introduced by Green, Sellin, and Zachor, is used in conjunction with Dirac's equation to determine independent-particle-model electronic energy levels for neutral atoms in their ground states. The parameters are determined for each atom so that the predicted energy levels approximate observed electronic separation energies in accordance with a weighted least-squares sum. The agreement with experimental data is as good as for relativistic Hartree-Fock results. Electronic energies are given for a random selection of elements with $Z=10, 20, \dots , 90$.

The work of Balling, Hanson, and Pipkin on the density-matrix equations for spin-exchange collisions is extended and is simplified in the case of ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ atoms. The results allow straight-forward calculation of the detailed effects of spin exchange on the density-matrix elements. The equations are useful when dealing with an ensemble of atoms such as in the hydrogen maser, in the rubidium maser, and in optical pumping cells.

It is shown, as an extension to Ref. 1, that a relatively simple analytic potential, which was obtained from studies of bound electron states in atoms, gives differential cross sections in good agreement with experimental values for the rare gases Ar, Kr, and Xe.

The frequency shift in the hydrogen maser caused by the collisions of the atoms with the storage bulb surface, usually called the wall shift, has been investigated as a function of temperature from 100 to 400 °K. The wall shift for Teflon, negative at room temperature, passes through zero as the temperature is raised above 380 °K. This constitutes the first observation of a positive wall shift. Below room temperature the shift becomes increasingly negative. Both the homopolymer polytetrafluoroethylene (Dupont TFE-42) and its copolymer with hexafluoropropylene (DuPont FEP-120) exhibit similar behavior. Changes in the shape of the temperature dependence have been found at temperatures where phase changes are known to occur in Teflon, connecting the wall shift directly to properties of the surface material. A theory is advanced which correctly predicts the wall shift at room temperature, but gives a temperature dependence much smaller than that found experimentally.

The sequences of partial sums for quantities such as bound-state energies that one obtains from high-order perturbation theory often have poor convergence qualities. Here it is pointed out that use of nonlinear sequence-to-sequence transformations may dramatically improve the convergence properties of the perturbation theory results. This technique is illustrated by application to data from a recent paper.

We have resolved quantitatively different collisional-quenching processes of $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ by means of a calculation using measured charge equilibrium fractions and cross sections. The results show that at 5 keV and for neon as a target, quenching to the ground state $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ is the dominant process.

The evolution of electronic angular momentum due to spin-exchange collisions between two species of ground-state alkali atoms is shown to depend substantially on nuclear spin when the effects of spin precession between collisions are included with the effects of the collisions themselves. General results are illustrated for nuclear spin ½ and 1.

A comparison between the nonrelativistic total $K-\mathrm{LL}$ Auger rates of McGuire and our calculations is presented. The effects of the exchange approximations on the Auger rates are also presented.

The formulas for the rotational excitation of diatomic molecules in the adiabatic theory are generalized to include rotational excitation within molecular states of arbitrary $\Lambda$ symmetry. For $\Lambda$ not equal to zero (non-$\Sigma$ states), the rotational quantum number can change by any integer, and not only an even integer as is the case for $\Sigma$ states.

Core shielding effects in atomic hyperfine structure are examined within the framework of relativistic electron theory in the Hartree-Fock-Slater approximation. Expressions are developed for shielding factors pertaining to electric and magnetic hyperfine constants of arbitrary order. Known values of the nuclear magnetic moments for alkali and halogen atoms are used to obtain theoretical predictions of the dipole hyperfine constant "$a$" with shielding effects included. These theoretical values of $a$ are then compared with experiment as a test of the atomic model. Experimental values of the quadrupole and octupole hyperfine constants "$b$" and "$c$" for various halogen atoms are analyzed using the model to give revised values for nuclear quadrupole moments, as well as new values for octupole moments of Cl, Br, and I, including screening corrections.

Annihilation converts positronium hydride into photons and a hydrogen atom. We calculate the probability that the residual hydrogen atom will relax to each of number of bound states. The results suggest an experiment for detecting positronium hydride in a system in which excited hydrogen atoms do not exist except as the residue after annihilation. The experiment consists of measuring the intensity increase of the Lyman -$\alpha$ line upon quenching the $2s$ atoms to $2p$ atoms. We predict that the intensity will increase by a factor of 35.

The radiative lifetime of the $2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and $3{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of atomic helium has been measured by the level-crossing technique. In the experiment, a beam of $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ metastable atoms was first produced and then excited to the $2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ or $3{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state with resonance radiation. The lifetimes were measured by observing the zero-field level-crossing signals in the detected 584- or 537-Å fluorescent radiation when these ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ states decayed to the $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground state. The results are $\tau \left(2\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=(5.57\mathrm{}\pm 0.15)\times {10}^{-10\mathrm{}}$ sec and $\tau \left(3\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=(1.73\mathrm{}\pm 0.11)\times {10}^{-9\mathrm{}}$ sec. These values are in excellent agreement with theory.

A measurement of the isotope shift in the ($2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$) line of atomic helium has been made and is in excellent agreement with theory. Both ${\mathrm{He}}^4$ and ${\mathrm{He}}^3$ $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ metastable beams were irradiated in a magnetic field with 20 582-Å ($2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$) radiation from ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ resonance lamps, respectively. In each case, a magnetic sublevel of the $2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state was Zeeman shifted so as to scan the resonance-lamp profile. The 584-Å ($2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}-1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$)-decay photons served to monitor the excitation. A shift $\nu \left({\mathrm{He}}^3\right)-\nu \left({\mathrm{He}}^4\right)=0.1408\mathrm{}\pm 0.0019$ ${\mathrm{cm}}^{-1\mathrm{}}$ was obtained.

A new Fock-type operator is defined which varies between the Hartree and the Hartree-Fock operator depending on a cutoff parameter in the exchange potential. The corresponding pseudo-Hartree-Fock equations require each orbital ${\phi }_i$ to behave asymptotically as $\exp [-{(-2\mathrm{}{\epsilon }_i)}^{\frac{1}{2}}r]$. Calculations are reported for the Ne atom.

Correlation energies for $M$-shell and mixed $\mathrm{LM}$-shell electron pairs have been computed for the ground states of the atoms listed in the title. For open-shell atomic states, one-electron effective correlation energies are also computed. The method used is a formulation of Brueckner's theory in which one- and two-particle Bethe-Goldstone equations are solved by a variational procedure that uses $N$-particle trial wave functions expressed as linear combinations of Slater determinants. Individual pair-correlation energies are computed to an expected accuracy of a few percent, based on previous calculations on $L$-shell atoms. The computed correlation-energy data are used to analyze the various energy contributions to the first ionization potentials of the atoms considered.

In the limit of high vibrational and electronic principal quantum numbers, a semiclassical model for the auto-ionization of diatomic molecules has been constructed. The molecular vibrations are treated as classical oscillators, whose parameters are chosen from a knowledge (which can be taken either from theory or experiment) of the positions of the quantal vibrational levels and the position and depth of the minimum of the adiabatic potential curve of the residual molecular ion. The theory is designed for the case where vibrational quantum numbers are greater than about 10. Electronic quantum numbers are restricted by the requirement that they be high enough so that (i) the excited-electron-core-electron interaction can be represented by the monopole term in the region where the excited electron is always farther from either nucleus than the core electron is, and (ii) the excited-electron-nuclear interactions can be represented by the monopole terms in all regions. An advantage of the theory over the perturbed-stationary-state theory is that its validity extends into the region of very high electronic quantum numbers ($n=100\mathrm{}$), where the electron and nuclear velocities are comparable and the Born-Oppenheimer theory is not valid. Numerical estimates for the auto-ionization rates are presented for several sample cases for vibrations in the neighborhood of $n^{\prime }=10\mathrm{}$, excited electrons from $n=10\mathrm{} \mathrm{to} 20$, and zero-energy ejected electrons. Numerical results are also included for the lower vibrations ($n^{\prime }\le 5$), $n=8, 9, 10$ excited electrons, and zero-energy ejected electrons, and comparison is made with experimental and other theoretical results.

Beam-foil excitation was used to populate the $3p$, $4p$, and $5p$ states in atomic hydrogen in order to measure their mean lives. The results were 5.41 ± 0.18, 11.25 ± 0.78, and 21.9 ± 3.0 nsec, respectively. All three decay curves displayed a long-lived component. It was found that compensation must be made for Rutherford scattering in order to avoid introducing significant errors. An experimental technique for eliminating these errors is presented.