The interatomic forces between sodium and hydrogen atoms which are responsible for the broadening of the sodium $D$ lines are discussed in terms of calculated interatomic potential curves for the NaH molecule. The importance of including overlap interactions and of considering both upper and lower states of the transitions is emphasized. A calculation of the line broadening using a molecular model for the pair of colliding atoms with the correct adiabatic limits yields damping parameters of 8.3 × ${10}^{-9\mathrm{}}$ rad ${\sec }^{-1\mathrm{}}$ with an estimated accuracy of 5-10% under the conditions of the solar photosphere and fits well with the observed wings of the absorption line profiles. The temperature dependence of the broadening is found to be approximately $T^{0.42}$, and the width/shift ratios are of the order of 30:1 for both resonance lines. Cross sections for transitions induced between the fine-structure states ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ are estimated, and the value ${\sigma }_{\frac{1}{2}\to \frac{3}{2}}=(70\mathrm{}\pm 10)\pi a_0^{}{}_{}{}^2$ at a velocity of 1.28 × ${10}^6$ cm ${\sec }^{-1\mathrm{}}$ is in agreement with previous calculations. Ground-state spin-exchange cross sections are estimated for hydrogen-sodium collisions as $22\pi a_0^2$ in the same velocity range.

$S$-matrix elements typically encountered in atom-atom scattering may be phenomenologically parametrized using meromorphic functions of complex angular momenta. The contribution to the scattering amplitude of each pole of the $S$ matrix is of such a simple nature (effectively, decaying oscillations for parameters encountered in practice) as to greatly facilitate the deduction of the phase shifts from scattering data. Some of these poles should be close to the true (Regge) poles of the exact $S$ matrix about which much theoretical information is available. There is some discussion outlining how many diverse phenomena such as rainbows, orbiting, and curve crossing can all be parametrized under the same scheme, thus leading to their unified treatment.

The inelastic energy loss $Q$ has been measured for ${\mathrm{Kr}}^{+}$-Kr single collisions at incident energies of 20 and 30 keV and scattering angles ranging from 6° to 15°. For distances of closest approach $r_0$ around 0.385 Å, the inelastic energy-loss distribution is triple peaked, and the differences in energy between the three peaks are independent of $r_0$. This structure is interpreted as being due to the production of one or two $M_{IV,V}$ vacancies.

An operator expansion of the $T$ matrix is shown to lead to an equation for describing charge polarization on elastic scattering similar to that reported previously by use of the infinite-channel close-coupling approximation in the second Born approximation. The resulting equations are used to calculate the charge-polarization corrections for elastic electron scattering from H and He at incident electron energies of 100 eV, 500 eV, and 40 keV over the angular range of 0° to 50°. The results agree well with those of Bromberg and LaBahn and Callaway for elastic scattering from He with an incident electron energy of 500 eV.

The cross section for elastic scattering by electron impact on NO shows resonances in the energy range 0-2 eV. These resonances, with a spacing of about 0.16 eV (${\omega }_e=0.17\mathrm{}$ eV), are associated with vibrational levels of ${\mathrm{NO}}^{-}$, and there is a near-coincidence in energy between the 4th vibrational state of NO and the 6th vibrational state of ${\mathrm{NO}}^{-}$. The width of these resonances increases monotonically from 0.02 to 0.10 eV as the vibrational quantum number of ${\mathrm{NO}}^{-}$ goes from 1 to 6. The energy dependence of the vibrational cross sections exhibits peaks at the positions of these resonances, and the magnitude of these peaks is measured. The vibrational states of ${\mathrm{NO}}^{-}$ can decay by the emission of an electron into various vibrational levels of NO. The branching ratio for a few of these decays is measured. A potential energy diagram of ${\mathrm{NO}}^{-}$ is drawn, using the experimental evidence.

Results are reported on the elastic scattering of low-energy electrons by potassium. The atomic-beam crossed-beam recoil technique is used, with velocity selection and spin selection and analysis of the atom beam. The results include total, differential, and differential spin-exchange cross sections, in the energy range 0.5-1.2 eV. Comparison is made with close coupling, as well as with adiabatic-type calculations. Additional total cross-section measurements up to 9 eV are also presented. These are significantly smaller and lack the pronounced structure of the early results of Brode.

Total quenching cross sections for metastable $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ atoms in collisions with helium, neon, argon, and krypton have been calculated over the incident-energy range 1.0 keV-1.6 MeV in the first Born approximation with the added approximation of closure used to describe target excitation. The first-Born-approximation cross sections for helium target atoms are one-third the measured values of Byron, Krotkov, and Medeiros over the incident-energy range 1.0-5.0 keV. The first-Born-approximation results for the heavier targets are much larger than experiment, although scaled results based on parameters determined from electron-loss data for $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ show fair agreement with recent experiments. The contributions of individual quenching processes are examined, and electron loss dominates for incident energies greater than 4.0 keV.

Vacuum-ultraviolet (vuv) studies were made of the emission from helium gas excited by 4-MeV protons, under conditions where the gas purity was monitored by concomitant total-ionization measurements. The relative intensity of the 584-Å resonance line was studied from 0.01 to 100 Torr. Three continua, near 600, 675, and 800 Å, respectively, were investigated from a few Torr to 800 Torr. Our studies of intensity as a function of pressure are consistent with the interpretation that the 675-Å continuum is the bound-continuum transition $D{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ in the helium diatomic molecule, where the $D$ state is formed by three-body collisions involving the atomic $2{}_{}{}^1{}_{}{}^{}P$ state. Some of the 800-Å continuum, as well as the narrow continuum near 600 Å, is produced, most likely, from a similar process involving emission from the $A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ molecular state, created from three-body conversion of a $2{}_{}{}^1{}_{}{}^{}S$ atomic state. Certain other details are given on the energy pathways following charged-particle excitation of helium gas, and comments are made on some of the recently published emission data for liquid helium.

Excitation functions and the pressure dependences of the apparent cross sections for the $4{}_{}{}^3{}_{}{}^{}S$, $3{}_{}{}^3{}_{}{}^{}P$, and $3{}_{}{}^3{}_{}{}^{}D$ levels are obtained for energies between 50-500, 50-600, and 50-500 eV, respectively, and for pressures in the region 1.0-10 μ Hg. The excitation function of the $4{}_{}{}^3{}_{}{}^{}S$ is found to be purely monotonically decreasing with energy at a slope of a - 3.0 ± 0.2. The $3{}_{}{}^3{}_{}{}^{}D$ and to a lesser extent the $3{}_{}{}^3{}_{}{}^{}P$ excitation functions are composed of two energy dependences, a slow one attributed to mixed $F$-level cascade, and an initially dominant fast component due to exchange excitation. The fast component falls as ${\mathrm{}\left(\mathrm{energy}\right)\mathrm{}}^{-3.5\pm 0.2}$ and ${\mathrm{}\left(\mathrm{energy}\right)\mathrm{}}^{-3.7\pm 0.5}$ for the $3{}_{}{}^3{}_{}{}^{}P$ and $3{}_{}{}^3{}_{}{}^{}D$ levels, respectively.

The algebraic close-coupling method is applied to slow collisions of electrons and positrons with atomic hydrogen. The wave function is assumed to be of the form appropriate for a $1s-2s-2p$ close-coupling calculation. The variational method proposed by Nesbet is used to calculate the appropriate phase shifts and cross sections. Excellent agreement with previously published results of Burke, Schey, Smith, and others is obtained for scattering below the $n=2\mathrm{}$ threshold. Information concerning resonance structure for positrons, and for electrons in the singlet and triplet state, is also obtained. Good results are also obtained above threshold in the $1s-2s$ and three-state approximations. Problems connected with the choice of asymptotic functions for the open $n=2\mathrm{}$ channels are discussed.

Scattering amplitudes are analyzed for the scattering of polarized or unpolarized electrons on polarized or unpolarized atoms (one-electron atoms). The elastic scattering of unpolarized electrons on partially polarized atoms provides the direct and exchange cross sections when the polarization of the scattered electrons and atoms are observed, respectively. The same quantities can also be obtained from the scattering of partially polarized electrons on unpolarized atoms, while the difference between the phases of the direct and the exchange amplitude can be derived from the spin analysis with polarized electrons and polarized atoms. When the degree of polarization of the colliding particles is known, the intensity of the scattered collision particles determines the interference term of the elastic cross section. The excitation process ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$, carried out with any combination of polarized and unpolarized electrons and atoms, has been analyzed in terms of differential and integral excitation amplitudes distinguished in terms of direct, exchange, and interference processes and also in terms related to the excitation of the magnetic substates $m_l=0\mathrm{} or \pm 1$. The analysis of the polarization of the inelastically scattered electrons gives differential excitation amplitudes for the direct, exchange, and interference terms of the excitation cross section without distinguishing between the magnetic substates. Based upon the observations of the intensity and the circular polarization of the emitted line radiation, the analysis of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ deexcitation process provides integral excitation amplitudes. Observation of the total intensity of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transition in an excitation process with polarized electrons and polarized atoms enables one to determine interference terms of the excitation cross section. Equal polarization for the exciting electrons and target atoms allows us to separate the interference amplitudes for the magnetic substates ($|F_1-G_1|$ and $|F_0-G_0|$). Analysis of the circular polarization of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ transition excited with unpolarized electrons and partially polarized atoms results in partial cross sections describing excitation processes in which the quantum number $m_j$ of the excited state differs from that of the ground state at most in sign. Excitation with polarized electrons and unpolarized atoms should also result in the emission of circular polarized light of the $P\to S$ transitions. In this context Farago's proposal for measuring electron-spin polarization by circularly polarized line excitation is discussed as it applies to alkali atoms. Finally, it is pointed out how sets of integral excitation amplitudes determined by collisions, as discussed above, can be used for comparing single-excitation amplitudes with theory.

An electron-electron coincidence measurement has been made of the energy spectrum of only those slow electrons emitted from violent ${\mathrm{Ar}}^{+}$-Ar collisions that produce known energy, fast $L\to \mathrm{MM}$ Auger electrons. The correlation between the number of ejected slow electrons and the energy of the fast electron is much less than expected from a model based on the generally assumed ordering of the inner-shell (Auger) and outer-shell transitions following inner-shell excitation. Furthermore, details of the spectra show that double Auger ($L\to \mathrm{MMM}$) processes do not occur in a large percentage of the events studied. It appears that the branching ratio of outer-shell auto-ionizing transitions to $L\to \mathrm{MM}$ transitions in argon is smaller than expected, possibly owing to the molecular properties of the ${\mathrm{Ar}}^{+}$-Ar collision system.

We treat three standard problems of the nonrelativistic quantum theory by a Brownian-motion method devised by Sokolov and Tumanov. In all three cases, the commutation (Poisson bracket) relations for the particle's dynamical variables are deduced from the corresponding relations for the components of the fluctuating electromagnetic field. In addition, the particle ground-state energy is determined by the zero-temperature vacuum fluctuations of the field. The ground-state energy includes the lowest-order radiative correction, although the calculation makes no use of traditional perturbation theory or mass renormalization. If the vacuum radiation temperature is high, the energy of the particle goes to its equipartition value.

The calculation of response functions in the Green's-function method for canonical ensembles is illustrated. The example given is the evaluation of the susceptibility of a lattice of magnetic ions in the mean-field approximation.

The long-range behavior of enthalpy fluctuations in bulk liquid helium at the superfluid $\lambda$ transition is deduced from the observed specific-heat singularity. In moderately thick films, the specific-heat singularity is rounded into a broad maximum. The growth of this maximum with film thickness is derived and recent experimental data are discussed.

Within the framework of the adiabatic theory of pressure broadening, an expansion of the spectrum in powers of the density is obtained by making use of a technique of local averaging in the time domain. The first term of the expansion, $I_c\left(\omega \right)$, is essentially the impact distribution; the second term is $n{J}_w\left(\omega \right)$ folded into $I_c\left(\omega \right)$, where $J_w\left(\omega \right)$ is the wing of the one-perturber distribution, that is, the intensity distribution obtained if there is only one perturbing atom interacting with the radiating atom. Higher-order terms are successive convolution powers of $n{J}_w\left(\omega \right)$, all folded into $I_c\left(\omega \right)$. The expansion should be useful mostly for understanding and predicting qualitative features of the spectrum. In particular, the results imply that structure in the wings, such as satellite bands, is broadened and shifted in the same way as the line center under increasing pressure, in agreement with experimental observations.

Projection-operator techniques are used to obtain a new exact equation for the momentum of a particle in a harmonic lattice. The equation, valid for all times and mass ratios, permits a simple physical interpretation in terms of a reference system with the particle held fixed. It is demonstrated that the random forces which arise through the use of two different projection operators are equal and identical to the force on the heavy particle in the reference mechanical system.

A force has been observed on a small thin disk which is immersed in a polyatomic gas when a thermal gradient is established and when a magnetic field is applied. This thermomagnetic force is normal to the surface of the disk and is an even function of the magnetic field. Measurements are reported of this force effect as a function of magnetic field and pressure for ${\mathrm{O}}_2$ and NO in the temperature range 30-35°C. These new results are compared to a related thermomagnetic effect on the thermal conductivity of a polyatomic gas (Senftleben-Beenakker effect).

The hydrodynamic equations of a superfluid helium film are solved numerically to yield the dispersion equation of third sound over a wide range of thicknesses, including both unsaturated and saturated films. An analytical approximation to the dispersion equation is found that is good for the entire range where the equations are valid, and which becomes particularly simple in the case of either very thin or very thick films. A clear physical picture is formed of the processes determining the properties of third sound in thick helium films.

The theory of homogeneous isotropic turbulence of current carriers in metals and semiconductors is developed in terms of the magnetic field fluctuations. A quasinormality hypothesis is used to truncate the chain of equations for the correlation functions. A $k^{-3\mathrm{}}$ spectrum in wave numbers and a $\frac{1}{f}$ spectrum in frequencies are obtained. The $\frac{1}{f}$ spectrum is also obtained for fluctuations of current and voltage in a ring-shaped circuit embedded in the turbulent field. These results are used to construct a universal theory of $\frac{1}{f}$ noise in electronic circuits.