The foil-excitation method has been used to study the extreme ultraviolet spectra of highly ionized oxygen and fluorine. Several previously unreported lines in heliumlike fluorine are reported and other newly reported lines in heliumlike oxygen have been measured to higher accuracy. Included in the measurements are certain heliumlike oxygen transitions of significance in interpretation of solar-flare spectral observations. The wavelength determinations are usually in good agreement with calculated results which includes relativistic corrections but discrepancies arise when nonrelativistic calculations are used. A comparison of the present results and those recently obtained by $\theta$-pinch and laser-induced plasma sources is made for both heliumlike and lithiumlike ions; a few discrepancies occur, with our results in most cases in better agreement with relativisitically corrected calculations. Certain unidentified lines in the spectra may be attributable to radiative transitions between quartet states of lithiumlike ions.

The $e^8$ corrections to the decay rate of orthopositronium are calculated. For this calculation, as for bound-state problems in general, special attention must be given to infrared and Coulomb terms. The final result of this calculation is that the $e^8$ corrections yield a decrease in the lifetime of approximately 0.4% which represents a discrepancy of 2½ standard deviations with the current experimental value.

The retarded interactions between neutral molecules at very large separations are calculated by perturbation of the electromagnetic vacuum state. This state is represented by the Wheeler form of the electromagnetic vacuum functional. Besides the well-known Casimir attractive $R^{-7\mathrm{}}$ potential energy between polarizable bodies, the repulsive interaction between one electrically and one magnetically polarizable molecule proportional to $R^{-7\mathrm{}}$ is computed. Also the specific discriminating force between optically active molecules, with potential proportional to $R^{-9\mathrm{}}$, is shown to follow similar calculations. For isomeric molecules this force is repulsive for identical handedness and attractive between enantiomers.

Necessary conditions for the existence of bound states for positron-atom systems are derived in terms of an adiabatic-type approximation by assuming that (i) their mutual potential energy has the form of a Morse potential and (ii) the first ionization energy of the atom exceeds the binding energy of an electron to a unit charge of infinite mass. Use is then made of the potential energies of the appropriate proton-atom systems, which have been determined by ab initio calculations or fitted to spectral or scattering data, to investigate the seven positron-atom systems to which the present theory is applicable. It is concluded that helium, nitrogen, and neon, in their ground states, should be incapable of binding positrons. Binding of positrons to hydrogen, oxygen, argon, and krypton, in their ground states, is not precluded by the theory, but the binding to krypton seems most likely.

A classical description is given of the bremsstrahlung spectrum function for nonrelativistic Coulomb interactions in the dipole approximation. The description is complete for repulsive Coulomb interactions with no ad hoc cutoffs in impact parameter or frequency. The spectrum function is given for attractive interactions for those orbits for which perturbation theory is valid. The techniques used here can be extended readily to the evaluation of spectrum functions for higher-order multipoles as well as for various cutoff models which would give the classical part of the spectrum. A rationale for these classical calculations is given. The principal new results are (i) an explicit analytical formula valid in the low-frequency limit at arbitrary values of the orbit eccentricity $\epsilon$, (ii) a numerical evaluation of the spectrum function for intermediate frequencies, and (iii) improved error estimates for the asymptotic spectrum valid at zero impact parameter for repulsive interactions.

Excitation functions and absolute cross sections for Sn $K$- and $L$-shell and Ta $L$-shell x-ray production by proton impact have been measured over the energy range 1.4-4.4 MeV with a Si(Li) detector. The results, combined with our measurements on other elements, are compared with existing theories. In the calculation of ionization cross sections from the plane-wave Born approximation, we discuss the effect of a relativistic correction for the ionization potential. The plane-wave Born approximation with the correction due to the Coulomb deflection gives the best fit for Sn $K$ x-ray production and the binary-encounter approximation is the best for Sn $L$ and Ta $L$ x-ray production. The semiclassical approximation based on the impact-parameter treatment predicts values which are not in agreement with the data on Sn $L$ x rays. The scaled universal excitation curve based on the binary-encounter approximation gives good fits to $K$-shell ionizations but seems to show some disagreement for $L$-shell ionizations. The dependence of the $\frac{K\alpha }{K\beta }$ ratio of Sn on the target thickness was investigated but it was found that the ratio is constant within the experimental uncertainty. Relative intensities for the transitions $L\alpha$, $L\beta$, $L\gamma$, and $L_l$ are also compared with the theories.

This is a continuation in the theoretical study of scattering initiated by two coherent beams. Here the scattering by multiple independent centers is discussed. The presence of these centers involves some problems, which are not present in scattering with a single beam. I show how these problems may be overcome, thus allowing the phase of the scattering amplitude to be determined experimentally.

The cross sections for the rotational excitation of polar diatomic molecular ions by electron impact are formulated within the Coulomb-Born approximation. The cross sections are finite at threshold. Explicit calculations are reported for the excitation of C${\mathrm{H}}^{+}$.

Absolute cross sections for the production of positron-electron pairs by photons incident on a pure tin target have been measured at photon energies of 1.1205, 1.3325, 1.8362, and 2.6145 MeV and also with the mixed 1.1732- and 1.3325-MeV $\gamma$ rays in the decay of ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$. The resulting cross-sections are $\sigma \mathrm{}\left(1.1205\right)=5.4\mathrm{}\pm 0.5$, $\sigma \mathrm{}(1.1732+1.3325)=42\mathrm{}\pm 4$, $\sigma \mathrm{}\left(1.3325\right)=65\mathrm{}\pm 3$, $\sigma \mathrm{}\left(1.8362\right)=419\mathrm{}\pm 20$, and $\sigma \mathrm{}\left(2.6145\right)=1090\mathrm{}\pm 50$ mb. The comparison of these results with recent calculations shows that the importance of the screening correction appears rather sharply as the energy decreases. For $Z=50\mathrm{}$, we observe a sharp and sudden disagreement between the present measurements and the unscreened theoretical values below about 1.3 MeV. While screening corrections result in cross sections in much better agreement with the present experimental values, there is still a small discrepancy. The measurements were performed using a new technique in which a small spherical radioactive source is placed at the center of a spherical target. It was shown earlier that the corrections necessary to account for internal scattering of the $\gamma$ rays in the target can be accurately made using Monte Carlo methods. The corrections were very small in all cases studied.

Formation of H atoms in the $n=2\mathrm{}$ states for the nearly resonant charge-transfer process ${\mathrm{H}}^{+}$ + Cs (energy defect: 0.49 eV) is studied in the energy range 0.25-3.0 keV. The outgoing $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ atoms are quenched in a transverse electric field. The cross section for formation of $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ atoms exhibits typical nearly resonant characteristics. The principal maximum, (6.0 ± 0.25) × 1$0^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ occurs at 0.5-keV ${\mathrm{H}}^{+}$ energy; a secondary maximum is observed at 1.35 keV. Structure is discussed in terms of the potential-energy curves of the quasimolecule ${\mathrm{}\left(\mathrm{CsH}\right)\mathrm{}}^{+}$. The cross section for formation of $\mathrm{H}\mathrm{}\left(2P\right)\mathrm{}$ atoms is obtained by an indirect method. The $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ fraction $f$ relative to the outgoing neutral beam for a thin Cs target is obtained; $f$ is close to the statistical value of 0.25 for ${\mathrm{H}}^{+}$ energies greater than 1 keV, and has a maximum value of 0.55 ± 0.075 at 0.6 keV. Multiple collisions are studied for Cs targets of variable thickness. The $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ fractional yield $F_m$ relative to the total outgoing beam has a maximum for a Cs target thickness of about ${10}^{14}$ atoms/${\mathrm{cm}}^2$. The largest value of $F_m$ is 0.30 at 0.5 keV. $F_m$ approaches zero as an equilibrium value. A four-component charge-exchange model is used to show that the primary destruction mechanism of $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ atoms is collisional deexcitation, with a cross section of about 5 × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$. The influence of scattering and calibration of a secondary-emission neutral detector are discussed. Finally, the polarization $P$ of Lyman-$\alpha$ radiation from quenching of $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ atoms in a transverse electric field is measured as a function of applied electric field. $P$ is negative, varying from -0.31 ± 0.03 in a near-zero electric field to -0.50 ± 0.06 for a field of 475 V/cm. Data are in agreement with an adiabatic theory; in addition, oscillations about the theoretical curve are observed.

The multiphoton excitation of cesium through potentially resonant continuum molecular states is investigated over the 6200-5000-Å wavelength region with a tunable dye-laser source having a 0.06-0.08-Å linewidth and a space-charge ionization detector sensitive to a few ions per second. Conditions are established under which the lifetime of the resonant intermediate state against photoexcitation exceeds the lifetime against dissociation. Single- and double-photon resonances occur for the same wavelength and give absorption maxima corresponding to the line spectrum from the intermediate state following dissociation. These lines are modulated in amplitude as a function of wavelength by the more slowly varying absorption resonance from the initial to the intermediate continuum state. As a consequence, the resulting dispersion curve for two-photon absorption in cesium shows what appear to be resonant intermediate $d\pi \left({}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}\right)$ terms dissociating to give a $5^{2}D$ atom and resulting in the strong development of features corresponding to the fundamental series ($5^{2}D\to n^{2}F$) of atomic cesium in absorption. Components to $n=50\mathrm{}$ were observed and recorded to a precision sufficient to determine the average quantum defect for $F$ states to be $〈n-n^{*}〉=0.033\mathrm{}$ in the limit of large $n$. More complex structure is attributed to $p\pi \left({}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}\right)$ and $p\sigma \left({}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}\right)$ terms dissociating to give a $6{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ atom and resulting in the development of the $n=8\mathrm{}$ to 32 components of the $6{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to n{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ part of the diffuse series in absorption. Terms dissociating into $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ were found only at higher photon energies (∼2.27 eV) corresponding to the $n\ge 10$ members of the $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to n{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ series.

An experimental investigation has been made of the scattering of metastable hydrogen formed in collisions of neutral hydrogen with helium; projectile energies were in the range 1 to 20 keV and scattering angles investigated range from 0.2° to 1.5°. In addition angular distributions of scattering H${}^0$ and ${\mathrm{H}}^{+}$ were measured in an extended angular range of 0.2° - 5.0°. Total cross sections for $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ formation in helium and argon targets have also been measured. The total cross sections for $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ formation in helium are in good agreement with coupled-state theoretical predictions at energies above 4.0 keV; the measured differential cross sections show the same angular dependence as theory at 10-keV impact energy. Also, at low energies, a low-angle peak is found in the angular distribution of $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$; this is in accordance with theoretical predictions.

Variational calculations in Hilbert space and theorems from the theory of moments are employed in the construction of Stieltjes-integral approximations to the electric-dipole absorption and dispersion profiles in atomic helium. A spectrum of discrete transition frequencies and oscillator strengths obtained from variationally determined pseudostates furnishes accurate approximations to the necessary dipole spectral sums. Solution of the appropriate moment equations, or transformation to a basis set of principal pseudostates, provides the principal frequencies and strengths necessary for Stieltjes imaging the absorption profile, and for the evaluation of the associated dispersion profile. Rapid convergence is obtained to values in excellent agreement with the available experimental absorption cross section, refractive index, and Verdet coefficient, and with semiempirical estimates of the closely related dynamic dipole shielding factor and Rayleigh-scattering cross section. Moreover, comparison of the discrete pseudospectrum of frequencies and strengths with its Stieltjes average indicates the presence of approximations to autoionizing states and inelastic thresholds in the variationally determined photoabsorption profile. These results suggest that the Stieltjes technique for determining photoabsorption and dispersion profiles is a useful complement to more conventional methods which require the explicit construction of discrete and continuum eigenfunctions.

The independent-particle model of Green, Sellin, and Zachor is adjusted to describe the inner and singly excited states of neutral oxygen. It is found that the entire spectrum can be fitted using only two parameters. With the addition of a polarization potential, the ground state of ${\mathrm{O}}^{-}$ is also fitted with a Green-Sellin-Zachor independent-particle model. Low-energy elastic cross sections for electrons on neutral oxygen are then obtained. The calculated cross section fit the data reasonably well. The neutral-oxygen calculations are then extrapolated to zero energy using modified effective-range theory from which we obtain a scattering length of $0.485a_0$. At higher energies, the results of partial-wave calculations are compared to a two-parameter analytic Born approximation.

The Hartree-Fock-Bogoliubov equations for a homogeneous boson system at finite temperature are derived using linearized operator equations of motion. By a partial decoupling of two of the equations, a temperature-dependent form of the Lippmann-Schwinger equation for a local $t$ matrix emerges naturally with a fully dressed energy denominator. In order to use a realistic potential the theory is phenomenologically modified by (i) redefining the chemical potential to remove an unphysical energy gap, and (ii) removing (possibly divergent) Hartree-Fock-like terms from the single-particle energy. The resulting set of coupled nonlinear integral equations is solved self-consistently for the Morse-dipole-dipole and the Frost-Musulin potentials. The excitation spectra obtained are in qualitative agreement with the observed phonon-roton spectrum, but the temperature dependence is given incorrectly. The calculations were made at a realistic density and the condensate fraction is about 60% at absolute zero.

An integral equation is proposed whose solutions approximate the radial distribution functions of classical fluids whose single-type particles interact with pairwise radial forces. The equation contains a parameter which is adjustable to improve moderate- and high-density solutions. The equation is applied to the hard-sphere model of a fluid, solutions are obtained for four densities, and the pressure equation of state is expressed in terms of a 2 × 2 Padé approximant. A single value of the parameter yields pressures which are in excellent agreement with "exact" values.

We have measured the drift velocity of several positive impurity ions in He II in electric fields beyond the critical field for vortex-ring nucleation. The large differences in observed velocities for the various ions are satisfactorily accounted for by assuming that the ions differ in radius and hence in thermally activated escape rates from the vortex rings to which they are bound. These size differences are consistent with the low-field mobilities and are not consistent with the usual simple model for the ion structure.

We have studied the dynamic properties of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ and the ${\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ atomic and molecular metastable states of helium that are produced in electron-bombarded superfluid helium. The steady-state concentration of ${\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ molecules is shown to be limited by collisions between pairs of these molecules. Measurements of the rate coefficient for this bimolecular reaction as a function of temperature and pressure show that the reaction is diffusion limited and that the diffusion coefficient for the metastable molecules in the superfluid is determined by ${\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$-roton collisions. The bilinear destruction of metastable molecules has been monitored for times as long as 0.1 sec after the initial population of the state, and this establishes a lower bound of 0.1 sec on the radiative lifetime of the $\mathrm{}(v=0\mathrm{})\mathrm{} {\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ state in superfluid helium. The lifetime and decay mode of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ atoms are distinctly different from that of the corresponding ${\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ molecule. In particular, the characteristic lifetime of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ state in superfluid helium is essentially independent of the temperature between 2.08 and 1.4 °K and is measured to be about 15 μsec. Our experimental observations indicate that the destruction of metastable atoms results in the population of high vibrational levels of the $a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ molecular state. However, it is shown that the production of $\mathrm{}(v=0\mathrm{})\mathrm{} {\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ molecules responds immediately to the electron beam (response time < 3 μsec) and thus the formation of this state in the liquid does not depend upon the destruction of metastable atoms. Despite the fact that the lifetimes and decay modes of the metastable $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ atoms and $\mathrm{}(v=0\mathrm{})\mathrm{} {\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ molecules are not related, the production rates for these states are nearly equal and correspond to about 450 and 500 per incident 160-keV electron, respectively.

We have investigated the time dependence of the afterglow emission of pulsed-electron-bombarded superfluid helium, and in addition we have studied the effects of pressure on the steady-state intensities of the atomic and molecular emissions of the excited liquid. Our results indicate that two distinct mechanisms populate the excited states in the liquid. The first production mechanism basically determines the steady-state properties of the excited liquid and it is responsible for the rapid initial decay of the fluorescence during the first ${10}^{-8\mathrm{}}$ sec of the afterglow. This rapid decay time taken with the observed exponential decrease of the steady-state intensities with increasing pressure indicates that most of the excited states are nonradiatively quenched by the surrounding ground-state liquid. The second production mechanism results in a slowly decaying late afterglow fluorescence of the excited liquid. It is shown that this late time emission is due to the bilinear destruction of the long-lived ${\mathrm{He}}_2\left(a{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ metastable molecules which are produced also in the liquid by the electrons. It is shown further that most of the energy released during these bilinear reactions results in the population of the ${\mathrm{He}}_2\left(A{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\right)$ state which subsequently radiates in the vacuum-ultraviolet region of the spectrum.

The free energy for a system of hard spherocylinders with midpoints constrained to random motion in a plane, serving as a zeroth-order approximation to one layer of a smectic liquid crystal or a two-dimensional nematic liquid crystal, has been calculated for spherocylinders with a length-to-width ratio of 5. For $\rho$, the number density measured in fractions of close-packed density, less than 0.22, the partition function itself is evaluated by means of a Monte Carlo scheme employing 22 500 mesh points and 82 possible angles for 25 particles with periodic boundary conditions. For all $\rho$ the liquid-crystal free energy is calculated by minimizing a function of the hard-disk free energy plus the orientational free energy of a "liquid crystal." The low-density Monte Carlo free energy is found to lie below the liquid-crystal free energy, but can be extrapolated to cross it at $\rho =0.23\mathrm{}\pm 0.01$. Maxwell construction yields a phase-change region for $0.19\pm 0.01<\mathrm{}\rho <0.29\mathrm{}\pm 0.01$. A spline polynominal fit to the entire free energy, which interpolates across the phase-change region, does not give strictly constant pressure, but does imply a phase-change region of $0.20\pm 0.01<\mathrm{}\rho <0.30\mathrm{}\pm 0.01$ with $\frac{P{A}^{\prime }}{\mathrm{NkT}}=1.38\mathrm{}\pm 0.03, A^{\prime }$ being the cross-sectional area of a close-packed system of $N$ rods.