A new, more accurate calculation of the ground-state wave function of positronium hydride has been carried out. The method is variational and is similar to that reported by Lebeda and Schrader. The "molecule" is found to be stable against separation into positronium and hydrogen by at least 0.672 eV, an increase of 2% above the best previous value. The mean lifetime against two-photon annihilation is 0.407 nsec, as obtained from the energy-minimizing wave function. The "cusp value" of -0.477 is close to the exact value -½, giving an indication of the quality of the trial function.

High-temperature asymptotic expansions of $B_{\mathrm{dir}}$ for a hard-core-plus-attractive-well potential are calculated using a method developed by Hill and reformulated by D'Arruda and Hill. To lowest order, we find the first quantum correction from the well to be independent of the shape of the well and to depend only on the value of the potential at the core.

The leading quantum correction to the virial coefficients is calculated for the case where the intermolecular potential has a hard core. If the potential is bounded and continuous outside the core, the leading quantum correction to the second virial coefficient comes entirely from the region of the hard-core boundary, and depends only on the diameter of the core and the depth of the potential well at the core boundary. The leading quantum correction to the higher virial coefficients also involves the value of the classical radial distribution function at the core boundary. If the potential has discontinuities outside the core, these will give rise to additional first-order corrections.

It is pointed out that the variation-iteration method offers a fast and accurate means for solving the variable-phase equation. The method is especially useful for problems involving many partial waves.

Small-angle scattering of nuclear $\gamma$ rays is proposed for the investigation of the elementary rotational excitations (librons) in solid orthohydrogen. The differential cross section for the scattering of nuclear $\gamma$ rays from solid orthohydrogen is derived. It is shown that nuclear $\gamma$-ray scattering competes favorably with inelastic neutron scattering for studying the libron spectrum.

A modified form of the hypernetted-chain (HNC) equation is found that is suitable for the calculation of the pair-correlation function of a classical plasma. The changed equation involves only the short-range screened Coulomb potential and uses no further approximations than are involved in the ordinary HNC equation. The pair-correlation function is computed for a variety of one-component classical plasmas in the region of a dense fluid.

Measurements of the collisional quenching of the $2S$ state of atomic hydrogen by helium, neon, argon, and krypton have been made. The energy range was in the thermal region ($v\sim {10}^6$ cm/sec). The cross sections were determined by measuring the attenuation of a beam of $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ atoms in passing through targets of the various gases. Time-of-flight techniques were used to measure the velocity dependences of the cross sections. For an incident $\mathrm{H}\mathrm{}\left(2S\right)\mathrm{}$ velocity $\approx 1\times {10}^6$ cm/sec, the measured cross sections are $\sigma \left(\mathrm{helium}\right)=81\mathrm{}\pm 12$ ${\mathrm{\AA }}^2$/atom, $\sigma \left(\mathrm{neon}\right)=80\mathrm{}\pm 12$ ${\mathrm{\AA }}^2$/atom, $\sigma \left(\mathrm{argon}\right)=91\mathrm{}\pm 14$ ${\mathrm{\AA }}^2$/atom, and $\sigma \left(\mathrm{krypton}\right)=108\mathrm{}\pm 16$ ${\mathrm{\AA }}^2$/atom. The results for helium are 10-15% higher than theoretical results obtained by Slocomb, Miller, and Schaefer and 20-25% higher than a calculation by Byron and Gersten using a pseudopotential method.

A sum rule due to Inokuti et al. for the Bethe inelastic cross section for fast-charged-particle collisions with atoms and molecules has been applied to ${\mathrm{H}}_2$. Using an accurate two-center configuration-interaction wave function, the formula for nonrelativistic incident particles was found to be given as ${\sigma }_{\mathrm{tot}}=4\mathrm{}\pi a_0^{}{}_{}{}^2{z}^2\left(\frac{R}{T}\right)\left[1.5487\mathrm{}\ln \right(\frac{T}{R})+2.2212]$ to within an error of 0.5% in ${\sigma }_{\mathrm{tot}}$ for incident-electron energies above 1 keV. Although the theoretical values are in good agreement with the summed experimental (i) total ionization (including dissociation ionization), (ii) total dissociative excitation, and (iii) most important discrete excitation cross sections, an apparent systematic trend suggests that one or more of the current experimental total cross sections for electron impact on ${\mathrm{H}}_2$ may not be accurate and that omitted processes should be included for comparison in the incident energy range above 1 keV.

The Born approximation and free-scattering model have been used to calculate the electron-loss cross section from atomic helium incident on He, Ne, Ar, and Kr atoms and on ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ molecules. For the molecules the phase difference between the scattered wave emanating from the two atoms has been considered in the separated-atom approximation. The vibrational damping of the molecule is also taken into account. It is shown that the effect of phase is very small.

Beam-foil spectra of K II and Rb II were obtained at 600-keV bombarding energy. The lines identified in the spectrum of K II and the measured lifetimes of four $4p$ levels, three $4p^{\prime }$ levels, and one $5s$ level of the ion are presented and compared with other experimental results. The first experimental results on the lifetimes of three $5p$ levels, one $5p^{\prime }$ level, and two $5d$ levels of Rb II and the lines identified in the beam-foil spectrum of the ion are given.

Absolute emission cross sections for 3371-Å radiation resulting from $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}(v^{\prime }=0)\to B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}(v^{\prime \prime }=0)$ transition in molecular nitrogen have been measured for H, ${\mathrm{H}}^{+}$, He, and ${\mathrm{He}}^{+}$ projectiles. The energy range covered was from 10 to 100 keV for all projectiles except ${\mathrm{H}}^{+}$, where the lower limit was 40 keV. Excitation of the $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ upper state requires a spin change, usually accomplished by interchange of electrons. Thus the cross section for ${\mathrm{H}}^{+}$ impact is very small (≲${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$) and could not be measured reliably below 40 keV at this time. Some emission cross sections are presented for incident helium atoms in the $2{}_{}{}^3{}_{}{}^{}S$ metastable state. Comparisons are made of ${\mathrm{He}}^{+}$ and H data, where the minimum excitation energy required is the same, and of ${\mathrm{He}}^{+}$ and He data, where the minimum excitation energies are quite different. Cross sections are also presented for emission of the $\mathrm{N}_2^{}{}_{}{}^{+}$ (3914-Å) band for protons in the 8-30 keV energy range, permitting comparison with the measurements of other investigators.

Absolute measurements are reported of the total cross sections for charge transfer and stripping of ${\mathrm{Er}}^{+}$, ${\mathrm{Er}}^{2+}$, ${\mathrm{Al}}^{+}$, and ${\mathrm{Cr}}^{+}$ ions incident on He and ${\mathrm{N}}_2$ in the energy range from 15 to 100 keV. These measurements include ${\sigma }_{10}$, ${\sigma }_{12}$, and ${\sigma }_{21}$. The ${\sigma }_{12}$ cross sections are greater than those of the ${\sigma }_{10}$ at the same velocity for all ions except ${\mathrm{Cr}}^{+}$. Charge-transfer cross sections ${\sigma }_{10}$ have a velocity dependence which is not predicted by the simple adiabatic criterion.

The cross section for the charge transfer in ${\mathrm{H}}^{+}$-${\mathrm{H}}^{-}$ collisions has been theoretically investigated. An expansion in terms of products of atomic wave functions has been used which takes account of the possibilities of the capture of an electron into the $2s$, $2p_0$, and $2p_{\pm 1}$ states. Theoretical results for the capture cross section have been presented for the incident ion energy ranging from 0.5 to 8 keV. Variation with the impact parameter of the probabilities of capture into the excited states have also been shown for several incident ion energies. The present theoretical results for the total capture cross sections are found to be in much better agreement with the experimental findings than are the previously calculated values of Bates and Lewis.

Backscatter coefficients have been measured for positron spectra emitted by radioactive sources and incident on 20 elements ranging from Li to U. The technique, based on recording the annihilation-$\gamma$-ray spectrum in a Ge (Li) detector, eliminates uncertainties encountered in methods where the positrons themselves are detected. The coefficient $R$ for backscatter into $2\pi$ is found to vary with atomic number $Z$ according to the relationship $R=0.342\mathrm{} \ln Z-0.146\mathrm{}$.

The approximation scheme suggested by Schneider, Taylor, and Yaris is applied to the scattering and the bound-state properties of the helium atom. Elastic scattering phase shifts for $s$, $p$, and $d$ partial waves, ionization potentials, one-electron ground-state properties (i.e., electron densities, the natural orbitals, and the ground-state energy), and excitation energies from the ground to the excited states of helium have been calculated simultaneously from the linear-response function and one-particle Green's function. This simultaneity is made possible by concentrating all computational effort on calculating the one- and two- particle amplitudes rather than on the ground- and excited-state wave functions. These amplitudes can be directly related to almost all the properties of physical interest in atomic and molecular systems. Our results for both the scattering- and stationary-state properties are in good agreement with experiment and other previous calculations.

We consider the eigenfunctions of well-defined operator related to $\int {\Psi }^{*}(1^{\prime },2,\dots ,N)\times H(1,2,\dots ,N)\Psi (1,2,\dots ,N)d(2,3,\dots ,N)$, where $\Psi$ is a configuration-interaction (CI) wave function which includes the Hartree-Fock configuration and all double excitations and $H$ is the $N$-electron Hamiltonian of an atomic or molecular system. They satisfy for the energy the same optimum convergence properties as Löwdin's natural spin orbitals satisfy for the wave function. They are equal to the natural spin orbitals when $\Psi$ is the exact wave function or a full CI wave function; $\Psi$ may correspond to the ground state or to any excited state.

The differential cross section for scattering of 300-2000-keV ${\mathrm{H}}^{+}$ and 300-500-keV ${\mathrm{He}}^{+}$ and ${\mathrm{Li}}^{+}$ through 3°-15° by gold targets has been measured. The targets were thin (34-220 ${\mathrm{\mu }\mathrm{g}/\mathrm{c}\mathrm{m}}^2$), vacuum-deposited polycrystalline foils. To eliminate the influence of multiple scattering, several target thicknesses were used to allow extrapolations to zero thickness. The agreement between our experimental data, theoretical predictions, and published experimental data is found to be satisfactory.

Equilibrium charge-state fractions have been measured for tantalum and uranium ions with energies of 2, 4, 6, 8, 10, and 15 MeV, stripped in ${\mathrm{H}}_2$, He, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, Ar, Kr, Xe, carbon, and gold. Average charge and form of the charge distributions and the dependence on ion velocity and target species are discussed. The results on the average charge are compared with theoretical and semiempirical predictions. An anomaly has been found in the particular case of helium targets in which certain charge-state fractions are of unusual magnitude, leading to a relatively high average charge.