The Singwi-Tosi-Land-Sjolander (STLS) nonlinear integral equation for the plasma pair-correlation function $g$ is adapted to two-dimensional one-component plasma (ocp) systems whose Coulombic interactions are characterized by the logarthmic potential. The two-dimensional STLS integral equation has the remarkable property that it can be exactly solved. The resulting expressions for $g\left(k\right)\mathrm{}$ are extensively analyzed and are shown to be negative definite for all values of $k$ and the coupling strength. The implication here is that in the STLS approximation, the ocp liquid can never undergo a phase transition. Exact expressions for $g$ enable us to evolve exact formulas for the correlation energy and heat capacity. Finally, we demonstrate that the STLS approximation scheme exactly reproduces the correct equation of state for the two-dimensional ocp liquid.

The configuration-space properties of the pair-correlation function in the Singwi, Tosi, Land, and Sjolander approximation scheme for a two-dimensional one-component plasma are derived here, using the exact solution in $k$ space in the preceding paper. We also study in detail the effective static potential around a test particle for three cases representing weak, intermediate and strong coupling.

Annihilation lifetime spectra have been measured for positrons in ${\mathrm{H}}_2$ gas at 293, 250, and 77 K at densities in the range 5.9-429 amagat, and in ${\mathrm{H}}_2$-Ne gas mixtures at 77 K having ${\mathrm{H}}_2$ partial densities in the range 1.9-286 amagat and with Ne concentrations in the range 0.02-0.98. The annihilation rate of slow positrons with ${\mathrm{H}}_2$ has a complex dependence on gas density and temperature. Particularly at low ${\mathrm{H}}_2$ densities, the presence of various partial densities of Ne can dramatically affect the positron-${\mathrm{H}}_2$ annihilation process. The slow-positron annihilation rates are discussed in terms of positron-${\mathrm{H}}_2$ collision complexes and the self-trapping of positrons within clusters of ${\mathrm{H}}_2$ molecules. The annihilation in ${\mathrm{H}}_2$ of positrons bound in Ps atoms is discussed in paper II of this series.

The annihilation rate of positrons bound in $o$-Ps atoms and the fraction of positrons which form Ps have been measured for ${\mathrm{H}}_2$ gas at 293, 250, and 77 K at densities in the range 5.9-429 amagat, and for ${\mathrm{H}}_2$-Ne gas mixtures at 77 K having ${\mathrm{H}}_2$ partial densities in the range 1.9-286 amagat and with Ne concentrations in the range 0.02-0.98. Large deviations from the annihilation rates expected for free $o$-Ps atoms are observed and are attributed to the formation of localized cavity states. The results obtained with ${\mathrm{H}}_2$-Ne mixtures strongly support $o$-Ps-induced cavity formation. Complex density and temperature dependencies are observed for the Ps fraction in ${\mathrm{H}}_2$, and the addition of partial densities of Ne enhances positronium formation. The annihilation of slow positrons in ${\mathrm{H}}_2$ is discussed in paper I of this series.

The authors have analyzed the terms of relative order ${\alpha }^2\ln \left({\alpha }^{-1\mathrm{}}\right)$ that come from annihilation kernels in positronium, and have found a contribution of ${\alpha }^6\ln \left({\alpha }^{-1\mathrm{}}\right)\frac{m_e}{24}$ to positronium hyperfine splitting from annihilation kernels, including several new contributions. The resulting hyperfine splitting is 203.4003 GHz, with terms of order $\frac{{\alpha }^6{m}_e}{2}\sim 0.01$ GHz uncomputed. The contributions to the decay rates of ortho- and parapositronium have also been calculated. For orthopositronium the result is $-{\alpha }^2\ln \left({\alpha }^{-1\mathrm{}}\right)\frac{{\Gamma }_0}{3}$. The authors present in more detail the theoretical analysis leading to their previous $\alpha {\Gamma }_0$ calculation and improve on the numerical results. The resulting theoretical orthopositronium decay rate is 7.0386±0.0002 μ${\sec }^{-1\mathrm{}}$, with terms of order ${\alpha }^2{\Gamma }_0=0.0004\mathrm{}$ μ${\sec }^{-1\mathrm{}}$ uncalculated.

A new analysis of the Xe II spectrum is used to explain a number of reported discrepancies between optical data and results of Auger measurements. Some discrepancies for Kr are also resolved.

For electron capture from noble-gas atoms to the continuum of energetic bare projectiles an asymmetry has recently been observed in the cusp of the differential cross section at $v_e=v$ (where $v_e$ and $v$ are electron and projectile velocities, respectively). It is shown that the Oppenheimer-Brinkman-Kramers approximation can provide an asymmetry if terms linear in $\overrightarrow{\mathrm{k}}={\overrightarrow{\mathrm{v}}}_e-\overrightarrow{\mathrm{v}}$ are kept in the expansion of the outgoing Coulomb wave. In contrast to the predictions of the second Born approximation, the resulting shape is independent of the projectile charge.

It is proved that the quantum theory of stimulated light scattering predicts that the gain is bounded by the classical steady-state gain under monochromatic pumping.

A set of rate equations which gives results not previously obtained has been proposed for stimulated light scattering. These equations are shown to be invalid under the conditions where the novel results appear.

The asymmetry in the cusp discussed by Chan and Eichler decreases as $\frac{1}{v}$ with increasing projectile speed $v$. In contrast, the asymmetry originating in the second-order Born term persists as $v$ increases, seemingly in accord with experimental observations. Furthermore, it may be inconsistent to include the correction in the Brinkman-Kramers term discussed by Chan and Eichler without including similar corrections in the second-, third-, and possibly fourth-order Born terms.

The authors discuss the relativistic Thomas-Fermi model for atoms and derive a relativistic extension of the Dirac exchange term. As a result of this model the mutual cancellation of the exchange and relativistic corrections to the energies of inner-shell electrons in heavy atoms ($Z>\mathrm{}50\mathrm{}$) is demonstrated.

Experimental data on depolarized light scattering for gaseous helium are presented for densities between 60 and 250 amagat at room temperature. The author has measured for the low-density integrated depolarization ratio ${\eta }_s=(0.58\mathrm{}\pm 0.10)\times {10}^{-6\mathrm{}}$ ${\mathrm{amagat}}^{-1\mathrm{}}$, which is in good agreement with dipole-induced dipole (DID) approximation. However, the DID effect fails to reproduce the low-frequency experimental line shape and in this case a better agreement is obtained with the induced polarizability calculated by Oxtoby and Gelbart. Evidence of three-body interactions is found when the density increases.

${\mathrm{D}}^{-}$ negative-ion equilibrium fractions of deuterium in collisions with Mg, Ca, Sr, and Ba alkaline-earth-metal vapors have been measured over the energy range 1.25-100 keV. For Ca, Sr, and Ba targets, the yield of ${\mathrm{D}}^{-}$ ions is almost completely independent of the identity of the target over the energy range 4-35 keV. At low energies, an abrupt increase in ${\mathrm{D}}^{-}$ production is observed for targets of Ca, Sr, and Ba but not Mg, and occurs at approximately the same energy, 4 keV, in all three cases. Possible mechanisms responsible for the structure in ${\mathrm{D}}^{-}$ production are discussed.

Variational calculations of $s$- and $p$-wave phase shifts for $e^{-}$-He scattering have been carried out for energies less than 19 eV. The variational wave function represents target-atom electronic correlation, electric dipole and quadrupole polarizability response, and short-range electron-atom correlation at a level of accuracy sufficient for 1% accuracy in the differential cross section. The partial-wave Born approximation is used for phase shifts $l>\mathrm{}1\mathrm{}$. Calculated phase shifts are corrected for estimated systematic errors, and these estimated phase shifts are interpolated as smooth functions of energy by cubic spline fits to auxiliary interpolating functions. Comparison with recent experimental and theoretical cross section data indicates compatibility with the present error estimate of no more than 1%. Data given here make it possible to compute the differential cross section from simple formulas over the energy range considered. The present value of the scattering length is $1.1835a_0$ with 0.5% error.

High-Rydberg atoms are produced by an electron beam passing through each of the rare gases at ∼${10}^{-6\mathrm{}}$ Torr and are detected by electric field ionization after traveling 20.1 cm at thermal velocity. Their principal quantum number ($n$) distributions, time-of-flight distributions, absolute excitation cross sections ${\sigma }_T^{\mathrm{ex}}$, and excitation functions are measured. The atoms detected have $n$ ranging from 20-80 with the most probable $n$ varying with the gas from 28-46. From the measured ${\sigma }_T^{\mathrm{ex}}$ an apparatus-independent absolute cross section ${\sigma }^{\mathrm{ex}}\mathrm{}(n,E)\mathrm{} =\frac{{\sigma }^{\mathrm{ex}}\mathrm{}(n=1,E)\mathrm{}}{n^3}$, is determined. Values of ${\sigma }^{\mathrm{ex}}\mathrm{}(n=1,E)\mathrm{}$ range from 0.5-5 ${\mathrm{\AA }}^2$ at an incident electron energy $E=100\mathrm{}$ eV. Ne and Ar measurements taken for different values of electron current and gas density demonstrate that low-angular-momentum ($l$) high-Rydberg atoms collide with electrons and/or ground-state atoms, causing higher-$l$ states to be populated. The $l$-changing cross section for collisions with electrons is estimated to be ∼ ${10}^6$ ${\mathrm{\AA }}^2$ for Ne and Ar.

Reevaluations of the total $K$-shell cross sections of single-quantum annihilation of positrons have been made by taking into account the $L$-shell contribution. $Z$ dependence of the cross section was studied for five high-$Z$ elements, $Z=50, 73, 79, 82, \mathrm{and} 92$, and for 300-keV positrons. Energy dependence has also been investigated for the last two elements in the energy region of 250-400 keV. Comparisons with theoretical predictions including the screening effect are also made.

A drift-tube mass-spectrometer apparatus has been used to determine thermal-energy (300 K) charge transfer rate coefficients for reactions of the type ${R_a}^{2+}+R_b\to {R_a}^{+}+{R_b}^{+*}$ and ${R_a}^{2+}+R_b\to {R_a}^{+}+{R_b}^{2+}+e^{-}$ (transfer ionization), where $R=\mathrm{H}\mathrm{e},\mathrm{N}\mathrm{e},\mathrm{A}\mathrm{r},\mathrm{K}\mathrm{r},\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{X}\mathrm{e}$. Rate coefficients for ions in the low-lying, metastable excited states (${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^1{}_{}{}^{}D$) as well as the ground state (${}_{}{}^3{}_{}{}^{}P$) have been determined and, in some cases, deexcitation (quenching) coefficients for ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^1{}_{}{}^{}D$ ions have been measured. Reactions with an exoergicity $\Delta E\sim 4$ eV are found to be fast, approaching the limiting Langevin rate, while for $\Delta E<\mathrm{}2\mathrm{} \mathrm{and} >7\mathrm{}$ eV the rates fall off dramatically, in some cases dropping to the radiative value (${\mathrm{\sim }10}^{-14\mathrm{}}$ ${\mathrm{cm}}^3$/sec). The equilibrium constant for the three-body association reaction ${\mathrm{Xe}}^{2+}$ + 2 Ne⇄${\mathrm{}\left(\mathrm{Xe}\mathrm{Ne}\right)\mathrm{}}^{2+}$ + Ne has been determined at 300 K.