Total scattering cross sections have been measured in the same apparatus for positrons and electrons colliding with helium, neon, and argon atoms in the energy range from 15 to 800 eV using a beam-transmission technique. These measurements reveal a merging of the positron and electron cross-section curves for helium at energies above 200 eV while the available theories predict this merging to occur at considerably higher energies. For neon and argon the positron and electron total-cross-section curves are slowly approaching each other at the highest energies. The present experimental approach is analyzed with regard to the discrimination against small-angle forward elastic scattering, and estimates are made of other potential errors in the measured total cross sections. The present results are used to test the zero-energy sum rule, obtained from forward dispersion relations, and it is found that these data are consistent with prior measurements in that the sum rule is found to fail for electron scattering and to be valid for positron scattering.

Doubly excited states of helium sequence ($Z=1-10\mathrm{}$) are investigated by a complex-coordinate method. Some lower-lying ${}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ and ${}_{}{}^{1,3}{}_{}{}^{}P_{}^o{}_{}{}^{}$ states below the $N=2\mathrm{}$ hydrogenic thresholds are calculated by the use of Hylleraas-type wave functions. Results are compared with recent calculations and experiments.

A calculation of the photoionization cross sections is presented for alkali-metal atoms such as Li and Na in plasma environments. The computational scheme is based on the complex coordinate rotation method. A model potential formalism has been used to simplify the computational complexity of the problems of making quantitative predictions of properties and interactions of many electron systems in Debye plasmas. The plasma environment is found to appreciably influence the photoionization cross sections. In this regard the photoionization cross sections of isolated atoms are also discussed that is found to be in good agreement with the previous theoretical results. It is observed that the strong plasma screening effect remarkably alters the photoionization cross sections near the ionization threshold. The Cooper minimum in the photoionization cross sections of Na shifts toward the higher energy as the plasma screening effect increases. For Li, the Cooper minimum is uncovered in strong plasma environments. This is the first time such structures have been determined.

The complex-rotation method has been applied to investigate autoionization states of the positronium negative ion ($e^{-}{e}^{+}{e}^{+}$). Only the singlet $S$ states are considered, but both the lowest resonance below the $n=2\mathrm{}$ and $n=3\mathrm{}$ positronium thresholds are calculated. Using the Hylleraas-type wave function with 161 terms, the resonance parameters (position and width) are determined by the complex-rotation method. The higher members of the resonances are estimated by the stabilization method but no width and "shift" are provided. In addition, by varying the mass of the positron from $1m_e$ (electron mass) to $\infty$, we are able to investigate the lowest resonance for systems ranging from ${\mathrm{Ps}}^{-}$ to ${\mathrm{H}}^{-}$. From this analysis, the lowest resonance for other three-body systems ($e^{-}{\mu }^{+}{e}^{-}$, ${\mu }^{-}p{\mu }^{-}$, ${\mu }^{-}d{\mu }^{-}$, ${\mu }^{-}t{\mu }^{-}$) are deduced.

The ground-state energy of positronium negative ions, ${\mathrm{Ps}}^{\mathrm{-}}$, is calculated using double-basis-set Hylleraas functions in which four nonlinear parameters are used. The optimized result of E=-0.524 010 140 465 7 Ry obtained by using 744-term function represents the lowest variational energy for ${\mathrm{Ps}}^{\mathrm{-}}$ in the literature to date to our knowledge. The wave function is then used to calculate the positron annihilation rate for ${\mathrm{Ps}}^{\mathrm{-}}$.