We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the $S$-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length $a^{\mathrm{}(-)\mathrm{}}\simeq 2.36a_0$, compared with the static result $a^{\mathrm{}(-)\mathrm{}}=2.476\mathrm{}{a}_0$ of Hara and Fraser. The $S$-wave total and ortho-para conversion cross sections are calculated by making use of both ${}_{}{}^1{}_{}{}^{}S$ and ${}_{}{}^3{}_{}{}^{}S$ results. In the ${}_{}{}^3{}_{}{}^{}S$ case, we see no indication of any resonances below the excitation threshold at 5.1 eV.

In Slater's statistical exchange approximation, the Fermi hole is assumed to be spherical and uniform in density. This leads to an exchange potential that depends on an adjustable parameter $\alpha$ which is different for each atom. The value of this parameter is determined empirically for each atom, usually by equalizing the total energy of the atom calculated by the $X_{\alpha }$ method to that calculated by Hartree-Fock theory. In this paper an explicit dependence of $\alpha$ on the atomic number $Z$ is developed by considering a linear variation of the Fermi-hole density, with the proper boundary values. This permits the calculation of theoretical $\alpha$ values for all atoms in the periodic table; these are reported. Thesse theoretical $\alpha$ values reproduce the $Z$ dependence of the empirical $\alpha$ values in all details. Further, it is shown that electrons of opposite spin should have different $\alpha$ values—a result that has important consequences in $X_{\alpha }$ calculations of magnetic properties and hyperfine interactions.

We have combined the $L=0\mathrm{} \mathrm{and} 1$ partial-wave amplitudes obtained by a two-state coupled static approximation with correlation with the $L\ge 2$ Born amplitudes to obtain the differential cross section for positronium formation in positron-atomic-hydrogen collisions. For positron energies of 0.64 and 0.75 Ry, minima at the scattering angles of 57° and 51° are found. Total cross sections for positronium formation for low and intermediate impact energies are given. Measurement of the differential cross section for the process $e^{+}+\mathrm{He}\to \mathrm{Ps}+{\mathrm{He}}^{+}$ for the detection of possible minima is suggested.

Previous calculations of ion-atom interactions by the pseudopotential and asymptotic methods are used in the computation of the cross section for symmetric charge transfer at energies below 1 keV. The results for ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Rb}}^{+}$, ${\mathrm{Cs}}^{+}$, and ${\mathrm{Ca}}^{+}$ ions are compared with data obtained in beam experiments, and by optical-pumping techniques. The difference in the cross sections for ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ ions of ${\mathrm{Kr}}^{+}$ and ${\mathrm{Xe}}^{+}$ at thermal energies is studied, and the predictions are compared with recent mobility measurements. Cross sections are obtained for ${\mathrm{U}}^{+}$-U collisions, and the dependence of the thermal cross section on the polarizability is described. Symmetric charge transfer of the negative ions ${\mathrm{H}}^{-}$, ${\mathrm{Na}}^{-}$, and ${\mathrm{Cs}}^{-}$ is discussed briefly.

A systematic study is made of the $D$- and $F$-state fine structure of the helium isoelectronic sequence with particular regard to its $n$ and $Z$ dependence. Our theoretical results are compared with available experiments as well as with other theoretical calculations.

The mobilities of ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{K}}^{+}$ ions in ${\mathrm{CO}}_2$, ${\mathrm{CH}}_4$, and ${\mathrm{O}}_2$ gases have been measured at room temperature over a wide range of $\frac{E}{N}$, the ratio of electric field strength to gas number density. The zero-field reduced mobilities of the ions in the gases have been obtained. The mobilities of all the ions in ${\mathrm{CO}}_2$ gas decrease from the values of the respective zero-field reduced mobilities with an increase in $\frac{E}{N}$ before rising to peaks. The mobility of ${\mathrm{Li}}^{+}$ ions in ${\mathrm{CH}}_4$ gas also decreases, though slightly. It is indicated that the phenomena are due to the attractive $r^{-6\mathrm{}}$ term of the ion-neutral interaction potential.

Photon, scattered-atom coincidence measurements with polarization analysis have been made for 3.0-keV ${\mathrm{He}}^{+}$-He charge-transfer collisions leading to $\mathrm{He}\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)$ excitation. The phase difference between the scattering amplitudes for $m_l=0\mathrm{}$ and $m_l=\pm 1$ magnetic-sublevel formation is an approximately constant function of scattering angle. We interpret our results using the electron promotion model and show that the phase difference should be a constant function of scattering angle and incident kinetic energy.

Absolute values of doubly differential cross sections are obtained for electron production in helium by 5- to 100-keV proton impact. The measured values along with earlier data at higher energies are compared with theoretical plane-wave Born-approximation functions obtained from a Hartree-Fock potential. Not only is good agreement obtained at high impact energies (above 300 keV), but fairly good agreement is found at low energies (below about 20 keV). For electrons ejected in the backward hemisphere, unexpectedly poor agreement is noted at intermediate energies where the measured cross sections dip to 50% of the calculated values in some cases. Singly differential cross sections integrated over all angles agree quite well with the theoretical calculations over all ranges of parameters studied. Singly differential cross sections integrated over all electron energies tend to be more isotropic in angle as the proton energy is decreased from 100 to 5 keV. Total cross sections for electron production are also obtained which compare reasonably well with those of Solov'ev et al. but which are higher than those of de Heer et al. It is shown that the contribution to the cross section by the mechanism of charge transfer to the continuum decreases as the impact energy decreases, contrary to the prediction of Salin's treatment.

$L$ x-ray production cross sections have been measured for thin targets of Sn, Te, Nd, Tb, Tm, Au, and Pb using 30- to 80-MeV alpha particles. Theoretical atomic parameters were used to deduce $L$-subshell ionization cross sections for Tb, Tm, Au, and Pb, and average $L$-shell fluorescence yields were used to obtain total $L$-shell ionization cross sections for Sn, Te, and Nd. The experimental results are compared with previous proton and alpha-particle measurements, and with the predictions of plane-wave Born, semiclassical, and binary-encounter approximation treatments of $L$-shell ionization. Generally good agreement with the PWBA calculations is found for these relatively high-energy measurements, although several systematic discrepancies are observed.

The impact-parameter dependences of $L\alpha$, $L\beta$, and total $L$-shell x-ray production of Pb by 2-, 3-, and 6-MeV proton bombardment have been measured and compared with theoretical calculations based on the semiclassical approximation (SCA) and the binary-encounter approximation (BEA). The SCA satisfactorily reproduces the details of the ionization probabilities but overestimates the results at large impact parameters. The BEA does not predict the appropriate structure observed in the x-ray production probabilities. The BEA results are too low at small impact parameters, but in good agreement with measured values at large impact parameters. The behavior at large impact parameters explains the failure of the SCA in predicting the $L$-shell x-ray production total cross sections (the calculated values are too high), whereas the BEA cross sections are in close agreement with experiment.

Ab initio calculations have been performed to provide the basis for a molecular study of the elastic and the lowest charge-transfer channels in ${\mathrm{H}}^{+}$ + Kr collisions. The adiabatic ground-state potential-energy curve agrees satisfactorily with that predicted from elastic scattering experiments. In the Hartree-Fock treatment, the charge transfer into $\mathrm{H}\left(1\mathrm{}s\right)+{\mathrm{Kr}}^{+}\left(4\mathrm{}{p}^5\right)$ appears to be mainly caused by a double virtual electronic transition via a doubly excited state. A "projected valence bond" (PVB) treatment involving single-configuration diabatic states built from projected H and Kr atomic orbitals is also presented. With such diabatic states the charge-exchange process is suitably described as occurring directly under the effect of an exponentially decreasing coupling between closely lying and almost parallel energy curves. The defects of the PVB approximation arising at small internuclear distances ($R$) are discussed. Diabatic states for the spin-orbit coupling are suggested for studying the population sharing between the $\Omega =0^{+}$ states dissociating into $\mathrm{H}+{\mathrm{Kr}}^{+}(4\mathrm{}{p}^5:{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{},{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})$. A procedure involving a basis change from the adiabatic states at small $R$ to the PVB states at large $R$, together with the diabatic states for spin-orbit coupling is proposed to solve effectively the relevant scattering close-coupling equations.

The atomic-beam recoil technique has been used to obtain the ratio of spin-flip to full differential cross sections for the elastic scattering of electrons by rubidium at 0.80, 1.10, and 1.40 eV. Data are presented for a range of angles between 30° and 180° at each of these energies. These measurements were partly motivated by the expectation that relativistic effects, particularly the spin-orbit interaction, will be significant in electron scattering by the heavier alkali metals, even at low energies. In this context, we show how our measurements are related to the relativistic scattering amplitudes recently discussed by Burke and Mitchell for one-electron atoms. These experiments were performed at intermediate magnetic fields, where the nuclear and valence electron magnetic moments are not fully decoupled. The necessary corrections are discussed and taken into account.

The stopping cross section of bulk graphitic carbon for $\alpha$ particles of energy 0.3-2.0 MeV has been measured absolutely and relative to vapor-deposited carbon, and is found to be ∼6-28% higher than the corresponding value of vapor-deposited carbon. The difference is attributed to an allotropic effect.

An experimental technique utilizing the methods of laser saturation spectroscopy that enables a direct observation of the momentum transfer distribution generated by rotationally inelastic molecular collisions is presented. This method has been applied to ${\mathrm{CO}}_2$ in collision with a wide variety of partners including ${\mathrm{CO}}_2$, ${\mathrm{H}}_2$, Ne, ${\mathrm{NH}}_3$, and ${\mathrm{CH}}_3$F. The observations indicate that in a large number of cases the rotational transition results primarily from peripheral collisions which are effective in transferring angular momentum, but which communicate a relatively small linear momentum transfer.

Nuclear-polarization energy shifts are calculated for the low-lying levels of muonic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. In ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, the shift of the $2s_{\frac{1}{2}}$ level is found to be - 3.1 meV, in agreement with the result of Bernabeau and Jarlskog. The corresponding shift in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is - 4.9 meV. Other corrections to the energy levels are calculated, with the improved result that the total theoretical $2s_{\frac{1}{2}}-2\mathrm{}{p}_{\frac{3}{2}}$ energy difference in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is $1.8131-0.102r^2\pm 0.001$ eV, where $r$ is the nuclear rms charge radius (in femtometers). Together with the measured value 1.5274 ± 0.0009 eV, this implies $r=1.674\mathrm{}\pm 0.004$ fm, which is consistent with available electron scattering data.

The recently proposed analytic methods of Thomas and Chan, which reduce the Glauber amplitude for charged-particle-neutral-atom collisions to a one-dimensional integral representation involving modified Lommel functions, are used to study elastic $e^{-}$- Li scattering. The criterion for using the frozen-core approximation is discussed. The numerical results obtained using these two models are presented.

A trial wave function that is a linear combination of two traveling hydrogenlike basis functions which contain two variable-charge parameters and a polarization parameter has been used to obtain bounds on the second-order error term in the variational principles of Demkov and Storm that are comparable to the magnitudes of approximate $1s$ charge-exchange amplitudes. It is demonstrated that the error function ${\Delta }_1\left(X_i\right)$ can be employed to judge various calculations and as an aid in adjusting parameters in the trial wave function to obtain better bounds. Based upon the use of ${\Delta }_1$ as a measure of error in an approximate trial wave function, we conclude that the Euler-Lagrange variational method is not the optimal approach. Suggestions are made for future work which might improve the calculated bounds.