Electron-capture cross sections have been evaluated for high-velocity protons impinging on a ground-state helium target. The scattering matrix element was formulated within the quantum-mechanical impulse approximation and the resulting cross sections were examined as a function of various levels of sophistication for the description of the target atom. The helium wave functions used here were of a simple one-parameter ($\lambda$) variational form, a Hartree-Fock (HF) equivalent function and, finally, a configuration-interaction (CI) description. The projectile energy ranged from 25 keV to 3.5 MeV and, where possible, the cross sections were compared with experiment.

By measuring the energy and time of flight of fragment ions from molecular breakup, the fragments can be separated according to their mass to charge ratios and the kinetic-energy spectra for each recorded. This technique is applied to the dissociative ionization of ${\mathrm{N}}_2$ caused by 1-MeV ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ projectiles. The energy spectra for ${\mathrm{N}}^{+}$ is not unlike that produced by electron bombardment, but the ${\mathrm{N}}^{++}$ spectra show some high-energy structure that has not been previously observed. An ${\mathrm{N}}^{3+}$ spectrum is obtained with a maximum near 25 eV, and the reflection method is used to obtain a potential curve for a presumed ${\mathrm{N}}_2^{3+}$ state.

Total cross sections in the energy range 25-450 keV for destruction of metastable helium atoms (i.e., electron loss and deexcitation) penetrating ${\mathrm{H}}_2$, He, ${\mathrm{N}}_2$, Ne, or Ar gas targets have been measured by the beam-attenuation technique. The fast, metastable helium atoms were formed by electron detachment from ${\mathrm{He}}^{-}$ ions in either a strong electric field or under single-collision conditions in ${\mathrm{H}}_2$ or He gas. Apparent metastable fractions of the beams, which have also been extracted from the attenuation curves, depend strongly on the attenuation gas used. This shows that not only electron loss but also deexcitation is an important destruction mechanism for metastable helium atoms in these gases. The measured total destruction cross sections and apparent metastable fractions define upper as well as lower limits for both the electron loss and the deexcitation cross sections for metastable helium atoms. Generally, these limits lie close to each other. The experimental electron-loss cross sections for metastable helium atoms are in good agreement with semiempirical cross sections calculated in the classical impulse approximation of Bates and Walker. The experimental upper limit for the deexcitation cross section in a given gas is close to the electron-capture cross section for ${\mathrm{He}}^{+}$ in the same gas.

Cross sections for single- and double-electron capture have been measured for incident ions of C, N, and O with initial charges + 3 to + 6 colliding with molecular hydrogen at velocities between 0.3 × ${10}^8$ and 1.2 × ${10}^8$ cm/sec. The single-electron-capture cross sections for a particular incident charge are nearly constant with changing velocity. The single-capture cross sections range from about 7 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ for + 3 incident ions to 40 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ for + 6 incident ions. Double-electron-capture cross sections are roughly one order of magnitude smaller. The data are qualitatively interpreted on the basis of the molecular potential-curve model for slow collisions.

We have studied the charge distributions of oxygen ions after small-impact-parameter collisions with Ne, Ar, Kr, and Xe gases. Bombarding energies in the 10-30-MeV range and incoming charge states between $4^{+}$ and $7^{+}$ were scattered to angles between 5° and 8° in a single collision process. The measurements indicate that for the heavier gases an equilibrium charge distribution is obtained after a single collision. Interpretation of the experimental results on the basis of a statistical "compound-atom" model is suggested.

Energies of the transitions between high-lying ($n\ge 6$) states of muonic lead were accurately determined. The results are interpreted as a ∼2% test of the electron screening. The agreement between experiment and theory is good if it is assumed that the refilling of the electron $K$ shell is fast. The present results furthermore severely restrict possible ionization of the electron $L$ shell.

Energy spectra of electrons with velocities near the ion velocity were measured and angular distributions were derived for both the ${\mathrm{He}}^{++}$/Ar and ${\mathrm{He}}^{+}$/Ar systems at 2 MeV. The data were compared to charge-exchange theories for target ionization and to an electron-scattering model for projectile ionization. It was found that in the forward direction target ionization and projectile ionization were indistinguishable on the basis of the ejected electron spectra.

We present ab initio calculations of inelastic energy loss and ionization phenomena associated with ${\mathrm{Ar}}^{+}$ -Ar collisions at small distances of closest approach and for laboratory collision energies ranging from several keV to several hundred keV. Outer-shell excitations are handled statistically; inner-shell excitations are calculated from the viewpoint of quasidiabatic molecular orbital promotion. Auger electron yield, average state of ionization, and average inelastic energy loss are calculated per collision as a function of distance of closest approach of the collision partners for several laboratory collision energies. Average charge-state probabilities per collision partner are calculated as a function of the average inelastic energy loss per atom. Our calculations agree with the available data. It is shown that the structure in the data is due to the underlying structure in the inner-shell independent-electron quasimolecular promotion probabilities. In particular, the fact that the dominant promotion mechanism involves rotational coupling means that all corresponding probabilities decrease dramatically for collisions involving laboratory scattering angles greater than 45°. Thus, a sharp decrease in Auger electron yield, average ionization, and average inelastic energy loss is predicted for these supposedly more "violent" collisions.

The self-energy corrections of order $\alpha$ to the $K$-electron binding energy in high-$Z$ atoms are studied numerically throughout the range $Z=70-160\mathrm{}$. Nuclear finite-size effects are included in the electron wave functions and in the electron propagator to avoid the Coulomb singularity at $Z\alpha =1\mathrm{}$. Denoting the self-energy correction by $\Delta E=\frac{\alpha {\left(Z\alpha \right)}^{4}F\left(Z\alpha \right)m{c}^2}{\pi }$, it is found that $F\left(Z\alpha \right)$ increases smoothly from a minimum near $Z=90\mathrm{}$ through $F\left(100\mathrm{}\alpha \right)=1.46\mathrm{}\pm 0.01$ to $F\left(160\mathrm{}\alpha \right)=3.34\mathrm{}\pm 0.16$. For comparison purposes, the self-energy corrections in a Coulomb field for $Z$ between 50 and 130 are evaluated, and the values of $F\left(Z\alpha \right)$ thus obtained are in close agreement with previously published values; the Coulomb field values of $F\left(Z\alpha \right)$ are very close to the finite-nucleus results for $Z<\mathrm{}90\mathrm{}$.

Many-body perturbation theory is developed within the algebraic approximation, i.e., parametrization of state functions by expansion in a finite basis set. This considerably extends the applicability of the theory to molecules, allowing all two-, three-, and four-body contributions to the energy to be evaluated through third order. Within this context, a comparison is presented between perturbation calculations and previously reported configuration-interaction calculations which employed the same basis sets. The [2/1] Padé approximants to the energy are constructed and upper bounds to the energy expectation values are determined. Two zeroth-order Hamiltonians are used, and the convergence of the resulting perturbation series is compared. Both of these perturbation expansions yield Padé approximants to the energy which are within 0.9% of the corresponding configuration-interaction results. The variation-perturbation upper bounds for the energy are all within 3.2% of the corresponding configuration-interaction bounds. Considering this agreement and the tractability of the diagrammatic perturbative scheme, it appears that the perturbation expansion is highly competitive.

The Feshbach-Rubinow approximation, with a modification to take better account of screening, is first applied to an illustrative one-dimensional problem. The same method is then used in realistic two-electron atoms to obtain analytic expressions for the ground-state energy and wave function. Numerical results are presented to show the improvement from earlier unmodified Feshbach-Rubinow calculations.

New configuration-interaction (CI) ideas are tested and utilized to yield the most accurate determination to date of the Be nonrelativistic energy $E_{\mathrm{nr}}=-14.667358\mathrm{}\left(28\right)\mathrm{}$ a.u. Be, including a mass-polarization correction of -0.000030(3) estimated from literature data. A 650-term CI series gives a rigorous upper bound $E_u=-14.666902\mathrm{}$. The truncation error of the $10s9p8\mathrm{}d7f5\mathrm{}g3\mathrm{}h1i$ carefully optimized Slater-type orbital set is estimated largely from studies of apparent energy limits for each harmonic; it amounts to -0.000407(22). An additional -0.000019(2) energy error arises from truncating the full CI expansion. A relativistic energy correction $E_{\mathrm{expt}}-E_{\mathrm{nr}}=-0.001987\mathrm{}\left(30\right)\mathrm{}$ is predicted, which agrees well with an ab initio estimate of -0.001986 obtained by combining the Hartree-Fock quality results of Hartmann and Clementi with Pekeris's exact result for ${\mathrm{Be}}^{2+}$, thus including $K$-shell correlation effects in the relativistic correction. The correlation energy is determined with 0.03% of uncertainty, $E_c=-2.56604\mathrm{}\pm 0.00068$ eV. Particular attention is given to construction of basis sets, energy extrapolation procedures, and compact approximations to the full CI expansion. Comparisons with previous calculations are made, and it is pointed out how the present results may be improved.

Hartree-Fock calculations with the inclusion of a relativistic correction for more than 30 configurations of UI indicate the existence of many simple relationships between spin-orbit coupling constants and Slater integrals for different configurations. These are discussed in detail and compared with experimental values wherever possible. The use of these relationships in empirical least-squares energy-level fits should allow considerable reduction in the number of parameters required to analyze these complex configurations with open $f$, $p$, and $d$ shells. The calculated integrals also provide some bounds on parameter values and guidelines to further analysis of energy levels of U and other actinides.

Variational expressions for arbitrary quantum-mechanical matrix elements involve not only trial wave functions but also trial auxiliary Lagrange multipliers, which can be constants, functions, Green's functions, etc. Recently an extremum principle has been proposed as a useful tool for the approximate determination of any Lagrange functions that appear; it is the first such tool of general applicability. This extremum principle has here been applied to the variational determination of the diamagnetic susceptibility and form factor of helium; each requires the approximate determination of one Lagrange function. The results, reported on in this paper, demonstrate that the extremum principle can in fact be used in the sense that no singularities appear and the functional that determines the trial Lagrange function $L_t$ converges monotonically. The results indicate that provided $L_t$ is roughly as accurate as the trial wave function, the variational estimate of a matrix element can be a significant improvement over the first-order estimate. The present method provides an alternative to the direct approach in which the trial bound-state wave functions are obtained in the course of a Rayleigh-Ritz calculation of the energy. Further studies are needed to determine the relative advantages of the two approaches.

Using gas targets, $K$ x-ray cross sections have been measured as a function of projectile charge state in nearly symmetric collisions for highly ionized S and Cl ions at a velocity comparable to that of the $K$-shell electrons. For bare nuclei, the projectile cross sections are accurately described by the cross section for capture to excited states calculated in a Brinkman-Kramers approximation and normalized by a single scaling factor. With lower-charge-state incident ions, the total $K$-vacancy cross section is in good agreement with the $2p\pi -2\mathrm{}p\sigma$ cross section for rotational coupling.

In collisions of 0.2-3.0-MeV ${\mathrm{Na}}^{+}$ with thick targets of Ti through Zn, relatively flat molecular-orbital continua are observed that extend from the characteristic separated-atom lines to the united-atom $L$-shell limits. The broadening of these continua beyond their respective united-atom limits is essentially target independent and can, to a good approximation, be fitted with half-Gaussians characterized by widths proportional to $E^{\frac{1}{4}}$, where $E$ is the energy of the incident ion. Similar continua are observed for ${\mathrm{Na}}^{+}$-target combinations that have as their limit the united-atom $M$ shell.

X rays resulting from $L$-shell vacancies in uranium atoms, produced by bombarding thin targets with protons (2.0-18.0 MeV) and alphas (3.0-16.0 MeV) were measured using a Si(Li) x-ray detector. $L$-subshell ionization cross sections for uranium were extracted from the $L{\alpha }_{1,2}$, $L{\gamma }_1$, and $L{\gamma }_{4,4^{\prime }}$, x-ray transitions. The observed projectile energy dependences are reasonably well reproduced by plane-wave Born, semiclassical, and binary-encounter approximation calculations at the higher energies, but show significant discrepancies below 2 MeV/amu. The ratios of $\frac{{\sigma }_{L_1}}{{\sigma }_{L_2}}$ and $\frac{{\sigma }_{L_3}}{{\sigma }_{L_2}}$ also show departures from theoretical predictions at low energies.

Crossed beams of electrons and ${\mathrm{Hg}}^{+}$ ions have been used to measure absolute cross sections for emission of 284.7-nm radiation, resulting from excitation of a predominantly ground-state ${\mathrm{Hg}}^{+}$ target to the $7s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state. Values range from 3 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ near threshold, where the cross section is strongly peaked, to 1.3 × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 280 eV. Also reported are some measurements of emission of 479.7-nm (Hg III) radiation, resulting from electron impact on both ${\mathrm{Hg}}^{+}$ and ${\mathrm{Hg}}^{++}$ targets. Cross sections range from approximately 5 × ${10}^{-19\mathrm{}}$ to 5 × ${10}^{-20\mathrm{}}$ ${\mathrm{cm}}^2$, and in the case of electron-${\mathrm{Hg}}^{++}$ collisions, are more than an order of magnitude smaller than predicted by an available semiclassical binary-encounter calculation.

We have measured the probability per collision for the production of Cl and Ar $K$ vacancies in the bombardment of argon gas targets by 15- and 30-MeV chlorine projectiles. By detecting the Cl and Ar $K$ x rays in coincidence with Cl ions scattered to a known angle we have deduced the dependence of the probability on impact parameter $b$. The sum of Ar and Cl $K$-vacancy production probabilities, presumably a measure of $2p\sigma$ vacancy production, is found to depend in magnitude on the charge state of the Cl projectile, but the shape of the summed probability curve, when plotted versus $b$, is not charge-state dependent. The measured shape is close to that expected for $K$-vacancy production via $2p\sigma$-$2p\pi$ rotational coupling. The data suggest that, for these collisions, the production of $2p\pi$ vacancies at large internuclear distances is important and that a two-step mechanism for the production of the $K$ vacancies is operating.

Cross sections for relaxation of circular and linear polarization of $6{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ cesium atoms, induced in collisions with ground-state He, Ne, Ar, and Xe, have been determined by Zeeman scanning techniques. A fluorescence cell containing low-pressure cesium vapor together with a buffer gas was irradiated with circularly or linearly polarized 8521-Å Cs resonance radiation, producing excited and polarized Cs atoms which became depolarized in subsequent collisions with the buffer-gas atoms. The resulting depolarization of the cesium resonance fluorescence was monitored in relation to buffer-gas pressure (0-10 Torr) and to the strength of the ambient magnetic field (0-10 kG). At low fields at which the nuclear spin $\overrightarrow{\mathrm{I}}$ is coupled to the electronic angular momentum $\overrightarrow{\mathrm{J}}$, the measurements yielded depolarization cross sections $Q(\mathrm{circ}.\mathrm{})$ and $Q(\mathrm{lin}.\mathrm{})$, which agree within experimental error with theoretical values calculated for spin-coupled conditions. At kilogauss fields with $\overrightarrow{\mathrm{I}}$ and $\overrightarrow{\mathrm{J}}$ decoupled, the experiments produced cross sections for disorientation and disalignment, which are also in satisfactory agreement with the appropriate theoretical predictions. The results indicate that the nuclear spin has a more pronounced effect on the collisional relaxation of the atomic dipole than of the quadrupole.