Hartree-Fock-Roothaan-Clementi (HFRC) densities are used to calculate the total kinetic energies and the total binding energies of neutral atoms according to the Thomas-Fermi-Dirac formulas with inhomogeneity corrections. The strength of the Weizsäcker inhomogeneity correction is multiplied by the Kompaneets and Pavlovskii, and Kirzhnits factor of 1/9. Of the atoms considered ($Z=2\mathrm{}$ to $Z=36\mathrm{}$; $Z=54\mathrm{}$) almost all the total kinetic energies agree with the HFRC expectation values to better than 1%, and the largest disagreement is 1.7%. Except for He, Li, Be, and B, the total binding energies agree with the HFRC expectation values to better than 0.7%. Higher-order corrections of the Thomas-Fermi-Dirac-Weizsäcker formulas are therefore very small.

The atomic-beam magnetic-resonance technique has been used to measure the hyperfine-structure tensor polarizability (quadratic Stark effect) in the $6^2{P}_{\frac{1}{2}}$ ground state of atomic thallium. Electric fields of up to 460 kV/cm were used to lift the degeneracy between the $m_F=0\mathrm{}$ and the $m_F=\pm 1$ substates in the absence of an external magnetic field, and focusing transitions between these Stark-separated states were observed. Measurements were also made between Zeeman-separated substates. The results are ${\alpha }_T=-(3.74\mathrm{}\pm 0.09)\times {10}^{-8\mathrm{}}$ Hz/${\mathrm{}(\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^2$, or $k=-(5.62\mathrm{}\pm 0.14)\times {10}^{-8\mathrm{}}$ Hz/${\mathrm{}(\mathrm{V}/\mathrm{c}\mathrm{m})\mathrm{}}^2$, where $\delta \nu =k{E}^2$ is the Stark shift of the $(m_F=0)\leftrightarrow (m_F=-1)$ "flop-in" transition.

The single-electron stripping cross section for $\mathrm{N}_1^{}{}_{}{}^{+}$ ions in targets of Ne, Ar, and Kr have been measured in the energy range 35 to 140 keV. It was found that the observation of the linear relationship between the target pressure and the counting rate is an inadequate test for single-collision conditions in these reactions. The angular spread was found to be significant, and the lack of agreement among previous measurements seems to be explainable in terms of the different ways in which the angular spread was handled. The two-state and the Firsov theories of charge-changing cross sections are unable to account for the considerable differences in the cross sections between the three targets.

The observation and identification of $K$ x rays resulting from one-photon two-electron rearrangement are made for Mg, Al, and Si following heavy-ion bombardment. Two types of rearrangement processes, which lead to $K$ x rays below the energy of the characteristic $K\alpha$ x ray, are delineated: the radiative Auger effect (RAE) and radiative electron rearrangement (RER). The RAE process previously described by Åberg and Utriainen competes with the characteristic $K\alpha$ x ray. The observed energies and relative intensities $\frac{\mathrm{RAE}}{K\alpha }$ from heavy-ion bombardment agree with those from electron and photon excitation. The RER process which we have recently proposed is the emission of a photon from the ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n}$ to ${\mathrm{}\left(2s\right)\mathrm{}}^{-2\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n+1\mathrm{}}$ electron rearrangement for $n=1-6\mathrm{}$. This model gives good agreement between measured and Hartree-Fock calculated RER energies. $K{L}^n$ RER and $K\alpha L^n$ satellites are competing decay branches of the ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n}$ initial configuration. The $\frac{\left(K{L}^n\mathrm{RER}\right)}{K\alpha L^n}$ branching ratios are measured. The RER transitions are shown to be allowed by configuration mixing of final states with the same spin and parity. The branching ratio is a product of the mixing coefficient and a ratio of fluorescence yields. The theoretical branching ratios $\frac{\left(K{L}^1\mathrm{RER}\right)}{K\alpha L^1}$ and $\frac{\left(K{L}^2\mathrm{RER}\right)}{K\alpha L^2}$ are calculated and compared to experiment.

We briefly discuss four of the principal energy-apportionment techniques currently used in energy-deposition calculations—the Fowler equation, the Monte Carlo approach, the discrete-energy-bin method, and the Peterson-Green integral equation in the context of the continuous-slowing-down approximation (CSDA). Using a complete set of analytic inelastic cross sections for molecular hydrogen, we calculate, by each of these four methods, the energy per ion pair $W$ associated with the degradation in ${\mathrm{H}}_2$ of incident electrons with initial energies ranging between the ionization threshold and 1000 eV. We find that the results obtained from the first three of these methods are in very good agreement with one another, while the values of $W$ obtained by the last method in the CSDA are consistently larger than the corresponding values obtained from any of the discrete-energy-loss approaches. Lastly, we isolate the cause of the CSDA discrepancies and propose two techniques for modifying the low-energy predictions of the CSDA so that they are in much better agreement with those of the three discrete energy-apportionment methods for all incident-electron energies.

Polarization-free excitation cross sections in the extreme vacuum ultraviolet have been measured for electron impact on Ar. Observed spectral features were those lines of ArI and ArII which lie between 700 and 1100 Å. Excitation functions were measured for the ArI resonance line at 1048 Å and the ArII resonance line at 920 Å. Peak cross sections for these two lines were found to be (39.4 ± 7.9) × ${10}^{-18\mathrm{}}$ and (6.9 ± 1.4) × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$, respectively. At low energies, excitation of the ArII resonance line is dominated by an electron exchange transition.

Absolute and relative cross sections were obtained for the Penning-ionization (PI) reaction ${\mathrm{Ne}}^{*}+\mathrm{Kr}\to \mathrm{Ne}+{\mathrm{Kr}}^{+}+e$ and the associative-ionization (AI) reaction ${\mathrm{Ne}}^{*}+\mathrm{Kr}\to \mathrm{Ne}{\mathrm{Kr}}^{+}+e$. The studies were made by a merging-beams technique for a relative kinetic energy of the reactants from nominally 0.01 to 10 eV for PI and 0.01 to 0.6 eV for AI. The ${\mathrm{Ne}}^{*}$ represents a composite of $\mathrm{Ne}\left(3s{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ and $\mathrm{Ne}\left(3s{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)$. At thermal energy the measured cross sections are compared with values obtained by beam-gas and beam-beam techniques.

Absolute charge-transfer cross sections for the production of 10 excited levels of the lithium atom produced in the ${\mathrm{Li}}^{+}$ + ${\mathrm{H}}_2$ → ${\mathrm{Li}}^{*}$ + $\mathrm{H}_2^{}{}_{}{}^{+}$ reaction have been determined as a function of the lithium ion energy over the 0.2-3.0-keV energy range. These cross sections are observed to follow the functional form $\sigma (\nu ,\Delta E)=K\exp \left(\frac{-\Delta \mathrm{Ea}}{\hslash \nu }\right)$, where $\nu$ is the ion velocity and $\Delta E(n,l)\mathrm{}$ is the "energy defect" for the charge transfer into the $n$, $l$ excited level of lithium. This functional dependence can be rationalized in terms of a semiclassical coupled-harmonicoscillator model. We find that at constant $\nu$ the relative magnitudes of the capture cross section are governed by the energy defect and the angular momentum quantum number of the final state. Specifically, we observe that ${\sigma }_{\mathrm{CT}}\mathrm{}\left(\mathrm{nd}\right)>{\sigma }_{\mathrm{CT}}\mathrm{}\left(\mathrm{np}\right)>{\sigma }_{\mathrm{CT}}\mathrm{}\left(\mathrm{ns}\right)\mathrm{}$, where ${\sigma }_{\mathrm{CT}}$ is the charge-transfer cross section.

The adiabatic spectrum of potential energy curves, corresponding to the ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Pi$ states of the molecular complex, have been calculated using an ab initio configuration-interaction method. Curve-crossing phenomena are found in all the curves with the exception of the lowest ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ state, corresponding to the ${\mathrm{Ne}}^{+}\left({}_{}{}^2{}_{}{}^{}P\right)+\mathrm{He}\left({}_{}{}^1{}_{}{}^{}S\right)$ asymptotic level. An approximate threshold of 22 eV is predicted for the neon ${}_{}{}^1{}_{}{}^{}S$ to ${}_{}{}^1{}_{}{}^{}P$ excitation, which is in good agreement with available experimental predictions. The charge-exchange excitation of Ne in the ${\mathrm{Ne}}^{+}$ + He collision occurs at about 29 eV in the ${}_{}{}^2{}_{}{}^{}\Pi$ state for an internuclear separation of $1.5a_0$. Three additional crossings for the ${}_{}{}^2{}_{}{}^{}\Pi$ spectrum are also found at lower energy and larger separation. The cross section for the first ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ crossing is calculated as a function of collision energy using the Landau-Zener-Stueckelberg method, and including the phase-interference effect. Phase-interference ("Stueckelberg") oscillations are found in the cross section and are in qualitative agreement with oscillations found in the experimental cross sections.

Ionization rate coefficients of He-like boron and carbon have been deduced from the time histories of the spectral lines emitted by BIV and CV ions in a small $\theta$-pinch plasma. The radial electron density (∼5× ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$) and temperature (∼220 eV) profiles were determined by 90° Thomson scattering. After making appropriate corrections for two-step ionization via the metastable $\mathrm{}\left(1s2s\right)\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ level, theoretical estimates were found to agree with experimental results. A comparison of the above and previously measured ionization rates for various ions with existing theoretical predictions shows that the semiclassical theory of Burgess yields values that are in good agreement with experiment, especially at higher temperatures. For removal of $1s$ electrons, semiempirical rate coefficients are also in agreement with experiment, but are too large by a factor ∼2 for other electrons.

The recombination coefficients $\alpha$ of ${\mathrm{N}{\mathrm{H}}_4}^{+}·{\left(\mathrm{N}{\mathrm{H}}_3\right)}_n$ series ions for $n=0\mathrm{} \mathrm{to} 4$ have been determined using a microwave afterglow-mass-spectrometer apparatus. For $\mathrm{NH}_4^{}{}_{}{}^{+}$ ions, under conditions where the electron, ion, and neutral temperatures are equal ($T_e=T_{+}=T_n$), $\alpha \left({18}^{+}\right)=(2.5\mathrm{}\pm 1), (1.5\mathrm{}\pm 0.3) \mathrm{and} (1.3\mathrm{}\pm 0.2)\times {10}^{-6\mathrm{}}$, ${\mathrm{cm}}^3$/sec at 200, 300, and 410 K, respectively. The electron-temperature dependences of the recombination coefficients for the first and second cluster ions are found to be (in ${\mathrm{cm}}^3$/sec) $\alpha \left({35}^{+}\right)=2.82\mathrm{}\times {10}^{-6\mathrm{}}{\left[\frac{300}{T_e\mathrm{}\left(K\right)\mathrm{}}\right]}^{0.147}$ and $\alpha \left({52}^{+}\right)=2.68\mathrm{}\times {10}^{-6\mathrm{}}{\left[\frac{300}{T_e\mathrm{}\left(K\right)\mathrm{}}\right]}^{0.050}$, accurate to ± 10% over the range $300\le T_e\le 3000$ K. At 200 K, the third and fourth clusters yield $\alpha \left({69}^{+}\right)=\alpha \left({86}^{+}\right)=(3\mathrm{}\pm 1)\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/sec. A new recombination mechanism, cluster-detachment recombination, is postulated to account for the very weak variation of $\alpha$ with electron temperature observed for the (${35}^{+}$) and (${52}^{+}$) ions.

We present results for direct radiative capture of 1-100-keV electrons by Ar-like, Ne-like, and completely ionized Mo ions. The dependence on incident electron energy and degree of ionization is discussed.

The energy-loss spectrum of fast charged particles penetrating a dilute molecular gas target has been analyzed theoretically, with a homogeneous gas mixture in the state of complete dissociation as a reference standard. It is shown that the geometrical structure of molecules causes the energy-loss straggling and higher moments over the energy-loss spectrum to be greater than the corresponding quantities for a completely dissociated gas of equal composition. Such deviations from additivity are shown to be most pronounced at energies around the stopping-power maximum. Supporting evidence is found in the experimental literature.

With the use of restricted numerical Hartree-Fock-Slater wave functions and the perturbation-numerical approach of Sternheimer, the ionic antishielding factor ${\gamma }_{\infty }$ has been calculated for the following three isoelectronic series of ions: ${\mathrm{Cr}}^{+}$, ${\mathrm{Mn}}^{2+}$, ${\mathrm{Fe}}^{3+}$, ${\mathrm{Co}}^{4+}$, ${\mathrm{Ni}}^{5+}$, ${\mathrm{Cu}}^{6+}$; ${\mathrm{Mo}}^{+}$, ${\mathrm{Tc}}^{2+}$, ${\mathrm{Ru}}^{3+}$, ${\mathrm{Rh}}^{4+}$, ${\mathrm{Pd}}^{5+}$, ${\mathrm{Ag}}^{6+}$; and ${\mathrm{W}}^{+}$, ${\mathrm{Re}}^{2+}$, ${\mathrm{Os}}^{3+}$, ${\mathrm{Ir}}^{4+}$, ${\mathrm{Pt}}^{5+}$, ${\mathrm{Au}}^{6+}$. For the ions of the first two series, ${\gamma }_{\infty }$ values have been correlated to their distance of outermost maximum in the total radial electron density distribution function. Also, it has been observed that within an isoelectronic series, ${\gamma }_{\infty }$ values can be satisfactorily represented in terms of a polynomial in ${\mathrm{Z}}^{-1\mathrm{}}$, the reciprocal of atomic number.

The electric field gradient for the lowest ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state in the aluminum atom has been calculated by many-body perturbation theory. We find that the quadrupole shielding factor has a much larger antishielding contribution coming from the radial excitations of the $2p$ core than previously estimated. This substantially larger contribution has not been considered in earlier work. It arises from the fact that only one of the $2p$-core electrons undergoes a monopole ($K=0$) exchange interaction with the valence $3p$ electron, breaking the spherical symmetry of the $2p$ core. Two-particle excitations consisting of correlation and consistency effects lead to a significant shielding contribution. The total quadrupole shielding factor is found to be antishielding in nature and has a value of $R = -11.8\mathrm{}\pm 1\%$. The net field gradient at the nucleus is $q=0.487\mathrm{}\pm 0.004$ a.u. From the measured quadrupole coupling constant we deduce the nuclear moment ${\mathrm{of}}^{27}$ Al as $Q=0.165\mathrm{}\pm 0.002$ b.

The hyperfine structure of a system of two fermions of arbitrary masses is considered. Gauge invariance is demonstrated through order $m{\alpha }^5$ for a wide class of covariant gauges. The results agree with those previously obtained in the radiation gauge. New calculational techniques are also developed.

The previously reported general correlated wave function for three-particle Coulomb systems is analyzed term by term for the cases of ${\mathrm{H}}^{-}$, $e^{-}{e}^{+}{e}^{-}$, $p\mu p$, $d\mu d$, $t\mu t$, and $p\mu d$ to find how sensitive the single terms are to the configuration of the Coulomb systems, and how effective they are in giving accurate results. It is found that on going from one-center Coulomb systems to systems with increasing two-center configuration, the leading terms in the wave function become those containing powers of the relative distance between the particles with the same sign of the charges. For mesonic molecular ions, a two-term wave function has been found to give highly accurate ground-state energy results: -2776.87 eV for $p\mu p$, -2982.97 eV for $d\mu d$, -3069.15 eV for $t\mu t$, and -2867.77 eV for $p\mu d$. All of the wave-function parameters are tabulated together with a number of useful expectation values.

A relativistic version of the random phase approximation (RPA) is used to study allowed and forbidden radiative transitions in atoms. The theory is applied to the He isoelectronic sequence to test its utility. Precise numerical solutions to the relativistic RPA equations are obtained describing the transitions $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{} \mathrm{}\left(M1\mathrm{}\right)\mathrm{}$, $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^{1,3}{}_{}{}^{}P_1^{}{}_{}{}^{} \mathrm{}\left(E1\mathrm{}\right)\mathrm{}$, and $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{} \mathrm{}\left(M2\mathrm{}\right)\mathrm{}$. The resulting excitation energies and transition probabilities are in good agreement with accurate nonrelativistic calculations for low-$Z$ elements. For intermediate- and high-$Z$ elements where relativistic effects are more important, the results are expected to be very accurate also. Extensive comparison shows good agreement of the calculated forbidden transition rates with available beamfoil measurements and the calculated transition energies with several lines from solar corona for high-$Z$ ($Z\sim 25$) elements.

Wave functions, which include interelectron coordinates $r_{\mathrm{ij}}$ explicitly, are employed for the $1s^2\mathrm{ns}{}_{}{}^2{}_{}{}^{}S$ and $1s^{2}2p{}_{}{}^2{}_{}{}^{}P_1^{}{}_{}{}^{}$ states of LiI in obtaining lower bounds and Hylleraas variation-perturbation estimates of dipole polarizabilities for the four lowest ${}_{}{}^2{}_{}{}^{}S$ states of LiI. The results of this study are polarizabilities for the four lowest ${}_{}{}^2{}_{}{}^{}S$ states of LiI with probable accuracy 2-5%. In addition, the latest experimental result for the $2{}_{}{}^2{}_{}{}^{}S$ state of LiI is found to be in excellent agreement with our result.

A reduced coupling matrix-element formula has been developed for application to the class of reactions $A^{+z}+B\to A^{+z-1\mathrm{}}+B^{+}$, where $4\le z\le 54$. The reduced coupling matrix elements have been combined with an absorbing-sphere model based on the Landau-Zener method to obtain a relatively simple formalism for obtaining the electron transfer total cross sections. The method assumes a large number of final product channels available for reaction and is applicable for relative velocities $v_{\mathrm{rel}}\le 1\times {10}^8$ cm/sec. For such electron transfer reactions, the cross sections at a given velocity are dependent primarily on the charge state of the incident ion and the ionization potential of the target atom; also, for a given colliding pair, the cross section is found to be almost independent of the relative velocity. Cross sections have been calculated for H, He, Ne, Ar, Kr, Xe, and ${\mathrm{H}}_2$ targets. For the cases of ${\mathrm{H}}_2$ and Ar there are experimental data available; the comparison between theory and experiment is quite favorable.