Current use of electron gas theory for exchange allows calculations of Hartree-Fock (HF) energies through the use of local potentials. A recent proposal of Gopinathan, Whitehead, and Bogdanović to use a realistic pair correlation function $f_{\uparrow \uparrow }(1, 2)$ that incorporates the boundary conditions of Kutzelnigg, Del Re, and Berthier, which consider the finite number of electrons of a given spin, showed much better agreement with atomic HF calculations. This paper explores the use of an improved $f_{\uparrow \uparrow }(1, 2)$ either with the electron cloud form (exponential) or with a modified Wigner form. The total energies obtained from this method are in excellent agreement with HF total energies. The calculated total energies lie above the HF values; we interpret this as an open possibility for the inclusion of refinements such as the inhomogeneity corrections.

We consider stationary scattering from a lattice of separate scatterers which are immersed in a medium with constant properties. The scattering process can be electromagnetic, acoustic, or quantum mechanical. In all cases the scattering objects or their potentials have to be separated in a fairly weak sense. The result is expressed in the terms of a modification of the $T$ matrix for a unit cell of the lattice. The modification involves two different sums of the product of translation operators and eigenvalues of the regular translation operator. One of these sums can be expressed as a geometric series and thus is easily summed.

The atomic-beam magnetic-resonance technique has been used to measure the hyperfine structure of the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$. This metastable state is populated in an electrical discharge located just in front of the oven orifice. The measured frequencies are $\Delta \nu (F=\frac{13}{2}-\frac{11}{2})=1346.497\mathrm{}\left(6\right)\mathrm{}$ MHz and $\Delta \nu (F=\frac{11}{2}-\frac{9}{2})=1170.208\mathrm{}\left(6\right)\mathrm{}$ MHz. Using these transition frequencies the hyperfine interaction constants, corrected for the perturbing interactions due to neighboring fine-structure levels, are $A=-212.765\mathrm{}\left(1\right)\mathrm{}$ MHz and $B=67.215\mathrm{}\left(15\right)\mathrm{}$ MHz. The errors quoted are only those arising from the uncertainty in the experimental data. We have also used these data with the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ hfs separations measured by zu Putlitz to calculate the quadrupole moment $Q=0.335\mathrm{}\left(20\right)\mathrm{}$ b using the antishielding correction estimated by Sternheimer. The error quoted for $Q$ includes the error in Sternheimer's estimate.

X-ray-production cross sections measured in $K$-shell ionization of ${}_{21}{}^{}{}_{}{}^{}\mathrm{Sc}$, ${}_{22}{}^{}{}_{}{}^{}\mathrm{Ti}$, ${}_{29}{}^{}{}_{}{}^{}\mathrm{Cu}$, and ${}_{32}{}^{}{}_{}{}^{}\mathrm{Ge}$ by 52-MeV ${}_{14}{}^{28}{}_{}{}^{}\mathrm{Si}_{}^{+q}{}_{}{}^{}$ projectiles with $q=7\mathrm{} \mathrm{to} 14$ are reported, which demonstrate, through their charge-state dependence, the validity of a recently developed electron-capture theory with a reduced binding effect. Furthermore, the data provide evidence for the applicability of the perturbed stationary-state theory of direct ionization for values of $0.44\le \frac{Z_1}{Z_2}\le 0.67$.

The space-translation method is shown to be equivalent to more frequently used Green's-function methods for computing probabilities of free-free transitions. These methods are reliable only when the Born approximation is valid. The method of Mohan is shown to offer no particular advantage over more standard treatments using plane-wave states.

The yield of ${\mathrm{H}}^{+}$ fragments from ${\mathrm{H}}_2$ by fast beams (0.5-4 MeV) of ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{O}}^{+}$ is measured as a function of projectile velocity. The yields of ${\mathrm{H}}^{+}$ from both the dissociative states of ${\mathrm{H}}_2^{+}$ and from the double ionization of ${\mathrm{H}}_2$ are identified. The ${\mathrm{H}}_2^{+}$ projectile is comparable to ${\mathrm{He}}^{+}$ in producing ${\mathrm{H}}^{+}$ fragments from the single ionization of the ${\mathrm{H}}_2$ target, but unlike ${\mathrm{He}}^{+}$ it produces no appreciable double ionization.

Using intrinsic Ge as x-ray detector, $K$-shell ionization cross sections have been determined for Ho, Tm, Lu, Ta, W, Pt, Au, Pb, and Bi under bombardment with 40-110-MeV $\alpha$ particles. The target-atom $K$-shell ionization cross sections are compared with the predictions of different models. The agreement is considerably improved when relativistic effects are taken into account. Intensity ratios have also been measured and found to agree with previous determinations. X-ray satellite emission, following nuclear rearrangements, was also observed and a calculation made in the case of Ho to relate nuclear reactions and $K$ x-ray production cross sections. Small peaks in the spectra of Au, Pb, and Bi have been tentatively attributed to double $J$-shell ionization, and hypersatellite energy is given for these atoms.

An expression is given for the ($n_i$, $l_i=0\mathrm{}\to n_f$, $l_f=0\mathrm{}$) excitation cross section in terms of a single one-dimensional integral with the aid of a transformation to prolate spheroidal coordinates. Results are given for the $1s-2s$ excitation of arbitrary-$Z$ hydrogenic targets. For our choice of wave functions the cross sections are found to scale as $Z^{-4\mathrm{}}$ at fixed $\frac{E_{\mathrm{inc}}}{Z^2}$. The principal difference between the Coulomb-projected Born-approximation (CPBA) and Born results is in the large-angle portion of the differential cross section. This, however, leads to CPBA and Born momentum-transfer cross sections which differ by less than 20% at high energies for $1s-2s$ transitions.

The stopping cross sections of three saturated alcohols, C${\mathrm{H}}_3$OH, ${\mathrm{C}}_2$${\mathrm{H}}_5$OH, and ${\mathrm{C}}_3$${\mathrm{H}}_7$OH, and two saturated ethers, (C${\mathrm{H}}_3$)${}_2{}^{}{}_{}{}^{}\mathrm{O}$ and (${\mathrm{C}}_2$${\mathrm{H}}_5$)O, have been measured in a differentially pumped gas cell with probable random errors of 0.5-1.1%. The results confirm that $\epsilon \left(\mathrm{C}{\mathrm{H}}_2\right)$ quoted in a previous paper can be used to predict the stopping cross sections for single-bonded C-H-O compounds. The values for the stopping cross section of single-bonded oxygen are extracted and found to be 3-17% lower than $\left(\frac{1}{2}\right){\epsilon }_{\mathrm{expt}}\left({\mathrm{O}}_2\right)$, thereby demonstrating the effect of chemical bonding on the stopping cross section. Comparison is made between the stopping cross sections for oxygen and those calculated from metal-oxide yield ratios.

The measurement of electron-transfer cross sections $\sigma$ in ion collisions with atomic hydrogen has been extended to iron ions with mass number $A=56\mathrm{}$, charges $q$ between +4 and +13, and specific energies $\frac{E}{A}$ between 27 and 290 keV/amu. The charge-state dependences of $\sigma$ range from $q^{1.5}$ at lower values of $q$ and $E$ to $q^3$ for higher values of these quantities. An empirical scaling relationship is found for converting ${\mathrm{H}}^{+}$ +H cross sections into those for ${\mathrm{Fe}}^{q+}$ + H. Several effects correlated with shell structure in the incident ion are observed. Our results are not explained by presently available theoretical calculations.

The range of applicability of the Born approximation is evaluated, and represented graphically, as a preliminary to the application of frame-transformation theory beyond this range. The contribution of all partial waves beyond a lower cutoff has been thus evaluated, and is discussed explicitly.

We present the total cross section for elastic electron-nitrogen scattering for incident energies 0-1000 eV. The calculations were based on the multiple-scattering model utilizing fixed-nuclei and Slater-exchange approximations, and represent a prototype for application of this method to larger molecular targets for which it is primarily intended. We are able to reproduce the ${\pi }_g$ shape resonance at 2.4 eV and achieve quantitative agreement with absolute measurements at high incident energies by adopting, respectively, two potentials whose difference is based on reduced exchange and polarization interactions for high incident energy. New insight into the dynamics of electron-molecule scattering is gained by inspecting the decomposition of the cross section into component symmetries over the entire energy range covered.

A previously developed binary-encounter model describing the slowing down of energetic heavy charged particles over a broad range of incident-particle energies is employed to calculate energy straggling as a function of target $Z_2$ for incident helium and hydrogen. This model seriously overestimates the measured stopping cross sections at high incident-particle energy for helium on heavy target atoms, but appears to yield more reasonable results for energy straggling. The large results in the stopping calculation are attributed to the neglect of the distortion of the electron charge cloud during the collision. A screened interaction, based on screening in a free-electron gas, is employed to estimate the size of the effect on both the stopping and straggling results for 10-MeV incident ${\mathrm{He}}^{++}$ on target atoms $1\le Z_2\le 36$, and for equilibrium-charge-state beams of hydrogen at energies 1 keV to 1 MeV on a number of targets. It was found that the neglect of distortion may result in errors equivalent to or greater than those due to the neglect of the long-range dipole interactions when estimating $S$, particularly at higher energies. For the straggling calculation both of these effects result in considerably smaller correction to the binary-encounter method.

High-resolution x-ray spectral measurements are used to determine the relative intensity of x-ray transitions for ions such as fluorine excited in collisions with various-pressure Ne, Ar, and Kr gas targets, thin carbon foils, and a thick carbon slab. The relative intensities are observed to be nonlinearly dependent on both target density and incident charge $Z$. These effects are attributed to strong collisional quenching of initial states by subsequent large-impact-parameter collisions. The data permit extraction of the total quenching cross sections (${\sigma }_Q$) for fast fluorine ions in various states. A strong enhancement of the relative intensity of $2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ is observed for ${\mathrm{F}}^{7+}$ and ${\mathrm{O}}^{6+}$ projectiles. This strong enhancement is attributed to selective excitation of metastable states in the beam, i.e., $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$, into the $1s2p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ state. Finally, the data for foil and solid targets are used to obtain information on the excitation states of ions moving in solids.

The time-dependent Hartree approximation is compared with an exact solution for the scattering between two $N$-particle bound states in the case of a 1-dimensional system of bosons with attractive $\delta$-function interactions. It is shown that to leading order in $N$, the approximation is exact, and arguments are presented relating this asymptotic agreement to the nonsaturation of the bound states.

Several years ago Potapov showed that in the high-momentum-transfer limit the leading contribution to the differential cross section for excitation of hydrogen atoms by fast electrons comes from the second-Born term, and not the first-Born term, if the proton is treated as infinitely massive. In this paper further insight into the origin of this remarkable result is provided. I discuss, in the high-momentum-transfer limit, the excitation of an "atom" composed of two particles of arbitrary masses $m_1$ and $m_2$. In the case that $m_1=\infty$, a simple heuristic derivation of the second-Born differential cross section is given. For $m_1$ finite it is found that there are two competing mechanisms for producing excitation; one corresponds to the first-Born and the other to the second-Born term. Both the first- and second-Born terms have a "near singularity" at the "critical" mass $m_1=\infty$; these near singularities radically alter the asymptotic dependence of the matrix elements on the momentum transfer and cause the second-Born term to dominate over the first-Born term at the critical mass. Away from the critical mass, however, the second-Born term may not dominate over the first-Born term.

We derive a simple Hamiltonian representing the coupling of an electronic level of positive energy to the continuum of scattering states as well as to the molecular vibrations. By summing the perturbation series for the $S$ matrix to infinite order in the bound-state-continuum interaction, an effective non-Hermitian boson Hamiltonian describing the dynamics of vibrational motion in the resonance state is obtained. It is shown that the effective Hamiltonian can be diagonalized, yielding explicit expressions for the vibrational excitation cross sections. The theory is applied to two representative examples, the 3.8-eV shape resonance in C${\mathrm{O}}_2$ and the 2.4-eV shape resonance in ${\mathrm{N}}_2$. The results exhibit a clear improvement over those obtained with existing theories, which express the cross sections in terms of conventional Franck-Condon factors. The influence of the anharmonicity of the potential functions on the structure of the vibrational excitation functions is discussed.

Charge states of the two fragments produced in a single dissociative collision of ${\mathrm{H}}_2^{+}$ (energy range 300 to 900 keV) in gas targets (${\mathrm{H}}_2$, He, air, and Ar) have been determined by coincidence techniques. The dependence of the charge-state distributions on the energy of the incoming ${\mathrm{H}}_2^{+}$ and on the pressure of the various targets has been determined. Correlation coefficients between the distributions are deduced, and a simple model for the dissociation is discussed.

The use of in situ ion detection in alkali vapors coupled with multiphoton ionization provides a technique of highest sensitivity for the investigation of the spectroscopy of excimer states involving alkali atoms. This technique has been applied in this work to the molecular components of the spectrum of the $6S-7P$ absorption doublet of cesium. The dispersion curve was obtained with a tunable dye laser for the two-photon ionization of cesium over the 4500-4600-Å wavelength range as a function of vapor pressure and source intensity. Strongly developed satellite bands were observed to be associated with the atomic lines $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 7{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 7{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$, and were found to have well-defined band heads at 29.4 and 31.4 ${\mathrm{cm}}^{-1\mathrm{}}$ to longer wavelengths, respectively. Sensitivity was observed to be an order of magnitude in excess of that obtained from classical absorption techniques, and the observation of a quadratic dependence of the molecular components confirmed the multiphoton nature of the detection sequence.

Theoretical multiplet x-ray and Auger rates to the $2p$ level of S and Cl atoms containing one $2p$ hole and a partially filled $3p$ shell have been computed. The initial state is treated in intermediate coupling, and the final state, in $\mathrm{LS}$ coupling. Fluorescence yields for each state as well as statistical-average fluorescence yields for each configuration are reported. The spin-orbit interaction is found to have a remarkable effect on the Auger transition probabilities and x-ray fluorescence yields of $2p^{5}3s^{2}3p^n$ configurations; this effect decreases with increasing stages of ionization.