The model previously derived for the electron-gas exchange in atoms is extended to include Coulomb correlation effects. Exchange, Coulomb-correlation, and total energies for the atoms He through Ar, calculated within this spin-density model, are found to correspond closely to the exact values.

The equivalence of the results is pointed out for certain lattice sums occurring in the study of a system of ideal bosons derived by the use of the Poisson's summation formula with those obtained by using the expression for the density of single-particle states, given recently by Baltes and Steinle, and arrived at by the use of Walfisz's formula for the number of lattice points in a hypersphere of $p$ dimensions. Further, expressions are given for the density of single-particle states in one and two dimensions for periodic, Dirichlet, and Neumann boundary conditions. In the end the equivalence is shown between the Poisson's summation formula and Walfisz's formula directly.

The per-atom Coulomb capture ratio $A(\mathrm{N}\mathrm{b},\mathrm{V})$ of negative muons in the solid solution Nb-V has been measured for five stoichiometric ratios $S(\mathrm{Nb}/\mathrm{V})$ ranging from 0.046 to 18.5. No change of $A(\mathrm{N}\mathrm{b},\mathrm{V})$ with $S$ was observed. The weighted mean is 1.21±0.04. There is also no experimental evidence for a variation of the muonic-Lyman-series intensity patterns of both elements with $S$.

We propose a simple analytic wave function for the $1s2s{}_{}{}^1{}_{}{}^{}S$ state of the two-electron atomic system. This is orthogonal to the ground-state function of Morse et al. The wave-function parameters are evaluated by the method of variational calculation for the eigenenergy. Using the present $2{}_{}{}^1{}_{}{}^{}S$-state function we have calculated the values of the physical quantities mean square radius and scattering cross section in a few cases. We compare these with the relevant values that are available using many-parameter wave functions and obtain good agreement.

The relativistic random-phase approximation is applied to the calculation of excitation energies and oscillator strengths for the $2p^6{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2\mathrm{}{p}^{5}3s{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and $2p^6{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2\mathrm{}{p}^{5}3d{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ transitions of elements of the neon isoelectronic sequence. The results are compared with those of other calculations and experiment. The variation of oscillator strength along the isoelectronic sequence is depicted for each of the transitions. Anomalous behavior occurs which is attributed to level crossings.

A unified interpretation of single-channel quantum-defect behavior is presented, and illustrated with the example of a square well. As an application the quantum defects for the lowest three partial waves of potassium are calculated and discussed as continuous functions of the energy above, near, and far below the ionization threshold, with emphasis on their non-Rydberg spectral properties; results for other atoms are discussed. The quantum defect for the radial motion of a ${}_{}{}^1{}_{}{}^{}P_{}^{\circ }{}_{}{}^{}$ electron pair of ${\mathrm{H}}^{-}$ is also calculated, thereby combining Macek's hyperspherical-coordinate approach with quantum-defect theory.

The radiative lifetimes of the $7s-11s$ and $5d-9d$ states of potassium have been measured by means of a time- and wavelength-resolved laser-induced-fluorescence approach. The observed lifetimes (in μsec), measured at a temperature of 355 K, of the $7s-11s$ states are 0.165(12), 0.260(14), 0.441(38), 0.60(13), and 0.91(12). The observed lifetimes (in μsec) of the $5d-9d$ states are 0.61(9), 0.89(6), 1.21(10), 1.59(13), and 2.04(30). The measured $s$-state lifetimes are roughly a factor of 2 shorter than the hydrogenic ones, and the measured $d$-state lifetimes are roughly a factor of 10 longer than the hydrogenic ones. The $d$-state lifetimes are reduced from the 0-K radiative lifetimes by as much as 20% by stimulated emission and absorption induced by blackbody radiation. For both $s$ and $d$ states the calculated and observed values of 355-K lifetimes agree to within 10%.

The total rate of dielectronic recombination of Mo xxxiii to form Mo xxxiii is computed by means of the fundamental atomic physics of the process and atomic data calculated for this problem. Agreement with a simple analytic expression suggested by Burgess for the total rate is good in the temperature range 1.0-6.0 keV, but poor below 1.0 keV. Considerable disagreement exists with the analytic expression when the details of the process are examined.

Self-consistent-field (SCF) calculations have been performed for the short-range interaction between two aluminum atoms. The ground-state potential curve (${}_{}{}^3{}_{}{}^{}\Sigma _g^{-}{}_{}{}^{}\to {}_{}{}^5{}_{}{}^{}\Sigma _u^{-}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to {}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$) is presented for internuclear separations between $R_e$ and 0.1 a.u. (repulsive energies up to ∼ ${10}^3$ a.u.). Basis sets consist of scaled eventempered Slater orbitals of double-$\zeta$ quality, augmented by diffuse functions, with the addition of united or semiunited atom-basis sets centered on the bond. The SCF potentials are compared with Thomas-Fermi theory and with the electron-gas calculations of Wilson, Haggmark, and Biersack. A kink in the SCF screening function is found near $R=2\mathrm{}$ a.u. This feature is believed related to changes in the ground-state configuration that occur in this region. Additional calculations (SCF and linear combination of atomic orbitals) were performed on ${\mathrm{Al}}_2^{6+}$ to determine individually the core overlap and the valence-electron contributions to the interatomic potential. The core-overlap interaction is compared with Gordon-Kim electron-gas calculations. Schematic calculations were also performed on the A1-${\mathrm{A}1\mathrm{}}^{3+}$ system to estimate the interaction between an atom and an energetic ion.

In this paper the variational cellular method is extended to the self-consistent calculation of diatomic molecules. This extension is based on a new variational expression for the total molecular energy the extremum of which defines the one-electron potential of the Schrödinger equation. The method was tested in the calculation of ${\mathrm{N}}_2$ and CO and the results are very good: the binding energy and the equilibrium interatomic distances were calculated to be within less than 10% of the known experimental results.

The author shows how the position-momentum uncertainty products may be obtained analytically for the eigenstates of the exactly solvable symmetric Pöschl-Teller, symmetric Rosen-Morse, and one-dimensional Morse potentials.

The study of the hyperfine structure of the muonic helium atom (${\alpha }^{++}{\mu }^{-}{e}^{-}$) can provide a test of quantum electrodynamics and yield precise values for the magnetic moment and mass of the negative muon. In the lowest-order approximation the hyperfine structure interval $\Delta \nu$ is given by the Fermi formula. The principal corrections, which contribute about 10 MHz to the splitting, arise from the relativistic, radiative, and recoil effects. The theoretical hyperfine structure of the ground state of muonic helium is given as $\Delta \nu =4465.1\mathrm{}\pm 1.0$ MHz.

By applying the hypervirial relations with the Hellman-Feynman theorem to screened Coulomb potentials, the authors derive the energy levels of atoms correct to the sixth order of the perturbation parameter $\lambda$ explicitly without any calculation of perturbed wave functions. The energies of atoms up to the twentieth order of $\lambda$ are also calculated by computer. In the case of the Yukawa potential, the authors demonstrate by explicit calculation that the $K$-shell energy converges, at least for $Z\ge 5$, with the value of ${\lambda }_0=0.85\mathrm{}$, and that the $L$-shell energy converges, at least for $Z\ge 24$, with ${\lambda }_0=0.70\mathrm{}$.

The energy level of the ${}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}$ state of ${\mathrm{He}}^{-}$ is found to be lower than that of the $\left(2p2p\right){}_{}{}^3{}_{}{}^{}P$ state of He by about 0.328 eV. It is metastable against autoionization and decays through radiation to the triply excited autoionization state of ${}_{}{}^4{}_{}{}^{}P_{}^e{}_{}{}^{}$ and its associated continuum. For Li and three-electron positive ions, the ${}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}$ state also decays to the doubly excited ${}_{}{}^4{}_{}{}^{}P_{}^e{}_{}{}^{}$ bound state. The energy levels of these states are calculated and transition wavelengths are also predicted.

The Schrödinger eigenvalue problem for a Yukawa potential is reexamined from a group-theoretical perspective. By using the Fock transformation, the Schrödinger operator is transformed into a compact or "inverse Sturmian" operator which is a linear superposition of local representation operators of SL(2,$R$). It may be approximated by finite-rank techniques, which provide a very useful method for obtaining accurate numerical results.

Most theoretical calculations of cross sections for low-energy electron- and positron-molecule collisions include the important induced-polarization effects in the interaction potential by means of a semiempirical adiabatic approximation based on the known asymptotic form of the potential. In order to examine the validity of the assumptions implicit in this procedure, ab initio adiabatic polarization potentials have been calculated at the self-consistent-field level of accuracy for the $e$-${\mathrm{N}}_2$ and $e$-C${\mathrm{O}}_2$ systems. The resulting potentials deviate from the asymptotic form for intermediate electron positions outside the molecular charge cloud. In addition, the angular dependence of the potentials differs from that assumed in the semiempirical form.

The author has measured charge-state ($q$) spectra of recoil ions generated in single collisions of 25-45-MeV chlorine ions with targets of helium, neon, and argon. A high-efficiency time-of-flight spectrometer was used to identify the charge-to-mass ratio of the slowly moving recoils. Recoil $q$ up to + 8 (neon) and + 11 (argon) were observed. Cross sections for recoil production were measured as a function of projectile energy and incident charge state. The energy dependence of the cross sections is quite weak, while the recoil-$q$ dependences show clear shell effects in argon. For the lower-$q$ recoils, the cross sections are reasonably well described by the model of Olson, which treats the target electrons as moving independently. For higher $q$, a model based on energy deposition by the projectile with the target electrons, followed by statistically weighted electron emission, gives a better description of the data.

Glauber-approximation scattering amplitudes for charged-particle-hydrogen-atom elastic and inelastic collisions are derived directly in terms of the known particle-electron and particle-proton Coulomb scattering amplitudes and the known hydrogen-atom form factors. The authors show that the particle-hydrogen amplitude contains no single-scattering term. The double-scattering term is obtained as a two-dimensional integral in momentum space. The authors show how the result can be used as the starting point for an alternative and relatively simple derivation, in closed form, of the Glauber particle-hydrogen scattering amplitude for transitions from the ground state to an arbitrary ($\mathrm{nlm}$) state.

Single-electron-capture cross sections have been measured for boron ions ${\mathrm{B}}^{q+}$ with initial charges $q=2, 3, \mathrm{and} 4$ incident on helium, molecular hydrogen, and argon gas targets. The cross sections show little dependence on the incident ion energy for the range studied, $6q-23q$ keV. Also reported are double-electron-capture cross sections for ${\mathrm{B}}^{3+}$ incident on ${\mathrm{H}}_2$ and Ar and for ${\mathrm{B}}^{4+}$ incident on He, ${\mathrm{H}}_2$, and Ar, as well as a survey of single-electron-capture cross sections for ions of carbon ($2\le q\le 4$), nitrogen ($2\le q\le 5$), and oxygen $2\le q\le 6$) at the single energies $8q$ keV incident on He and Ar targets. In general, it is found that the cross sections do not vary monotonically with the initial charge state, for a fixed colliding atomic species. Each reaction depends in detail on the level structures of both the incident ion and the target atom or molecule.