Recent advances in the unitary group, or Weyl tableau, approach to the theory of complex spectra have provided great simplification of calculations in atomic and molecular applications. We show that the subduction coefficients employed by Patterson and Harter to generate mixed-orbital-configuration $\mathrm{LS}$-adapted states can be derived using simple vector-coupling considerations. Using lowering and projection operator techniques based on the idea of "highest tableau," which we show are automatically eigenstates of the $L^2$ operator, we generate equivalent states. These states are used to calculate reduced matrix elements of the spin-own-orbit operator for the case ${}_{}{}^2{}_{}{}^{}\left(p^{2}d\right)$. We discuss the generalization of the existing minicomputer programs to treat mixed-orbital configurations.

A variational solution of the Thomas-Fermi differential equation is obtained. The proposed solution is used to calculate the total ionization energy of atoms, and also the repulsive interaction energy between rare-gas atoms. It is shown that the results obtained by the proposed function are better than those obtained from Csavinszky's function for medium and high atomic number elements.

The theory of the time-dependent response and autocorrelation function has been rewritten in the language of quantum-mechanical phase space and the correct method whereby semiclassical approximations may be obtained are discussed. Several new relationships occurring in Moyal's phase space are derived as a prelude to the actual study of the correlation functions.

Calculations of the binding energies of electrons in fermium by using a relativistic local-density functional theory are reported. It is found that relaxation effects are nonnegligible for inner core orbitals. Calculated orbital binding energies are compared with those due to nonlocal Dirac-Fock calculations and also with those determined experimentally from conversion electron spectroscopy. Finally the usefulness of the local-density approximation for the study of heavy atomic and condensed systems is discussed.

It is shown that the Fredholm-Laplace solution of the Schrödinger integral equation of the evolution operator in the cases of harmonic or constant external perturbations can be put into a physically meaningful determinantal quotient form. The solution exhibits the usual multiple transitions and corresponding linewidth upon expansion. The result lends itself fairly well to the setting up of correct tractable formulas in the important case of continuous spectra capable, for instance, of dealing with resonance phenomena. Furthermore, the determinantal form can be shown to obey the unitary requirement at all times and any order with respect to the applied field or the collision potential. An illustration is given in the simple model of a system submitted to a perturbation of constant matrix elements, in the spectral range of interest assumed of constant density of states.

The Thomas-Fermi model and the $Z^{-1\mathrm{}}$ perturbation expansion for ions with nuclear charge $Z$ and $N$ electrons are considered in the limits of large $Z$ and $N$ where the Thomas-Fermi model becomes exact. It is shown that the Baker expansion of the Thomas-Fermi function $\phi \mathrm{}\left(x\right)={\Sigma }_{n=0\mathrm{}}^{\infty }{C}_n{x}^{\frac{n}{2}}$ may be rearranged into $\phi \mathrm{}\left(x\right)={\Sigma }_{n=0\mathrm{}}^{\infty }{B}_n\mathrm{}\left(y\right)\mathrm{}{x}^{\frac{3n}{2}}$, where $y=C_{2}x$ and the $B_n$'s are polynomials in $y$. The functions $B_n$ are obtained through a recursive set of differential equations where $B_0=1+y$ is known. It is then shown that the function $f\left(q\right)\mathrm{}$, $q=\frac{N}{Z}$, which determines the total binding energy by means of $E(N,Z)=Z^{\frac{7}{3}}f\left(q\right)\mathrm{}$ in both the Thomas-Fermi theory and the $Z^{-1\mathrm{}}$ perturbation theory, is given by $f\left(q\right)=q^{\frac{1}{3}}{\Sigma }_{n=0\mathrm{}}^{\infty }{a}_n{q}^n$. The first few coefficients in this series are determined. The function $f\left(q\right)\mathrm{}$ is then computed through numerical integrations of the Thomas-Fermi equation with different initial slopes. The results are tabulated for $0\le q\le 1$ and analytically continued beyond $q=1\mathrm{}$. Finally the ratio $\frac{V_{\mathrm{ne}}}{E}$ ($V_{\mathrm{ne}}$ being the nuclear-electron attraction energy) is obtained in terms of $f\left(q\right)\mathrm{}$ for both positive and negative ions and found to be in agreement with the corresponding Hartree-Fock ratios. It is an extension of the well-known ratio of $\frac{7}{3}$ for neutral atoms.

Analysis of the coupling matrix elements between quasibound and free states of doubly excited helium provides an unambiguous mechanistic interpretation of autoionization by electron correlation. The analysis is based on the dependence of the integrand of the matrix elements on the distances $r_1$ and $r_2$ and the angle ${\theta }_{12}$, and on the separation of the total amplitude into a part containing only one-electron operators and a part comprising $\frac{1}{r_{12}}$. The former gives rise to the normally dominant part, a generalized $S_N-2\mathrm{}$ mechanism; the latter, usually a smaller part, is the direct electron-electron, binary-collision contribution.

Muonic x-ray spectra from 57 oxides have been measured with Ge detectors at the muon channel of SIN. Coulomb capture ratios and muonic x-ray intensities were deduced. A novel method was applied for oxides of heavier elements. The results exhibit for the first time systematic relations between capture ratios, the x-ray intensities in the oxidized element and in the oxygen, and the radius of the atoms. Periodic behavior with $Z$ was established in many cases.

An almost a priori method based on a simple theoretical model is developed for obtaining good estimates of the radius of convergence of Rayleigh-Schrödinger (RS) perturbation expansions. The procedure is applicable to the RS expansions of all stationary states of any system described by a Hamiltonian linear in a real perturbing parameter, e.g., the $\frac{1}{Z}$ expansions of $N$-electron atomic isoelectronic sequences. The only system- and state-dependent information required is the norm of the first-order eigenfunction $\parallel {\psi }_1\parallel$. In those cases where $\parallel {\psi }_1\parallel$ is inaccessible or unavailable, it is shown how adequate perturbational-variational (PV) approximations can be simply obtained. The procedure has been applied to the $\frac{1}{Z}$ expansions of the ground states and several low-lying states of the $2\le N\le 10$ isoelectronic sequences. Where comparison is possible, the estimates are in close agreement with numerically obtained accurate convergence data and are greatly improved over the weak Kato-type bounds. For example, for the $1s^2{}_{}{}^1{}_{}{}^{}S$ state of the helium isoelectronic sequence, convergence is found for $Z\ge 1$, hence for the first time predicting convergence for ${\mathrm{H}}^{-}$. Further, in harmony with physical expectations, our findings indicate that the effect of increasing $N$ on radii of convergence is drastic; thus, for the ground states of the $3\le N\le 10$ isoelectronic sequences, the predicted region of convergence can be represented approximately by $Z\ge 3N-7$. The influence of screening the nucleus in compensating for the effect of increasing $N$ is investigated and it is shown how the radius of convergence can be maximized by optimal screening. A PV method is introduced for obtaining estimates of the optimal screening parameter for arbitrary $N$ and states. It is predicted that for the ground states, the optimally screened expansions will converge for $Z\ge 3$ for the beryllium isoelectronic sequence, for $Z\ge N$ for the boron through oxygen isoelectronic sequences, and for $Z\ge N+1\mathrm{}$ for the fluorine and neon isoelectronic sequences, thus extending the application of such expansions to at least $N=10\mathrm{}$. Optimal screening is quantitatively tested for the $\frac{1}{Z}$ eigenvalue expansion of the $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S$ state of the beryllium isoelectronic sequence and the results are found to be in accord with predictions.

By forming the Padé approximants to the energy perturbation series for screened Coulomb potentials, we study the cases of an electron in the Yukawa potential and a representative screened potential of the atom in the form of the Yukawa potential. It is found that the [6,6] and [6,7] Padé approximants to the energy series can account for the energy eigenvalues of various energy eigenstates to a very high accuracy.

Ab initio self-consistent field (SCF), and configuration interaction (CI), calculations have been performed for the diatomic transition metal hydrides NiH and PdH to study the behavior of the $d$ electrons and their effect on chemical bonding. SCF calculations have been carried out for the three low-lying states, ${}_{}{}^2{}_{}{}^{}\Delta$, ${}_{}{}^2{}_{}{}^{}\Pi$, and ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$, which can be formed with the metal atom in the ($d^9{s}^1$) configuration. The ground state of NiH is ${}_{}{}^2{}_{}{}^{}\Delta$ with the ${}_{}{}^2{}_{}{}^{}\Pi$ and ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ states only about 0.1 eV above. In the case of PdH the ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ state is the lowest with the ${}_{}{}^2{}_{}{}^{}\Delta$ about 0.6 eV above. This difference can be attributed to the participation of the $4d$ electrons in the PdH bond. The $3d$ electrons in NiH seem to be more localized and "atomic $d$-like." In both cases the potential energy curves are too broad and the equilibrium bond lengths are longer than those found from spectral data. For both molecules, the CI results are considerably improved over those from the SCF calculations. However, there are still significant differences between the computed (CI) and observed values for the ground-state equilibrium bond length and force constant. Two effects are considered in order to understand these errors. For NiH, the limited CI is unable to properly account for the differential correlation energy of the $3d^{9}4s^1$ and $3d^{8}4s^2$ terms of the free Ni atom and this probably leads to the errors in the calculation. For PdH, differential atomic correlation energies are likely to be much less important, but relativistic effects are likely to be important. We have also investigated some excited states and the calculated vertical term energies are compared with experimental results.

Statistical correlation coefficients were introduced by Kutzelnigg, Del Re, and Berthier to provide overall measures of the difference between the electron pair density and the product of one-electron densities in atoms and molecules. Some properties of these coefficients are discussed, and it is shown that an angular correlation coefficient is experimentally accessible. Radial and angular correlation coefficients are computed from highly accurate wave functions for the $1{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}S$, $2{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}P$, and $2{}_{}{}^1{}_{}{}^{}P$ states of the heliumlike ions from He through ${\mathrm{Mg}}^{10+}$. It is found that positive angular correlation coefficients occur in the $2{}_{}{}^1{}_{}{}^{}P$ state of the two-electron positive ions but not in neutral helium. Moreover, the angular correlation coefficients for the $2{}_{}{}^1{}_{}{}^{}S$ and $2{}_{}{}^3{}_{}{}^{}S$ states of the positively charged two-electron ions show that a previously proposed reformulation of Hund's rule is incorrect.

We have studied the relative level populations in beam-foil-excited C iv, N v, O vi, and F vii by optical spectrometry in the range $n=3-12\mathrm{}$. These Li-like ions have the configuration $1s^2\mathrm{nl}$. The population distribution curves are quite different, ranging from a sharp, approximately ${\left(n^{*}\right)}^{-3\mathrm{}}$, decrease for C iv to flat maxima at $n\sim 7 \mathrm{and} 8$ for O vi and F vii, respectively. This gradual change may be explained as resulting from a near-resonant charge transfer from the valence band of the carbon foil to the projectile. For fixed $n$, states with large $l$ are preferentially populated. The consequences of these results in cascade analyses of lifetime data from beam-foil measurements are briefly discussed.

Excited-state formation in inelastic ${\mathrm{He}}^{2+}$-Li collisions at kinetic energies up to 7 kev (center of mass) has been diagnosed by dispersal and detection of both visible and soft x-ray radiation emanating from the intersection of ${\mathrm{He}}^{2+}$ and Li beams. The theoretical predictions of Shipsey et al., that ${\mathrm{He}}^{+}$($n=3\mathrm{}$) is preferentially formed, are found to be valid. The cross section for this selective process is sufficiently high to support the suggested application for production of super-radiance at the He ii Lyman $\alpha$ and Lyman $\beta$ wavelengths, 304 Å and 256 Å, respectively.

We report the efficient transverse deflection of all atoms in a well-collimated sodium atomic beam by the spontaneous radiation pressure of a beam of resonance light which illuminates the atomic beam at right angles. Our results are obtained using two cw single-mode dye lasers to excite the two ground-state levels of sodium; this enables all atoms to interact with the light and it also eliminates optical pumping of the ground state. We obtained deflection angles greater than 5×${10}^{-3\mathrm{}}$ rad which was ten times the divergence angle of the undeflected atomic beam; these deflections are due to the spontaneous scattering of more than 200 photons by each atom. The distribution of deflection angles is well described by a simple calculation. Fitting theory to experiment indicates that a fractional atomic excitation of 24 percent was obtained at an intensity of approximately 1 W/${\mathrm{cm}}^2$. When single-frequency light was used, only a fraction of the atoms were deflected, and the deflection angles were much smaller due to optical pumping.

The approach to electron capture previously developed by Chan and Eichler is extended to describe charge exchange in fast collisions between arbitrary hydrogenic states $\mathrm{nl}$ and $n^{\prime }{l}^{\prime }$ of target and projectile. A closed formula for the cross section is derived. As an illustration, cross sections for the reactions ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(2l\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(3l\right)+{\mathrm{H}}^{+}$ and ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(n\right)\mathrm{}\to \mathrm{H}+{\mathrm{H}}^{+}$ up to $n=10\mathrm{}$ are calculated. For the process ${\mathrm{He}}^{2+}+\mathrm{H}\mathrm{}(n=8,9\mathrm{})\mathrm{}\to {\mathrm{H}}^{+}+{\mathrm{He}}^{+}$, consistency with experimental results is obtained. Furthermore, a proposal is presented on how to apply the theory to multielectron targets by properly taking into account internal and external screening. As an example, Ar-$L$ capture by protons is considered. Finally, the post and prior versions of the theory are compared and it is argued that the prior form currently used is more adequate for electron capture. A comparison between experimental and theoretical total cross sections for $H\left(1s\right)\mathrm{}$ electrons is briefly updated.

Theoretical methods used previously for ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, and ${\mathrm{C}}^{6+}$ collisions with neutral argon atoms have been applied to collisions of ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{2+}$, and ${\mathrm{Li}}^{3+}$ projectiles with neon, and to collisions of ${\mathrm{H}}^{+}$ with carbon targets. The energy range covered by the calculations is 0.4 to 4.0 MeV/amu for the neon target, and 0.2 to 2.0 MeV/amu for carbon. We calculate single-electron amplitudes for target $K$-shell ionization and target $K$- and $L$-shell, to projectile $K$-shell, charge transfer. These single-electron amplitudes are used, in an independent-particle model that allows for multielectron processes, to compute $K$-shell vacancy production cross sections ${\sigma }_{\mathrm{VK}}^{\mathrm{IPM}}$, and cross sections ${\sigma }_{C,VK}^{\mathrm{IPM}}$ for producing a charge-transfer state of the projectile in the coincidence with a $K$-shell vacancy in the target. These cross sections are in reasonable agreement with the recent experiments of Rødbro et al. at Aarhus. In particular, the calculated, as well as the experimental, ${\sigma }_{C,VK}$ scale with projectile nuclear charge $Z_p$ less strongly than the $Z_p^5$ of the Oppenheimer-Brinkman-Kramers (OBK) approximation. For ${\mathrm{He}}^{2+}$ and ${\mathrm{Li}}^{3+}$ projectiles at collision energies below where experimental data are available, our calculated multielectron corrections to the single-electron approximation for ${\sigma }_{C,VK}$ are large.

The reaction-coordinate approach of Mittleman is used to generalize the method of perturbed stationary states. A reaction coordinate and an associated electron coordinate are defined for each state in the scattering expansion in terms of scalar parameters which depend on the internuclear separation. These are to be determined from a variational principle described by Demkov. The choice of parameters, the scattering expansion, and the Lagrangian for the radial scattering functions are given for a heteropolar one-electron system.

For one-electron heteropolar systems, a previously derived quantum-mechanical Lagrangian is simplifed using a semiclassical approximation. Unitarity and detailed balancing are retained. The variational method described by Demkov is used to determine the coupled differential equations for the radial scattering functions and the Euler-Lagrange equations for the translational parameters which are part of the theory. Specific semiclassical formulas for the translational parameters are given in a many-state approximation. For a one-state expansion the parameters agree with an earlier determination by Riley and Green.