Atomic $L_1$-level Auger and Coster-Kronig widths have been calculated for 14 elements with $33\le Z\le 85$. Nonrelativistic screened hydrogenic wave functions and $j-j$ coupling were used; all pertinent transitions were included that involve final vacancy configurations through $f_{\frac{7}{2}}{f}_{\frac{7}{2}}$. With the aid of Scofield's x-ray emission rates, $L_1$ fluorescence yields are calculated. Total $L_1$, $L_2$, and $L_3$ level widths are compared.

The Auger rates, x-ray rates, fluorescence yields, and $K\alpha$ linewidths are presented for all elements $Z=12\mathrm{}-55$ and $Z=60, 65, 70, 75, 80, \mathrm{and} 85$ when a vacancy is in the $2p$ shell. Numerical calculations have been performed using the Hartree-Fock-Slater approach with Herman, Van Dyke, and Ortenburger exchange. Comparisons of different exchange approximations on the Auger and x-ray total transition rates and the fluorescence yields are reported.

A general theoretical treatment of spectral line broadening of gas molecules is given using a resolvent operator formalism in Liouville space. The methods introduced previously by Mead for treating resonance broadening in monatomic gases are developed and generalized here for molecular spectral lines. The basic equation relating the susceptibility to resolvent operator matrix elements is derived here for the case of a molecular gas and takes into account the rotational-vibrational structure of the spectra and the presence of complicated molecular interactions.

The theory of pressure broadening in pure molecular gases is discussed, using the classical-path approximation and the resolvent operator formalism. Within the classical-path approximation, solutions for problems of pressure broadening are obtained by assuming two-body impact with static many-body corrections. The results are compared with available experimental data and good agreement is obtained.

Moment-perturbed calculations were carried out for the Fermi contact hyperfine constant for a selection of rare-earth atoms and ions. In the cases of neutral and divalent europium, a value that has the same sign as the experimental value but is larger in magnitude, was found. This is in disagreement with earlier published works of Bagus and Picart who, using an unrestricted Hartree-Fock approach, found a result of opposite sign compared to the experimental results. Results will be presented for divalent, trivalent, and neutral ions and atoms, and trends will be discussed.

The solution for the energy and wave function in degenerate Rayleigh-Schrödinger perturbation theory is obtained via a formula of Lagrange. The derivation involves manipulation of the Brillouin-Wigner formulas in a manner similar to the "repeated-partitioning" technique.

Configuration-interaction (CI) wave functions determined by Weiss for the ${}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}P$ states of a series of Li-like ions have been examined and compared by means of a natural spinorbital analysis. For each wave function we calculated one-particle properties such as $\rho \mathrm{}\left(0\right)\mathrm{}$—the electron density at the nucleus—and $〈r^n〉$ for $-2\mathrm{}<~n<~4$. Results were compared with an earlier analysis of the ${}_{}{}^1{}_{}{}^{}S$ state CI wave functions for the He-like series of ions. Consequently, comments could be made concerning the intershell and intrashell correlation effects for the ${}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}P$ states of the Li-like ions. Further, for each ion, energies and expectation values were compared with corresponding quantities derived from wave functions of single-determinatal form within the Hartree-Fock-Roothaan approximation.

The formation of wave functions of a particular symmetry out of particle-subgroup functions is discussed as an eigenvector problem to an interchange matrix. Some properties of this interchange matrix are derived and found to be insufficient to fully characterize the matrix and a connection with the $N$-representability problem is made. A number of special cases are discussed in detail and an indication of a systematic numerical approximation is made.

The fine structure (fs) and hyperfine structure (hfs) of the $N=1\mathrm{}$ rotational level of a single vibrational state of the $(1\mathrm{}{\sigma }_g,1\mathrm{}{\pi }_u)c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state of orthohydrogen has been measured by the molecular-beam magnetic-resonance method. Six independent frequency intervals have been measured to a precision of better than one part per million. The theory of fs and hfs, as developed by Fontana, Chiu, Jette, and Cahill has been used to fit the energy levels with four accurate, independent constants: the spin-orbit fs constant, $A=-3717.12\mathrm{}$ MHz; the spin-spin fs constant, $B_0-\sqrt{6B_2}=9562.50\mathrm{}$ MHz; the combined orbital and Fermi contact hfs constants, $\frac{1}{2}a+a_F=463.77\mathrm{}$ MHz; the dipolar hfs term, $c-3d=104.18\mathrm{}$ MHz; and the fifth, very much less accurately determined, orbital hfs constant, $a=26.6\mathrm{}$ MHz. The Fermi contact constant $a_F=450.5\mathrm{}$ MHz agrees remarkably closely with the value 440.1 found in ${\mathrm{H}}_2^{+}$ by Jefferts. This indicates that the contact hfs of this state arises largely from a single core electron which is virtually the same as in ${\mathrm{H}}_2^{+}$. The agreement between experimental energy levels and the theoretical fit is very good. The deviations are at worst 20 kHz, only a few parts per million in the measured intervals. If the previously measured fs of the $N=2\mathrm{}$ state is used, the spin-spin constants become $B_0=-1420\mathrm{}$ MHz, $B_2=-4480\mathrm{}$ MHz. The spin-orbit constants for the $N=1\mathrm{}$ and $N=2\mathrm{}$ levels disagree by 3%. The constants $\frac{1}{2}a+a_F$ and $c-3d$ disagree by several percent with a priori calculations by Jette. The level of discrepancies among different experimental and theoretical results is an order of magnitude larger than can be obtained within the framework of the pure case-$b$ coupling scheme. Evidence is found for nonadiabatic transitions of a new type for molecular-beam experiments. The discovery of new transitions proves that there is more than one metastable vibrational level of the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state of ${\mathrm{H}}_2$. It is likely, although not certain, that the present data are from the lowest ($v=0\mathrm{}$) level.

By using the Born approximation an analytic formula is derived for the phase shifts ${\delta }_l$ for scattering by a van der Waals $r^{-6\mathrm{}}$ potential. We find that at low energies $tan{\delta }_l$ varies as $k^{2l+1}$ for $s$ and $p$ waves, and $tan{\delta }_l$ varies as $k^4$ for all the higher partial waves. Comparison is made with available results from standard effective-range theory.

It is demonstrated that the Coulomb $T$ matrix $T({\overrightarrow{\mathrm{p}}}_2, {\overrightarrow{\mathrm{p}}}_1; E\pm i\eta )$ satisfies a modified off-shell unitarity relation with a phase factor which depends upon the region from which the on-shell limit is approached. However, the on-shell Coulomb unitarity relation is not well defined. The discontinuities across the on-shell Coulomb cut in the $p_2$ and $p_1$ planes are evaluated.

Upon careful examination of charged-particle scattering by a finite stationary dipolar system, it is found that the long-range nature of the dipole potential leads to divergence of the total scattering cross section. Thus, contrary to the results of Takanagi and Itikawa, the total cross sections for the finite dipole diverge in a manner similar to that found earlier by Mittleman and von Holdt for the point dipolar field.

A quantum-mechanical two-state close-coupling calculation of the inelastic cross section for the $2{}_{}{}^3{}_{}{}^{}S\to 2{}_{}{}^3{}_{}{}^{}P$ excitation has been carried out for collisions between $2{}_{}{}^3{}_{}{}^{}S$ metastable and ground-state helium atoms in the center-of-mass (c.m.) energy range 5-500 eV. The calculations were carried out in both the diabatic and adiabatic representations using two single-configuration valence-bond molecular wave functions and the corresponding adiabatic linear combinations, respectively. Both representations, as expected, gave identical results. In the diabatic representation, the coupling matrix element was found to be extremely large, resulting in a strong avoided crossing of the corresponding adiabatic potential curves and very small inelastic cross sections for energies $E\lesssim 100$ eV (c.m.), but increasing to a value of about 4 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 500 eV (c.m.), The semiclassical Stueckelberg-Landau-Zener approximation was found to be very poor at all energies considered. The JWKB distorted-wave approximation was found to be fairly good at energies $E\gtrsim 400$ eV (c.m.).

Quantum-mechanical close-coupling calculations of elastic and inelastic cross sections have been carried out for a two-level model problem with variable diabatic coupling. The purpose of these calculations is to illustrate explicitly how the behavior of the inelastic cross section changes as the diabatic coupling is reduced, eventually approaching the semiclassical Stueckelberg-Landau-Zener result.

An inversion procedure to recover the intermolecular potentials from low-energy (4-14 eV) differential scattering data for the systems He${\mathrm{H}}^{+}$, Ne${\mathrm{H}}^{+}$, Ar${\mathrm{H}}^{+}$, and Kr${\mathrm{H}}^{+}$ is presented. The first step in this procedure is to construct the phase shifts {$\eta \mathrm{}\left(l\right)\mathrm{}$} from the experimental differential cross section $\sigma \left(\theta \right)$ and, for reasons of intuition, the corresponding classical deflection function. This is accomplished by employing a new technique developed recently by Remler which involves singularities in the $S$ matrix. The Remler method is as accurate as, but less cumbersome than, the frequently employed standard partial-wave sum and in addition leads to an intuitive connection between $\eta \mathrm{}\left(l\right)\mathrm{}$ and $\sigma \left(\theta \right)$. Having found {$\eta \mathrm{}\left(l\right)\mathrm{}$}, the intermolecular potential may be determined by means of the transformation method of Vollmer. To test the entire inversion procedure, the intermolecular potential obtained from the ${\mathrm{H}}^{+}$ + He scattering data is compared to the ab initio calculation by Wolniewicz of the ground-state potential for He${\mathrm{H}}^{+}$. This method should be applicable to any spherically symmetric scattering system.

A total of 153 krypton resonances in the spectral region 500-337 Å, and 254 xenon resonances in the spectral region 600-375 Å are reported. The disposition of the detailed line lists are indicated. The analysis is very incomplete and will require detailed theoretical calculations to advance. In krypton, 45 resonances and in xenon, 56 resonances have been grouped into probable Rydberg series, for which classifications are suggested. In general, the resonances observed are due to the excitation of the inner subshell "$s$" electron ($n{s}^{2}n{p}^6\to \mathrm{nsn}{p}^6\mathrm{mp}$) or to the excitation of two of the outer electrons simultaneously ($n{s}^{2}n{p}^6\to n{s}^{2}n{p}^4\mathrm{ml}{l}^{\prime }$). These highlying excited states autoionize, resulting in resonances with window-, asymmetric-, and absorption-type profiles. The detailed lists for the subshell "$s$" electron excitations are given.

The cross-section profiles in krypton and xenon have been measured for one- and two-electron excitations of the type $n{s}^{2}n{p}^6\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)\to \mathrm{nsn}{p}^6\left({}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)mp$ or $n{s}^{2}n{p}^6\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)\to n{s}^{2}n{p}^4({}_{}{}^3{}_{}{}^{}P,{}_{}{}^1{}_{}{}^{}D,{}_{}{}^1{}_{}{}^{}S)ml{m}^{\prime }{l}^{\prime }$. These cross sections were assumed to have the form

$\sigma \mathrm{}\left(E\right)=C\left(E\right)+\Sigma \stackrel{}{i}\frac{(E-E_i)\left(\frac{{\Gamma }_i}{2}\right)a_i+{\left(\frac{{\Gamma }_i}{2}\right)}^2{b}_i}{{(E-E_i)}^2+{\left(\frac{{\Gamma }_i}{2}\right)}^2},$

where the adjustable parameters $C\left(E\right)\mathrm{}$, $b_i$, $a_i$, $E_i$, and ${\Gamma }_i$ were determined by a least-squares unfolding process which separated the smearing effect of the monochromator slit from the true optical density. Parameter values and cross-section curves are given for 12 krypton resonances and 11 xenon resonances.

Measurements of the electron-capture probability for close encounters in the reactions ${\mathrm{H}}^{+}+\mathrm{He}\to \mathrm{H}\mathrm{}\left(2s\right)+{\mathrm{He}}^{+}$ and ${\mathrm{H}}^{+}+\mathrm{Ar}\to \mathrm{H}\mathrm{}\left(2s\right)+{\mathrm{Ar}}^{+}$ are reported. The incident proton energies employed range from 3 to 20 keV. Measurements were made for particular impact parameters by selecting particular angles of scatter between 1 and 5 deg. The data show little angular dependence but exhibit structure as a function of collision time. For ${\mathrm{H}}^{+}+\mathrm{He}\to \mathrm{H}\mathrm{}\left(2s\right)+{\mathrm{He}}^{+}$ this structure is similar to that observed previously by Everhart and co-workers for capture into all states of hydrogen for the reaction ${\mathrm{H}}^{+}$ + He → H + ${\mathrm{He}}^{+}$, which is dominated by transfer to the $1s$ state of hydrogen. The present data are not in agreement with available coupled-state calculations for this process.

Studies have been made of differential scattering with charge exchange to the $2p$ state of hydrogen for the systems ${\mathrm{H}}^{+}$ + Ar and ${\mathrm{H}}^{+}$ + He. Fast hydrogen atoms in the state $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ resulting from the collision process were detected by making coincidence measurements between the $\mathrm{Ly}-\alpha$ photon emitted in the decay of the $2p$ state and the resultant fast neutral particle. The probability of transfer to the state $\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$, $P_{2p}$, is presented for ${\mathrm{H}}^{+}$ + Ar for the condition $\Theta T=20\mathrm{}$ keV deg, where $\Theta$ is the scattering angle and $T$ the incident-ion kinetic energy, which represents an impact parameter of 0.53 a.u. For the ${\mathrm{H}}^{+}$ + He system a comparison between experimental results for $P_{2p}$ and the many-state calculation of Sin Fai Lam shows the theory to overestimate $P_{2p}$ by an order of magnitude for $\Theta T=20\mathrm{}$ keV deg as well as for measurements where the impact parameter varied from 0.05 to 0.25 a.u.

The theory of measurements in which photons are detected in delayed coincidence with a scattered particle is developed in a form specifically applicable to atomic collisions. Equations are obtained which relate the measured coincidence rate to excitation amplitudes. These equations incorporate the polarization of the radiation, the fine and hyperfine structure of the atomic levels, the coherence of the radiation, and the time dependence of the radiation intensity. A semiclassical model for certain transitions is introduced to illustrate new features of coincidence measurements. The $\mathrm{Ly}-\alpha$ transitions in hydrogen and ${}_{}{}^1{}_{}{}^{}P\to {}_{}{}^1{}_{}{}^{}S$ transitions in He are treated in detail to illustrate the general theory.