The Beutler-Fano autoionizing resonances in the rare-gas atoms argon, krypton, and xenon are studied using the relativistic multichannel quantum-defect theory (MQDT). Dynamical parameters for the MQDT analyses are obtained from an ab initio relativistic-random-phase-approximation calculation. The position and profile of these resonances are in good agreement with experimental measurements. Angular distribution and spin polarization of photoelectrons in the resonance regions are also studied and are in close agreement with recent measurements.

We present an analysis of our recent experimental wavelengths for the $1s2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1s2p{}_{}{}^3{}_{}{}^{}P_{0,2}^{}{}_{}{}^{}$ transitions of ClXVI and compare the results with theory and other experiments for the HeI isoelectronic sequence. The limits of precision of wavelength measurements obtained using fast-ion-beam sources are detailed. We discuss the limited precision of present theory for the energies of bound states of the relativistic two-electron systems and show that higher-order quantum electrodynamic and relativistic corrections are needed to obtain agreement with our measurements. We present a similar comparison of experiment and theory for the resonance transitions $2s{}_{}{}^2{}_{}{}^{}S-2p{}_{}{}^2{}_{}{}^{}P$, of the LiI isoelectronic sequence and discuss recent results for systems of more electrons. We conclude that many useful tests of multielectron quantum electrodynamic and relativistic corrections can be made by existing and future measurements of wavelengths and fine structure in medium-$Z$ ions of a few electrons.

A coordinate transformation which exhibits the rotational invariance of the hydrogen atom in four-dimensional Hilbert space is introduced. The coordinates are shown to be directly related to the spherical polar and parabolic coordinates in position space. With the use of the transformation, the Schrödinger equation for the hydrogen atom left-multiplied by $4r$ is transformed into one for a four-dimensional harmonic oscillator. Solutions are obtained and related to the hydrogenic wave functions. Group-theoretical implications of the transformation and its application to the hydrogen Stark problem are briefly discussed.

For the purposes of astrophysical, aeronomical, and laboratory application, we seek a precise independent-particle model for electrons in negative atomic ions of the second and third period. The optimum-potential model (OPM) of Talman et al. is first used to generate numerical potentials for eight of these ions. Results for total energies and electron affinities are found to be very close to Hartree-Fock solutions. However, the OPM and HF electron affinities both depart significantly from experimental affinities. For this reason we develop two analytic potentials whose inner energy levels are very close to the OPM and HF levels but whose last electron eigenvalues are adjusted precisely with the magnitudes of experimental affinities. These models are (1) a four-parameter analytic characterization of the OPM potential and (2) a two-parameter potential model of the Green, Sellin, Zachor type. The system ${\mathrm{O}}^{-}$ or $e$-O, which is important in upper atmospheric physics is examined in some detail.

We present an analytic approximant to the electronic density of an atom in the form of a sum of two Yukawa terms $\frac{e^{-\delta r}}{r}$. We use the Thomas-Fermi theory of many-electron atoms to reduce the number of parameters in the approximant to just one. Then, the value of the remaining parameter is obtained by making the atomic energy extreme. Finally, we use the approximant to calculate the energy of lighter atoms. The results are surprisingly good.

The many-electron Dirac-Coulomb Hamiltonian ${\mathrm{H}}_{\mathrm{dc}}$, on which most calculations of relativistic effects in many-electron atoms are based, has no normalizable eigenfunctions corresponding to atomic bound states. Two alternative Hamiltonians ${\mathrm{H}}_{+}$ and $h_{+}$, which are derivable within the framework of quantum electrodynamics and hence do not suffer from this defect, are considered. They differ from ${\mathrm{H}}_{\mathrm{dc}}$ by the presence of external-field or free positive-energy projection operators in the interaction terms; the Breit operator can be included in ${\mathrm{H}}_{+}$ or $h_{+}$ without any difficulty arising thereby. The use of ${\mathrm{H}}_{+}$ or $h_{+}$ as a starting point for a systematic approach to the calculation of energy levels and transition amplitudes in atomic physics is described. Hartree-Fock (HF) approximations to the eigenfunctions of ${\mathrm{H}}_{+}$ and $h_{+}$ are defined and the related relativistic HF equations are derived. The results are used to clarify the meaning of the solutions of the Dirac-Hartree-Fock (DHF) equations associated with ${\mathrm{H}}_{\mathrm{dc}}$. The reduction of ${\mathrm{H}}_{+}$ and $h_{+}$ to fully equivalent relativistic Schrödinger-Pauli Hamiltonians ${\mathrm{H}}_P^{\mathrm{rel}}$ and $h_P^{\mathrm{rel}}$ is carried out in closed form. The HF equations associated with $h_P^{\mathrm{rel}}$ are found to be simpler than the DHF equations.

The static dipole quadrupole polarizabilities and shielding factors of Mg, ${\mathrm{Al}}^{+}$, ${\mathrm{Si}}^{2+}$, ${\mathrm{P}}^{3+}$, ${\mathrm{S}}^{4+}$, ${\mathrm{Cl}}^{5+}$, and ${\mathrm{Ar}}^{6+}$ have been calculated using the variation perturbation technique in a coupled Hartree-Fock scheme. For the dipolar calculation the two innermost cores have been kept frozen, whereas for the quadrupolar calculation all the cores have been relaxed. The results compare favorably with the existing values. For the quadrupolar shielding factor in all cases an antishielding effect is noted. Systematic behavior is observed for the isoelectronic polarizability values.

A general version of the formulas given by the author for the expansion of Slater-type orbitals (STO) in terms of STO's at a new origin is derived. By the use of these formulas multicenter electron-repulsion integrals are evaluated analytically. The final results are expressed in terms of both the overlap integrals and the usual $A$ and $B$ functions.

A formalism for determining pseudostate wave functions for use in modified close-coupling calculations is presented. Applications to low-energy electron-hydrogen scattering are discussed. The $\overline{2p}$ pseudostate proposed by Damburg and Karule is analyzed using this formalism and a reason for its success is given which is independent of the fact that it fully accounts for the ground-state polarizability of atomic hydrogen. The analysis suggests, in agreement with expectations of Burke and Schey and others, that short-range correlations are more important than long-range polarization in determining the best form of the pseudostates.

Total cross sections for capture of an electron by ${\mathrm{Xe}}^{q+}\left(2\mathrm{}\le q\le 12\right)$, ${\mathrm{Ar}}^{q+}\left(2\mathrm{}\le q\le 9\right)$, and ${\mathrm{Fe}}^{q+}\mathrm{}(q=5,6\mathrm{})\mathrm{}$ colliding with atomic and molecular hydrogen have been measured for velocities between ${10}^7$ and ${10}^8$ cm/s. The cross sections vary from below 1 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, with the measured values for $q\ge 4$ all greater than 37 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. The cross sections are independent of ionic species for a given $q$ and are generally constant with changing velocity. The cross sections increase linearly with $q$ up to $q=9\mathrm{}$, but for the highest-charge states $q=9-12\mathrm{}$, the data suggest that the cross sections do not continue to increase as rapidly with increasing $q$.

Comparison of emergent ${\mathrm{H}}^{-}$ yields for incident ${\mathrm{H}}^{+}$ and ${\mathrm{H}}_2^{+}$ beams of the same velocity (0.4, 0.8, and 1.2 MeV/amu) traversing carbon foils of 1-8 μg/${\mathrm{cm}}^2$ shows that, per incident proton, the ${\mathrm{H}}^{-}$ yield from ${\mathrm{H}}_2^{+}$ is generally inhibited, in striking contrast to the enhanced ${\mathrm{H}}^0$ yield previously observed. An explanation of the major inhibition effect is given in term of the Landau-Zener approximation to a "one-passage" charge transfer from the ${\mathrm{H}}^{-}$ to its ${\mathrm{H}}^{+}$ breakup partner.

Absolute total electron detachment cross sections for collisions of ${\mathrm{Cl}}^{-}$ and ${\mathrm{Br}}^{-}$ with the molecular targets ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, ${\mathrm{O}}_2$, ${\mathrm{N}}_2$, CO, C${\mathrm{O}}_2$, and C${\mathrm{H}}_4$ are presented. In each case, the experimental studies extend from collision energies below the threshold for detachment up to several hundred eV. All systems show detachment thresholds which exceed the electron affinity of the halogen atom involved. Detachment rate constants determined from the measured detachment cross sections are included.

The $K$-shell ionization of a heavy atom by a slow light ion is studied by allowing the initial electron state to relax under the potential of the projectile. General estimates are given for monopole and dipole transitions to continuum states, and for the range of impact parameters that contribute most to the process. The correction to the electron binding is now time dependent, and it is shown that it produces a reduction of the ionization probability for small collision velocities, while at larger velocities the time dependence of the binding may enhance $K$-shell ionization.

$K\alpha$ and total $L$ x rays resulting from $K$- and $L$-shell ionization in silver by electron and positron impact at 100, 150, 200, 300, and 400 keV have been measured using a Si(Li) x-ray detector. Within an experimental uncertainty ± 10% the $K\alpha$ x-ray production cross section by electrons, ${\sigma }_{K\alpha }^{-}$, and that by positrons, ${\sigma }_{K\alpha }^{+}$, were found to be the same in the impact-energy region higher than 200 keV, but in the region below this energy it was discovered that the ratio $\frac{{\sigma }_{K\alpha }^{-}}{{\sigma }_{K\alpha }^{+}}$ increases as the impact energy decreases. As for the $L$ x-ray production, no difference between electron and positron impact was found over the whole energy region studied in the present work, although the experimental uncertainty was rather large. Some discussion is included concerning the implications of the present experimental results.

Cross sections for $K$-shell ionization by 70- and 230-MeV-electron impact have been measured on the elements Na, Mg, Al, and Cl. Results for the lighter elements—Na and Mg—are smaller than the values predicted from the Kolbenstvedt theory and the plane-wave Born-approximation calculation. The rates of increase in the cross section with the increase in projectile energy from 70 to 230 MeV are also smaller than the predicted ones, and the cross section shows saturation at high bombarding energy. Furthermore, the increase rates of the cross section for lighter elements are compared with those for heavier elements by measuring relative x-ray yields with high accuracy on targets consisting of a pair of elements: (F,Al), (Na,Cl), (Mg,Mn), (Al,Mn), (Si,Mn), (Cl,Mn), and (Ca,Mn), and the increase rate for lighter elements is smaller than that for heavier elements except for the pairs (Cl,Mn) and (Ca,Mn). A similar result was obtained on the $L$-shell ionization of the pair (Zn,Sn). These results reveal the density effect in inner-shell ionization, which was predicted by Dangerfield, while the magnitude of the effect is not as large as that predicted from a simple theory. The discrepancy is discussed.

We present an iterative approach which uses the Schwinger variational principle to solve the Lippmann-Schwinger equation for electron-molecule scattering. This method combines the use of discrete basis functions to describe the effects of the noncentral molecular potential with an iterative procedure which provides systematic convergence of the scattering solutions. Results for electron-${\mathrm{H}}_2$ scattering in the static-exchange approximation show that the method converges rapidly and gives very accurate results.

Experiments related to the electron-cesium-atom momentum-transfer cross section $Q\left(v\right)\mathrm{}$ in the range of energies $\epsilon =\frac{m{v}^2}{2}$ from 0.05 to 2 eV are considered in which the following quantities are measured: (a) width of the electron cyclotron resonance, (b) attenuation of microwaves, (c) electrical conductivity in both equilibrium and nonequilibrium pure Cs or Ar - Cs plasmas, (d) electron thermal conductivity, (e) perpendicular electrical conductivity in a strong magnetic field, and (f) electron drift velocity. A convenient algorithm is proposed to vary $Q\left(v\right)\mathrm{}$ until the best fit to all data is obtained. As a result an almost unique curve $Q\left(v\right)\mathrm{}$ is found so that the rms deviation of the experimental values from the calculated ones is 20%. The recommended dependence $Q\left(v\right)\mathrm{}$ can be used for calculations in the range of electron temperatures (or equivalent mean energies) from 500 to 2500 K within an error less than 20%.

Crossed beams of electrons and ground state ${\mathrm{Be}}^{+}$ ions have been used to measure absolute cross sections for electron-impact excitation of the 313.1-nm resonance radiation corresponding to the transition ${\mathrm{Be}}^{+}\mathrm{}\left(2p\right)\mathrm{}\to {\mathrm{Be}}^{+}\mathrm{}\left(2s\right)\mathrm{}$. Polarization fractions of the emitted light were also measured. Cross sections are absolute in the sense that all measurables including photon flux at 313 nm have been compared to relevant standards. The doublet emission cross section in units of ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ can be represented as a function of electron energy by $\sigma =-5.10\mathrm{}\ln E+23.0\mathrm{}$ from 4.4 to 21 eV (extrapolating to 16×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at the 3.96-eV threshold) and by $\sigma =101\mathrm{}\frac{\ln E}{E}-\frac{151}{E}$ from 21 to 740 eV. Total uncertainties at a high (approximately 98%) confidence level are about ±10%. Coulomb-Born II calculations of Bely overestimate the value at threshold by a factor of 1.7, and a recent Coulomb-Born calculation by Mann is about 10% higher at 740 eV. Two- and five-state close-coupling calculations lie, respectively, 28% and 19% above the measurement at threshold. For energies from 5 to 300 eV the measured polarization fractions can be represented by $P=-0.0708\mathrm{}\ln E+0.284\mathrm{}$ which given $P=0.19\mathrm{}$ at threshold.

Various indices that characterize the statistical fluctuations in the ionization yield for electron incidence are discussed. The indices include the variance, the moments, the central moments, and the cumulants, all defined in terms of the probability $P(T_0,j)$ that an electron of kinetic energy $T_0$ causes, upon complete slowing down, exactly $j$ ion pairs. Like the mean ionization yield, each of the indices is expressible as an integral over the current energy $T$ of electrons. The integrand is a product of the Spencer-Fano degradation spectrum $y(T_0,T)$ for source energy $T_0$ with another factor, and displays contributions from different values of $T$ to the quantity of interest. It has been shown for the first time that the cumulant of any order (including the variance as a special case) receives contributions from different $T$ nearly the same way as the mean ionization yield. Therefore, $T_0$ greatly exceeding the first ionization threshold, every cumulant is roughly proportional to $T_0$, just as the mean yield is. This leads to a generalization of the Fano factor. Thus the present findings reinforce the importance of the cumulant notion in statistical physics in general. Numerical work on molecular hydrogen as an example substantiates the general conclusion and predicts the value 0.30 for the Fano factor for an electron of initial energy 10 keV.

Excitation and ionization of one-electron ions initially in the $2S$ state in collisions with neutral atoms are examined in the Born approximation for high-impact velocities. An expansion in $v^{-2\mathrm{}}$, where $v$ is the velocity magnitude, is utilized to determine the contributions to the total inelastic (sum-rule) cross sections which arise from transitions to either discrete or continuum final states. The total "excitation" contribution includes the collisional deexcitation transition $2S\to 1S$, the degenerate collisional transition $2S\to 2P$, as well as collisional excitation to bound states of higher energy. Target atoms considered include He, N, and Ar, and a systematic comparison with previous results for one-electron ions initially in the ground state is presented. A comparison with experimental data for $H^0\mathrm{}\left(1S\right)\mathrm{}$ and $H^0\mathrm{}\left(2S\right)\mathrm{}$ colliding with gases of these targets is also given, this latter case providing data directly on the ionization contribution to the total inelastic cross section.