We present a linear-algebraic approach to electron-molecule collisions based on an integral equations form with either logarithmic or asymptotic boundary conditions. The introduction of exchange effects does not alter the basic form or order of the linear-algebraic equations for a local potential. In addition to the standard procedure of directly evaluating the exchange integrals by numerical quadrature, we also incorporate exchange effects through a separable-potential approximation. Efficient schemes are developed for reducing the number of points and channels that must be included. The method is applied at the static-exchange level to a number of molecular systems including ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, LiH, and C${\mathrm{O}}_2$.

Eigenfunctions of a collision complex branch into different channels when propagating from a condensed-complex to a fragmented-complex limit. The branching ratios depend on separate processes localized where propagation becomes nonadiabatic. The cumulative effect of branching is represented by Jost matrices, which consist of the coefficients of the asymptotic expansion of a base set of eigenfunctions and serve to construct scattering matrices and cross sections. The formulation presented here blends theoretical elements of different origin and includes resonant and bound states of the complex.

In this paper we present the first study of the role of double $K$-shell-to-$K$-shell electron transfer in heavy-ion-atom collisions. Consistent analysis procedures for obtaining total cross sections for both single and double $K$-shell-to-$K$-shell electron transfer are outlined based on the charge-state dependence of the total x-ray-production cross sections for $K$-shell satellite and hypersatellite x rays, respectively. Theoretical calculations for the single and double electron-transfer cross sections based on the two-state atomic expansion model and the independent-electron approximation are presented and are found to be in excellent agreement with experiment.

$L_{23}\mathrm{VV}$ and $\mathrm{KLL}$ Auger spectra produced by 2-keV electrons, 3-MeV protons, and 0.8-2-MeV/amu ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ ions using solid targets of Al and Si were measured. No satellite lines of the $L_{23}\mathrm{VV}$ transition were observed, a result which can be explained by relaxation phenomena as an effect of the solid state. Additional structure at the high-energy side of the $L_{23}\mathrm{VV}$ peak can be ascribed to multiple $L$-shell vacancies in the initial state. The intensities of these hypersatellites are discussed within the statistical model of multiple ionization.

An exact expression is derived within the high-$Q$ approximation for the spectrum of energy losses of neutrinos interacting via their magnetic moment with electrons. A formula for the stopping power of matter for neutrinos is derived and applied to the study of the solar neutrino anomaly. The total inelastic cross section is given. An upper limit is deduced for the neutrino magnetic moment from the antineutrino spectrum as recently parametrized by Lee. It confirms the bound reported by Cowan and Reines. The distance for stellar neutrinos to thermalize by the interactions studied here, through encounters with stars is found to exceed the radius of the universe by many orders of magnitude. Stellar neutrinos should thus retain the energy given them at their creation and, rather than cluster around galaxies, permeate the universe uniformly.

A method of deriving the Glauber amplitude (directly from its Glauber formula) for elastic scattering of hydrogenlike ions by structureless charged particles is presented. It is shown that the scattering amplitude in this case is composed of two parts; one ($T_G^A$) is interpreted as the Coulomb-corrected Glauber amplitude of elastic scattering by the core neutral atom of the ion, and the other ($T_G^C$) as the elastic-scattering amplitude of the residual nuclear Coulomb field. Both these terms are proven to be expressible in closed form. The residual Coulomb scattering term is found to be exactly identical to the one obtained directly by Schiff. The present method of derivation also guarantees a correct relative phase for these two terms $T_G^C$ and $T_G^A$. The formula obtained is applied to compute the differential cross sections of $e^{-}-{\mathrm{He}}^{+}$ elastic scattering in the ground state.

Absolute cross sections for Auger-electron production were measured for the target atom Ar bombarded by ${\mathrm{B}}^{+}$, ${\mathrm{C}}^{+}$, ${\mathrm{N}}^{+}$, ${\mathrm{O}}^{+}$, and ${\mathrm{Ne}}^{+}$ ions at energies from 50 to 600 keV. Cross sections for $L$-shell excitation of the target atom and the $K$-shell excitation of the projectiles were deduced. The sum of the $L$- and $K$-shell excitation cross sections are found to increase monotonically with decreasing nuclear charge of the projectiles. The data are interpreted in terms of adiabatic molecular orbital (MO) diagrams. Evidence is found for electron promotion via the $3d\sigma$ MO being the dominant mechanism which is responsible for the inner-shell vacancy production.

Energy-loss measurements of direct-excitation and electron-capture processes are performed for the ${\mathrm{He}}^{+}$ -${\mathrm{N}}_2$, -${\mathrm{O}}_2$ collisional systems in the 0.2-4-keV energy range and in the 0°-3° angular range. Pure vibrational excitation and vibrational excitation in excited electronic states are studied using a high-resolution spectrometer (100 meV). Pure vibrational excitation is always found to be a weak process. The analysis of vibrational distributions in excited states strongly supports an interpretation in terms of the Franck-Condon principle. Relative probabilities as functions of energy and angle are reported for the identified excitation and electron-capture processes. The results show the importance of electron-capture processes among which quasiresonant and endothermic processes dominate exothermic processes. The striking resemblance of the present data with those available on the ${\mathrm{He}}^{+}$ -rare-gas systems conveys a similar quasimolecular interpretation of the collision mechanisms.

Differential cross sections for the proton-impact $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^1{}_{}{}^{}S$ and $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^1{}_{}{}^{}P$ excitations of atomic helium are calculated at 25-, 50-, and 100-keV proton energies using the Glauber approximation. The sum of the results are compared with an earlier multistate eikonal calculation as well as with a very recent measurement. The angular dependence of the cross sections predicted by the Glauber theory is in reasonable agreement with the eikonal results and the observed data.

We propose a new vairational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below $k^2=0.64\mathrm{}$ demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open- and closed-channel orbitals. Furthermore, we show that the convergence of the phase shift with respect to the number of expansion functions (exact states or pseudostates) is also fast. In our theory, the resulting phase shifts can be more accurate than those of the close-coupling method even if the same expansion basis is used. The phase shifts in our $1s-\overline{2s}-\overline{2p}$ calculation are comparable to those of $1s-2s-2p-\overline{3p}-\overline{3d}$ calculation of Matese and Oberoi [Phys. Rev. A 4, 569 (1971)], which are very close to the exact values. Several aspects of the convergence characteristics are also discussed.

Calculations of the photoionization of the $4f$ and $5d$ subshells in the mercury isonuclear sequence have been performed within the framework of a Hartree-Slater central-field model. The results, obtained from the neutral to ${\mathrm{Hg}}^{33+}$, show that removal of outer-shell electrons have virtually no effect on inner-shell cross sections even for subshells with delayed maxima and/or Cooper minima. The general systematics of the variation of $4f$ and $5d$ cross sections in the Hg isonuclear sequence is discussed.

A multichannel quantum-defect theoretic (MQDT) analysis of the high-resolution vacuum-ultraviolet spectrum of C${\mathrm{H}}_3$I in the energetic region below the first ionization limit is presented. The analysis is based upon, and substantiates a posteriori, quantum-defect analogies between Xe and C${\mathrm{H}}_3$I: that is, only purely electronic molecular channels are allowed to interact. A new $d$ series converging on the first ionization limit is assigned as a result of the MQDT analysis.

A modified WKB treatment of a hydrogenic atom in a static electric field $F$ is found accurate over all energies $\epsilon$ to within 1% for $F\le 5000$ kV/cm. This semianalytical technique describes the two properties of the wave function most relevant to photoionization and scattering: (1) the ratio of amplitudes at large and small distances $A_{n_{1}m}(\epsilon ,F)$, and (2) the asymptotic phase shift ${\delta }_{n_{1}m}(\epsilon ,F)$. The photoionization cross section from the ground state, given as a semianalytical function of $\epsilon$ and of the quantum numbers $m$ and $n_1$, describes the polarization-dependent shape resonances observed above the zero-field ionization threshold ($\epsilon =0\mathrm{}$) and agrees with the exact calculations of Luc-Koenig and Bachelier. Complex-contour integration of WKB phase integrals reveals an equipartition of phase between the two sides of the potential barrier formed by the Coulomb and Stark fields. The total phase shift increases by $2\pi$ (not $\pi$) between successive quasistationary levels of constant $n_1,m,F$. The WKB method originally applied to the Stark effect by Lanczos and generalized by Miller and Good is reviewed in an appendix.

We have measured lifetimes of sodium $s$ and $d$ levels in the range $17<n<\mathrm{}28\mathrm{}$. Lifetime shortening due to blackbody radiation has been effectively eliminated by carrying out the measurements in a thermally isolated container cooled to 30 K. The individual lifetimes have been determined to 5% and agree well with calculations based on the Coulombic approximation. The validity of the calculation has been further tested using non-Coulombic methods. An ${\left(n^{*}\right)}^3$ scaling law has been obtained from the lifetimes and is accurate to 2.4%.

Coherent anti-Stokes Raman spectroscopy (CARS) of the $Q$ branch of NO has been performed with a resolution of 0.05 ${\mathrm{cm}}^{-1\mathrm{}}$ by means of a pulsed-dye-laser system. The two $Q$-branch series originating from the ${}_{}{}^2{}_{}{}^{}\mathrm{II}_{1/2}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\mathrm{II}_{3/2}^{}{}_{}{}^{}$ electronic states could be resolved for higher $J$ values. CARS measurements were performed for various gas pressures in order to study the pressure dependence of the real and imaginary parts of the third-order nonlinear susceptibility ${\chi }^{\mathrm{}\left(13\right)\mathrm{}}$. Observed CARS spectra at a pressure of 1.33 × ${10}^4$ Pa allowed the determination of the ratio of the differential Raman-scattering cross sections for the two electronic states as ${\left(\frac{d\sigma }{d\Omega }\right)}_{{\Pi }_{\frac{1}{2}}}:{\left(\frac{d\sigma }{d\Omega }\right)}_{{\Pi }_{\frac{3}{2}}}=1.01\mathrm{}\pm 0.02$.

Using collinear fast-beam—cw-dye-laser modulation spectroscopy, precise transition energies have been measured and excited-state lifetimes determined in the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}_{}^{+}{}_{}{}^{}$ ion. Wave numbers are measured using a real-time fringe-counting interferometer calibrated against the ${\mathrm{I}}_2$ absorption spectrum. The lifetimes are obtained by modulating the cw-dye-laser output by an opto-acoustic wave. A total of 25 excited-state lifetimes have been measured in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ II, providing the first direct lifetime determinations in this ion.

The nonresonant-multiphoton-ionization problem for a diatomic molecule is formulated as the one-photon ionization of a perturbed orbital. The continuum and perturbed orbitals are calculated in the "frozen-core" Hartree-Fock potential of the molecular ion. These orbitals are expanded in spherical harmonics about the internuclear center of mass, and the projected, coupled radial equations are solved iteratively. The radial perturbed orbitals are obtained in every iteration using an exact Green's function calculated in the diagonal, local elements of the potential matrix. This step is of some interest since use of the Green's function to achieve, implicitly, the summations over complete sets of intermediate states has previously been confined to Coulomb or quantum defect method modified-Coulomb problems.

The transition rates for free-bound and bound-bound radiative absorption and emission in an intense laser field have been calculated. In the approximations used here, the rates may be represented by the product of two functions. One function, which contains all the details of the atomic structure, is independent of the laser field. The other function contains all the corrections caused by the intense laser field. The calculations were done using first-order perturbation theory to describe the effects of the intense laser field on the bound-state levels and using a low-frequency approximation for the laser field. It is shown that both these approximations are quite good for the states and laser intensities of interest. The intense-field-correction factor for the rate of bound-free transitions for electrons with a Boltzmann distribution of energies has been calculated. Numerical results for the correction factor for the Boltzmann case are presented. For typical laser-fusion parameters, the correction factor, which is the ratio of the thermal free-bound emission rate in the intense field to the rate at zero field, can be quite significant. The major effect of the strong field on the bound-bound rate is to increase the width of the lines. Since the linewidth is a function of the laser field strength, this effect may be used to measure the laser field at various positions in a plasma.

Stark broadening of prominent visible Xe I lines are measured in three independent experiments. The three studies all use quiescent shock-tube plasmas as emission sources, but each employs distinctly different instrumentation, shock-heating regimes, and analytical methods. Owing to conditions in the light sources, temperatures between 9200 and 12 500 K, and electron densities in the range (2.2 - 10.0) × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$, competing broadening mechanisms and radiative trapping do not seriously complicate the Stark-width determinations. The three sets of broadening results are in mutually close agreement. Generally, they also compare satisfactorily with previous measurements. For some lines, the observed broadening disagrees with theoretical predictions.

Intensity fluctuation characteristics of amplified-spontaneous emission are found using intensity rate equations and the noise-amplifier approximation for saturation coupling between two and four competing modes. The existence of more than one mode leads to the retention of relatively large fluctuations in each mode even as the amplifier gain is saturated, an operating regime which by contrast has been shown to reduce significantly the fluctuations when only a single beam is present. The noise-amplifier approximation is found to be an adequate approximation of the effects of the spontaneous emission distributed along the length of a laser amplifier. The intensity fluctuations in all cases approach limiting distributions functions as the amplifier becomes heavily saturated. Characteristics of these limiting distributions are found for one, two, and four beams; for combinations of beams copropagating and counterpropagating; in the presence and absence of loss; for differences in gain; and for saturation of the sources due to high intensities.