The scattering of electrons or positrons to discrete states of an atomic target is represented in momentum space by coupled integral equations. By introducing a local central potential one may set up a distorted-wave representation for the integral equations, which can be solved to arbitrary numerical accuracy by quadratures. The perturbative solutions of these equations are the commonly used distorted-wave first- and second-order Born approximations. The full coupled on-shell solution is the distorted-wave unitarized Born approximation. These approximations are tested for charged and uncharged targets. The formalism for inclusion of configuration interaction in the target is described, making a complete theory for electron-atom scattering in a truncated channel space, which can be extended by optical potentials to a fully realistic situation.

Atomic cross sections have been measured for the loss and transfer of an electron during a collision between a neutral iodine atom and a rare-gas atom. The neutral iodine beam, with energy between 20 to 110 keV, was unlikely to contain a significant mixture of metastable-state atoms because it was produced by neutralizing a negative-iodine-ion beam. The ${\sigma }_{0+}$ cross section is largest for the argon and krypton targets, not for xenon, as might have been expected. The ${\sigma }_{0\mathrm{-}}$ cross section is very small for the light targets and only becomes appreciable for xenon at the highest energy used.

The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{-}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (η-h${)}^{\mathrm{-}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.

We present an extension of the model-potential method of ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}${(2p${)}^5$(3p)}-Ne collisions. The role of the electronic inversion symmetry in the core–valence-electron separation for stationary nuclei is examined. This leads to approximate electronic eigenfunctions and corresponding adiabatic potentials. In this, an essential element is the R-dependent mixing of gerade and ungerade core potentials, associated with the R-dependent uncertainty of the valence electron being located at the ${\mathrm{Ne}}^{+}$ ion or the Ne atom. Subsequently, nuclear dynamics is included in the approximate wave function and the role of the identity of the nuclei is considered. With the aim of testing our extended approximate treatment, we also present experimental ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}_{}^{\mathrm{*}\mathrm{*}}{}_{}{}^{}$-Ne, and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}_{}^{\mathrm{*}\mathrm{*}}{}_{}{}^{}$-Ne total polarized cross sections $Q_{l\leftarrow k}^{\Vert M_k\Vert }$ for the {(2p${)}^5$(3p)${\mathrm{\}}}_{\mathrm{k}}$ (or {α${\mathrm{\}}}_k$→{α${\mathrm{\}}}_l$) transition, with $M_k$ the magnetic quantum number of the electronic angular momentum J of the initial {α${\mathrm{\}}}_k$ state with respect to the asymptotic relative velocity.

Considerable polarization effects have been observed, as well as some interesting differences with earlier ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$-He data, but no significant differences between the results for ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$. Preliminary quantum-mechanical coupled-channel calculations for the ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$-Ne problem, using valence-electron potentials from Hennecart and Masnou-Seeuws and core potentials from Cohen and Schneider as input, allow us to test theory against experiment, a procedure proven successful for the ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$-He system. We distinguish between the two limiting cases of complete and zero mixing of the gerade and ungerade core potentials. Complete mixing gives much better agreement. For example, the experimental polarization effect $Q_{6\leftarrow 5}^{\Vert 0\Vert }$/$Q_{6\leftarrow 5}^{\Vert 1\Vert }$=2.1 should be compared to the predictions 1.9 and 0.3 for complete and zero mixing, respectively. In general, the measure of agreement obtained for complete mixing indicates the relative lack of importance of symmetry effects for the thermal energies investigated.

A new class of diabatic states for atom-atom and atom-molecule collisions is obtained by formulating a diabatic Hamiltonian. The true Hamiltonian describing the collision system is decomposed by means of topologically defined projection operators into a diabatic Hamiltonian plus an interaction term. A pseudosymmetry operator, which commutes with the diabatic Hamiltonian, is constructed from these same projection operators. The diabatic states are simultaneous eigenstates of the diabatic Hamiltonian and the pseudosymmetry operator. They cross and maintain their character through the crossing region. Such level crossings do not constitute a violation of the noncrossing rule, because the diabatic states involved have different pseudosymmetry. The diabatic states are coupled by the interaction term of the Hamiltonian. A set of coupled equations of motion for the amplitudes of the diabatic states is derived from the time-dependent Schrödinger equation. The (${\mathrm{HeH}}_2$${)}^{+}$ triatomic molecular ion is considered as an example. A pseudoreflection operator is constructed from the projection operators, which reduces to the usual reflection operator in those geometries for which the potential energy has true reflection symmetry. Pseudoinversion symmetry is also considered for this molecular system, treating the ${\mathrm{H}}_2$ at small separations as a near He. In addition, a new configuration constant of the motion is constructed for multielectron systems which is not an extension of a conventional symmetry. The diabatic states obtained in this work predict a recently observed excitation of He to an n=2 state in ${\mathrm{H}}_2^{+}$ on He collisions.

The direct scattering in ${\mathrm{H}}_2^{+}$+He is studied at several energies in the range 1.0–3.0 keV. Excitation of the He target, primarily to n=2 levels, is found even at small scattering angles. The probability of exciting the He is shown to be energy dependent and in our energy and angular ranges has a maximum value of about 0.1. The experimental results are not in agreement with predictions of an extended molecular-orbital model. The same model, however, provided substantial insight into the excitation processes in the direct and electron-capture channels in ${\mathrm{He}}^{+}$+${\mathrm{H}}_2$ collisions and for collisional dissociation in ${\mathrm{H}}_2^{+}$+He→H(2p)+${\mathrm{H}}^{+}$. The excitation of the He in small-angle scattering suggests an interaction at moderate interparticle separation. Related theoretical work by Russek and Furlan [preceding paper, Phys. Rev. A 39, 5034 (1989)] addresses the excitation process.

The multiconfiguration Hartree-Fock method of Saha, Pindzola, and Compton [Phys. Rev. A 38, 128 (1988)] applied to photoionization of atoms has been extended in order to consider elastic scattering of electrons from neon atoms. The dynamical polarization and the electron-correlation effects, which are very important in this case, have been taken into account more accurately in the ab initio method through the configuration-interaction procedure. Phase shifts, and differential, integral, and momentum-transfer cross sections for electrons elastically scattered from neon atoms are reported for the impact-energy range from 0.136 to 70 eV. The calculated results are compared with experimental and other theoretical results. It is found that the present multiconfigurational self-consistent-field method yields high-quality results which show excellent agreement with experiment and compare well with other theoretical results.

The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as a (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates appearing as quadratic forms P and S in (P/S${)}^{\nu }$$K_{\nu }$(PS), where $K_{\nu }$ is a modified Bessel function of the second kind. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves. All angular dependence is then removed by invoking an orthogonal transformation that does not need to be explicitly calculated. The extension to excited states is outlined. The class of integrals over the shifted coordinates, containing plane waves in addition to this product of orbitals and potentials, is given in analytically reduced form, with the external momenta appearing as $S^{\mathrm{-}\gamma }$.

The entire class of integrals containing a product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials (with arguments that are linear combinations of the m≤N+M coordinates of integration) with m plane waves is analytically reduced from a 3m-dimensional integral to a (M+N-1)-dimensional integral.

Double-core-vacancy excited states are observed in the photoabsorption spectra of gas-phase silicon molecules, Si${\mathit{X}}_4$(X=H,${\mathrm{CH}}_3$,F,Cl,Br). We interpret the structures as originating from 1s2p and 1s2s electron excitations into unoccupied valence orbitals. The energies of the observed structures are found at much higher energy than the sum of individual core excitations primarily because of the Coulomb repulsion of the core holes within the silicon atom. Using Hartree-Fock calculations, we interpret the energy separation of the first doublet structure as the singlet-triplet splitting because of the 1s-2p (1s-2s) exchange term. Molecular effects due to the ligands are found in the absolute energies and in the second peak shape. We estimate the energy of the double-core ionization continua, 1$s^{\mathrm{-}1}$2$p^{\mathrm{-}1}$ and 1$s^{\mathrm{-}1}$2$s^{\mathrm{-}1}$, to be around 25 eV above the double excited states.

Based on a conjecture for the four-step recursion relation occurring in the series solution of the Coulomb-diamagnetic problem in two space dimensions, the energy eigenvalue spectrum that reproduces the known limits in full is obtained exactly. The resulting nonperturbative spectrum is a deceptively simple combination of the purely Landau and Coulombic spectra but gives the quasi-Landau levels with (3/2)ħ${\omega }_c$ spacing near the ionization threshold. The conjecture is made plausible in terms of an adiabatic continuation of solutions in the parameter ratio ħ${\omega }_c$/scrR.

We have studied ionization and fragmentation of ${\mathrm{Na}}_2$ via two-photon excitation of high-lying Rydberg states and absorption of one more photon. Using kinetic energy analysis of the fragments we see novel structures in the abundance of slow ${\mathrm{Na}}^{+}$ below the ionization thresholds for the different vibrational states of the ${\mathrm{Na}}_2^{+}$ core. Several processes are considered to be responsible for the observed spectra, revealing a close connection between autoionization, electronic excitation of the core, and fragmentation.

Multiconfiguration Dirac-Fock calculations in the average-level version with the inclusion of the transverse- (Breit) interaction, self-energy, and vacuum polarization corrections have been carried out on the Kα$L^n$ x-ray transitions of molybdenum in order to simulate its experimental ${}_{}{}^4{}_{}{}^{}\mathrm{-}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{induced}$ x-ray spectra. Lorentzian profiles convoluted with the Gaussian instrumental response have been assumed for the component lines. It has also been assumed that the spectrum is a linear combination of all the Kα$L^n$ lines and the coefficients of this combination have been chosen so as to obtain the best fit to experimental data. The ${}_{}{}^4{}_{}{}^{}\mathrm{induced}$ spectrum (without a significant contribution of the satellite lines) has been reproduced with excellent agreement, while in the case of the ${}_{}{}^{16}{}_{}{}^{}\mathrm{induced}$ spectrum the positions of the theoretical bands turned out to be shifted towards lower energies when compared with the experiment and their widths turned out to be smaller. These discrepancies are due to neglect of the effect of the M-shell holes, which results both in shifting of the bands’ centers towards higher energies and in broadening of the bands. The latter can be overcome by assuming larger Gaussian linewidths. It has also been concluded that due to the complexity of the Kα x-ray spectra in terms of the satellite lines, an analysis of the experimental Kα$L^n$ spectra without considering the theoretical studies on the structures of the Kα$L^n$ lines can lead to false interpretations.

A cloud of three-level ions (${\mathrm{Ba}}^{+}$) confined in a Paul trap was illuminated with two lasers and the resulting fluorescence was observed as a function of the laser detunings from the ionic resonance. The observed spectra show features due to the oscillatory motion of the trapped ions. In order to describe the observed line shapes, calculations are presented in which the ion ensemble is separated in classes of velocity amplitudes of the oscillatory motion rather than velocity classes.

Differential cross sections for coherent scattering of 84.3-keV gamma rays at 90° (scattering) by Cu, Mo, Ag, Cd, Sn, Pr, Sm, Gd, Dy, Ho, Yb, Ta, W, Pb, Th, and U were measured using a 133-${\mathrm{cm}}^3$ HpGe detector. From these accurately measured cross sections atomic form factors are extracted corresponding to 4.808-A${̊}^{\mathrm{-}1}$ photon momentum transfer. The results are compared with predictions of form-factor theories, and the appropriateness of these theories is discussed.

A nine-channel coupled-equation calculation for photoionization of the 1$s^2$ ground state of He is performed within the framework of many-body perturbation theory. Partial cross sections for leaving the ion in 1s, 2s, 2p, 3s, 3p, and 3d levels are obtained together with the angular asymmetry parameter for leaving the ion in n=2 states. The resonance structure in the 1s, 2s, and 2p cross sections and in the n=2 angular asymmetry parameter due to doubly excited autoionizing states below the n=3 threshold is calculated. Also, parameters describing the resonances in the 1s cross section below the n=2 threshold are obtained.

The 6$p_{3/2}$np states of barium have been observed for n values between 14 and 21. The energies, linewidths, and transition strengths have been measured and characterized in terms of one- and two-electron interactions, using a single-configuration approximation.

An equation describing the steady-state pulses circulating in a synchronously pumped mode-locked dye laser is derived and solved. The spontaneous-emission noise is included in the equation, and the results that include such effects differ from the usual results.

We present a systematic account of the different relations between squeezing, correlated-emission-laser (CEL) quantum-noise quenching, and general phase-diffusion noise expressed in terms of quadrature amplitudes. For a wide class of optical devices as described by a general Fokker-Planck equation, we establish conditions that lead to squeezing and CEL quantum-noise quenching.

Some model Hamiltonians of simple material systems in interaction with a radiation field are exactly solved by a new generalized recursion method. The linear and nonlinear optical responses are computed.