A formalism based on the unitary- and symmetric-group approaches to configuration-interaction methods has been applied to an evaluation of matrix elements of a spin-adapted reduced Hamiltonian (SRH). It has been shown that there is a simple closed-form expression for the matrix elements of the SRH matrices. This formula has been expressed as a linear combination of two-electron integrals with coefficients given as explicit functions of the parameters defining the finite-dimensional Hilbert space (number of orbitals, number of electrons, and the total spin quantum number).

For a study of the rotational and the vibrational motions of nonrigid molecular systems in terms of differential geometry, quantum molecular dynamics is set up without using the Eckart frame. The vibrational motions turn out to induce on the internal space a ‘‘gauge’’ field attached to the rotational motions. A method of obtaining the internal Hamiltonian for nonrigid molecules is presented. The space of internal wave functions on which the internal Hamiltonian acts is associated with the space of wave functions that are simultaneous eigenfunctions of P^ and J${^}^2$, where P^ and Ĵ denote the total linear momentum operator and the total angular momentum operator, respectively. The internal Hamiltonian to be obtained shows that the internal motions are coupled with the gauge field.

Besides characteristic target and projectile x rays, x-ray continua and radiative-electron-capture photons are seen in collisions with relativistic heavy ions ranging in energy from 82 to 422 MeV/amu and in atomic number from Xe to U. The angular distribution, centroid energy, cross section, and line shape of the broad radiative-electron-capture lines are analyzed. The observed continua are due to primary- and secondary-electron bremsstrahlung. In the projectile frame, primary bremsstrahlung is the radiative scattering of incident target electrons from the projectile nucleus. The continuum cross sections and angular distributions are calculated, and are compared with experiment. Secondary-electron bremsstrahlung, due to the radiative scattering of ionized target electrons from other target nuclei, is target-thickness dependent, and the cross section increases roughly with the square of the target atomic number. The calculated primary-electron bremsstrahlung cross sections are lower than experiment.

The fraction of positrons which survive below the positronium (Ps) formation energy in a low-density galactic environment can directly annihilate with bound electrons in the gas. The details of the measurement of the survival (direct-annihilation) fraction using a low-energy laboratory positron beam are presented for ${\mathrm{H}}_2$ and He. The fraction is found to be higher in ${\mathrm{H}}_2$ than had been predicted by Bussard, Ramaty, and Drachman. The galactic positron line has been shown to be consistent with the line shape expected for annihilation in a neutral medium based on this measurement and on a theoretical prediction of the direct-annihilation linewidth.

The quasiparticle treatment of the electron-hydrogen problem performed in a recent publication is extended. It is shown that the characteristic polarization effect is essentially contained in the third-order quasi-Born approximation of the effective interaction, i.e., in an order which has not been considered in the aforementioned investigation. Instead of incorporating the corresponding contributions exactly, phenomenological polarization potentials proposed in the literature are used in the present calculations. With an adequate choice of the cutoff parameter in these expressions, almost perfect agreement between theory and experiment is achieved. The dependence on this parameter is studied. Comparison of our method with other procedures is being made.

A coincidence has been observed between H(2S) and ${\mathrm{H}}^{+}$ fragments resulting from the bombardment of ${\mathrm{H}}_2$ with 100-eV electrons. A significant source of this coincidence is deduced to be the 2s${\sigma }_g$ state of ${\mathrm{H}}_2$${\mathrm{}}^{+}$. The time-of-flight distribution of these fragments was measured and converted to a kinetic energy distribution from which the potential energy of the 2s${\sigma }_g$ state in the Franck-Condon region was constructed. The result is in good agreement with a published calculation.

The semiclassical local-complex-potential theory has been widely used to describe detachment and ionization in atom-atom and ion-atom collisions. However, it has been shown that the resulting formulas do not conserve probability. In this paper, we show that the problem arises from the inconsistent treatment of the effects of interference, tunneling, and diffraction. A more complete theory is based upon the close-coupling expansion, which leads to an infinite set of coupled equations. A method for solving such sets of equations was developed in earlier work. Here we implement that method using a new iterative numerical scheme, and we show that the iteration converges to results in which probability is conserved.

The integral Rayleigh scattering (RS) cross sections of γ rays for Al, Cu, and Sn at 145 keV energy and for Al, Cu, Sn, and Pb at 279 keV energy have been determined at angles below 7° by a new method, and are compared with the theoretical integral RS cross sections computed using the non- relativistic form factors (NRFF) of Hubbell et al., the relativistic form factors (RFF) of Hubbell and Overbo, and the modified form factors (MFF) of Schaupp et al. The present experimental results are in fairly good agreement with each of these NRFF, RFF, and MFF theoretical values below 6° within the uncertainties quoted. However, the experimental integral RS cross sections for medium- and high-Z elements appear to be consistently closer to the MFF theoretical values as the scattering angle increases.

We treat low-energy electron scattering by atoms within a Kohn-Sham-type one-particle theory. In applying this theory, all many-body effects involved in the projectile-target interaction are absorbed into a one-particle potential. Hence, one merely has to solve an elementary potential-scattering problem. However, there are two crucial points to be observed in the construction of the scattering potential. (1) The Kohn-Sham-type exchange-correlation potential must be formed by using correlation factors which are required to have certain asymptotic and integral properties. (2) Since the scattering process is viewed as being quasistationary, the unbound projectile state must be modified by a bell-jar-type envelope function to account for the effect of a finite residence time in the target where the projectile causes a finite perturbation. During this time the entire system has to be treated as consisting of N+1 indistinguishable electrons which in a Kohn-Sham-type theory are described by only N+1 self-consistent one-particle states. Once the analytical forms of the correlation factors and the envelope function have been chosen, the calculational procedure is completely parameter-free. Although it is considerably simpler than well-established methods in this field, it provides comparably good results on differential cross sections and scattering-induced polarizations in a wide range of impact energies (5–100 eV).

Atomic single- and double-electron-detachment cross sections are reported for ${\mathrm{O}}^{\mathrm{-}}$ ions in He, Ne, Ar, Kr, and Xe gases, at collision energies from 10 to 115 keV.

Electron-impact excitations of C-like ions (O iii, Ne v, Si ix, and Ca xv) are studied theoretically by a distorted-wave (DW) method previously proposed [Y. Itikawa and K. Sakimoto, Phys. Rev. A 31, 1319 (1985)]. When compared with the calculations of the close-coupling method and R-matrix theory, the DW method is confirmed to give reasonably good results. By supplementing the R-matrix calculation, the present DW method thus extends the availability of reliable cross-section data to higher energies. A comparison is also made with the calculation by Mason, Bhatia, and co-workers using the DW-method computer package developed at the University College, London, to examine the reliability of the calculation.

In view of the inapplicability of the asymptotic expressions for the stopping number available in the literature at high energies, an alternative approach is taken to compute the shell correction to the stopping number of K electrons. Anholt’s formula for the K-shell ionization has been used to calculate the excitation function for longitudinal interaction and numerical integration over energy has been carried out to evaluate the shell correction. Comparison with other theoretical calculations is made. It is proposed that, with the inclusion of relativistic effects, an asymptotic expansion of the stopping number with a leading-term logarithmic in the energy of the incident particle would be more meaningful and might enable one to extract the relativistic contribution to the shell correction from it.

Absolute cross sections for the emission of Balmer-α radiation have been measured for low-energy ${\mathrm{H}}^{+}$ impact on He, Ne, Kr, and Xe atoms. Measurements were made at ${\mathrm{H}}^{+}$ energies of 2.0 and 1.25 keV for He, from 2.0 to 0.5 keV for Ne, and from 2.0 to 0.04 keV for Kr and Xe. The Balmer-β emission cross sections were also measured for Kr and Xe, as were the polarizations of the radiations, and the contributions to the radiations from decay of the 3s and 4s excited states of hydrogen were resolved for ${\mathrm{H}}^{+}$ energies above 0.2 keV. The data are compared with similar results for Ar reported earlier, and with the results of other workers at higher ${\mathrm{H}}^{+}$ energies.

Cross sections and annihilation rates for the elastic scattering of positrons off hydrogen and helium atoms are calculated in an approximation in which nonadiabatic distortions of the targets are treated with a model potential. The wave functions of the targets are calculated in a bicentric spheroidal coordinate system by modifying a computer code written for self-consistent-field calculations on diatomic molecules. Virtual positronium and correct long-range polarization of the targets are accounted for explicitly in the wave function by proper choice of basis functions. The wave function for each target is calculated on a grid of positron-nucleus distances, which generates a scattering potential for the positron. This is solved by applying partial-wave analysis and numerical integration. The calculated results for cross sections and annihilation rates for both systems are reasonably accurate, and suggest that the method can be extended to larger targets.

We calculate the energy transferred by a swift incident particle to a stationary atom as a function of the impact parameter. The calculation is based on a local-density approximation and on the electron-gas model. We apply Thomas-Fermi and Lenz-Jensen atomic models, and we study the general scaling properties of the energy loss as a function of the impact parameter and velocity, in terms of the target atomic number $Z_2$. With the same description we calculate the stopping cross section as a function of $Z_2$, and compare it with existing experimental results. Finally, we compare our theory with the experimental results of Eckardt et al. for the angular dependence of the energy loss of protons transmitted through thin solid foils.

Positronium formation by electron capture from a negative hydrogen ion is studied with use of the Coulomb-Born approximation. Differential and integral cross sections are calculated by using the prior and the post form of the approximation for incident positron energy varying between 20 and 500 eV.

A unified theory of coherent and incoherent resonance scattering of radiation in gases is presented. Expressions for the scattering rates in collisional redistribution and four-wave mixing (FWM) are obtained, starting from a microscopic formulation based on the Liouville–von Neumann equation. The derivation reemphasizes the point that coherent scattering depends on a product of scattering amplitudes at two separate points in the gas. The theory is extended to the nonimpact domain in which frequency detunings exceed the inverse duration of a single collision, taking into account intracollisional effects. Expressions are given in the so-called quasistatic limit (of semiclassical Franck-Condon transitions) for situations in which one or more radiative transitions occur during the collision. An extension of double-sided diagrams to collision-induced processes is introduced, and is used to illustrate the various phenomena described. Applications are suggested to the study of molecular dynamics, making use of the spectral features of FWM outside the impact domain. Investigations of long-range correlation effects, involving laser fluctuations, or cooperative excitations in dense fluids (utilizing the two-point nature of FWM), are also discussed.

Using ${}_{}{}^{137}{}_{}{}^{}\mathrm{Cs}$ γ rays, the effect of finite absorber dimensions on attenuation measurements has been studied. Copper and mercury targets were used. Absorber dimensions up to five mean free paths were used. A correlated effect was observed in the measurements due to absorber thickness and its dimensions in the transverse directions. The values of the attenuation coefficients for copper and mercury have also been determined.

Attenuation coefficients have been measured for aluminum for x rays in the energy region 7–15 keV. The x rays were obtained by proton excitation of copper, tantalum, and lead targets. A new method has been used to extract the attenuation coefficients of the individual components of the copper K x rays and the L x rays of tantalum and lead without necessitating an analysis of the component peaks of the x-ray spectrum for each absorber.

The effect of hyperfine-induced singlet-triplet mixing on radiative lifetimes has been studied in neutral strontium. Different lifetimes are, for the first time, observed for different hyperfine components in laser-spectroscopy measurements combining high spectral and temporal resolution. The experimental results are found to be in good agreement with theoretical calculations.