An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation.

Strong coupling at large electron-molecule distances modifies the threshold laws for photodetachment of a molecular anion near a rotational threshold. If the final polar molecule possesses a symmetry axis containing a nonzero component of angular momentum, cross sections of the type $\sigma \sim k^x$ with $x<\mathrm{}1\mathrm{}$ may result for certain ranges of molecular dipoles, depending on the specific rotational threshold considered.

An experimental investigation of the He- and ${\mathrm{He}}^{+}$-${\mathrm{H}}_2$ collisions is performed in the 200-eV - 3-keV energy range. The direct and charge-exchange processes are identified by their characteristic energy losses. The relative probabilities of the main processes are determined as a function of the scattering angle. For the He-${\mathrm{H}}_2$ case, selective population of $n=2\mathrm{}$ singly and doubly excited states of ${\mathrm{H}}_2$ is observed. In contrast with this finding, the whole Rydberg series $\mathrm{H}_2^{}{}_{}{}^{+*}\left(nl\lambda \right)$, $\mathrm{H}_2^{}{}_{}{}^{*}(1s\sigma ,nl\lambda )$, ${\mathrm{He}}^{*}\mathrm{}(1s,nl)\mathrm{}$ and the associated ionization continua are observed in soft ($E\theta \lesssim 2$ keV deg) ${\mathrm{He}}^{+}$-${\mathrm{H}}_2$ collisions. More violent ${\mathrm{He}}^{+}$-${\mathrm{H}}_2$ collisions, however, show trends similar to those of the neutral system. An interpretation is attempted within a triatomic extension of the electron-promotion model. In addition to the well-known diabatic II and rotational coupling mechanisms, a purely triatomic curve-crossing process is shown to account for the population of the $2p{\sigma }_u$ orbital of the molecule.

Electron excitation and transfer to $2s$ and $2p$ states in ${\mathrm{H}}^{+}-\mathrm{H} \mathrm{}\left(1s\right)\mathrm{}$ collisions is studied in the energy range from 1 to 20 keV with the use of a modified two-center atomic-expansion method. It is shown that the inclusion of united-atom orbitals, in addition to the atomic orbitals of the separated atoms, in a two-center expansion allows for the extension of this method to the low-collision-energy regime. The results of our calculations at low energies from 1 to 5 keV agree with experiments and with the recent multistate molecular-orbital calculations by Kimura and Thorson but differ from the molecular-orbital calculations by Crothers and Hughes. At higher energies our results agree qualitatively with experiments and confirm the dip in $2s$ and $2p$ excitation cross sections at $E\sim 11$ keV. The impact-parameter dependence of excitation and capture probabilities is also examined to illustrate the evolution of the excitation mechanism from the rotational coupling at lower collision energies to the direct excitation process at higher energies.

Absolute cross sections for the production of electron-positron pairs by 1.119-MeV photons have been measured with targets of iron, copper, tin, lead, and uranium. An improved internal-source spectrometer was used which utilized two large intrinsic Ge detectors. The results are in excellent agreement with the exact numerical calculations of Tseng and Pratt for $Z=26, 29, \mathrm{and} 50$, and show a systematic departure of 13 and 19% above the theoretical values for $Z=82\mathrm{} \mathrm{and} 92$, respectively. The present cross section at $Z=92\mathrm{}$ is lower than and slightly outside of the error limits from the results obtained with our older spectrometer. The present method has the definite advantage that the absolute activities of the radioactive sources need not be known. It also has the obvious advantages attributable to the high-energy resolution of the two intrinsic Ge detectors. A preliminary measurement in a lead target, using 1.0766-MeV $\gamma$ rays, clearly shows that this technique can be extended to lower photon energies with resulting errors comparable to those at 1.119 MeV.

Equilibrium charge-state fractions of energetic deuterium ions and atoms emerging from alkaline-earth (magnesium, calcium, strontium, and barium) vapor targets are reported in the range of 0.3- to 3-keV incident ${\mathrm{D}}^{+}$ energy. Deuterium negative-ion production in thick barium and calcium vapor targets equals similar production in cesium vapor (∼34%). Moreover, the maxium ${\mathrm{D}}^{-}$ production in strontium vapor exceeds that for all other known gas or vapor targets and reaches 50% at 500 eV. Theory does not quantitatively describe these results, although ab initio molecular-interaction-energy calculations on the neutral and negative-ion CaH systems lead to the prediction of large ${\mathrm{D}}^{-}$ yields at low energies. The theoretical prediction is based on the lack of a strong coupling between the negativeion and neutral molecular states. This implies that there are small ${\mathrm{D}}^{-}$ electron-detachment cross sections at energies less than 1 keV. The present measurements agree with previous measurements done at higher energies.

The $K$ x-ray-production cross sections for fluorine are measured as a function of charge state for 15-MeV ${\mathrm{F}}^{q+}+\mathrm{Ne}$ collisions. The measurements are differential in energy of the $K$ x rays with sufficient resolution to identify the final-state configurations of the fluorine ions following the collision. The final states are identified with the processes of single $K$-shell to $L$-shell excitation, single $K$-shell - multiple $L$-shell ionization, and single $L$-shell electron capture.

We report model-potential calculations of the elastic and absorption cross sections for $e-\mathrm{Ne}$ scattering at 10, 30, 50, and 100 eV. Altogether nine different model potentials are studied; these include the variational matrix-effective-potential method, an absorption potential calculated ab initio from a real energy-dependent polarization potential and a dispersion relation, and two different phenomenological absorption potentials. We get good agreement with experimental results by several methods at 30 — 100 eV and by one method at 10 eV. The tests of the various methods establish useful trends and expectations for future work.

As a generalization of the Schwinger variational principle (VP), the normalization-independent feature of the VP derived from inhomogeneous scattering equations is studied. An optimum form of the VP is derived which contains the "free" Green's function $G_0$. Quasipotentials are then introduced to improve the efficiency of the variational procedure. Various extensions are discussed to include the composite-system scattering, multichannel processes, and the exchange effect.

If the left ($\theta ,\phi =0\mathrm{}°$) and right ($\theta ,\phi =180\mathrm{}°$) rotationally inelastic differential cross sections are measured for the magnetic transitions, then in general the two results are not identical. It is shown, for a two-dimensional model and for linear molecules, that the origin of this asymmetry is due to multiple-collision effects of the atom with the molecule.

Absolute cross sections for the production of electron-positron pairs by photons incident on targets of iron, copper, tin, lead, and uranium were measured using an improved internal source spectrometer which employs two large intrinsic Ge detectors. The measurements were made for 2.615 MeV and a mixture of 1.1732- and 1.3325-MeV $\gamma$ rays in the decays of ${}_{}{}^{228}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$, respectively. The results are in excellent agreement with theory and clearly indicate that there are no deviations of the experimental cross sections from theory, of more than a few percent, down to the effective energy of the ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co} \gamma$ rays. The results also indicate that the improved spectrometer should yield cross sections near threshold with far smaller uncertainties than those measured with the older version.

It is shown that with use of some assumptions the cross sections for the broadening of optical lines originating from Rydberg levels can be interpreted with a simple model which takes into account the elastic and the quenching cross sections of the corresponding Rydberg states. The validity of the model is extensively discussed. Good agreement is observed in most cases between the values derived from the model and the available experimental data for the broadening and quenching cross sections of a wide set of Rb and Na Rydberg levels perturbed by noble gases. It is clearly demonstrated that inelastic processes can significantly affect the broadening cross sections even for large values of the principal quantum number $n$.

Photoelectron spectra have been taken of atomic Cd with synchrotron radiation between 19 and 27 eV using the double-angle time-of-flight method. Dramatically different energy dependences of the partial cross sections for producing the lowest ${}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ ionic states of ${\mathrm{Cd}}^{+}$ were observed for photon energies in the neighborhood of the $\left[4d^9\right(5s5p{}_{}{}^3{}_{}{}^{}P\left)\right]{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}6s{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ autoionizing resonance at 588 Å. Partial decay widths from the excited resonance state have been determined by fitting the resonance line shapes to theoretical expressions for the partial cross sections. Resonance profiles in the photoelectron angular-distribution asymmetry parameter for the ${}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ channels are also reported. The ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ satellite is found to decrease slightly relative to the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ main line in the 19-25-eV range. Three new satellite peaks have been detected with intensities enhanced by autoionization.

We show that the large discrepancies between single- and multiconfigurational Dirac-Fock calculations and experiment recently obtained for certain binding and Auger energies of Ar, K, Kr, Rb, Sr, and Xe, can be removed by including easily computed symmetric-exchange-of-symmetry correlations.

The cross section for anti-Stokes Raman scattering from inverted atomic iodine is calculated by a semiempirical procedure and shown to be dominated by the quadrupole component. Relative intensities for $F_2-F_1$ transitions $F_2$ and $F_1$ are the total angular momenta of the initial and final hyperfine split states) in the hyperfine split multiplets are calculated, and maximal intensity of 25% is found for the 2-4 transition. However, in stimulated Raman scattering maximal gain is expected at the position of the 3-2 line, where collisional broadening and Stark splitting lead to a strong overlap of three lines. The resulting effective cross section is about 33% of the total cross section. For scattering with pump radiation at $\lambda =1.06\mathrm{}$ μm an effective cross section of $\frac{d\sigma }{d\Omega }=0.71\mathrm{}\times {10}^{-28\mathrm{}}$ ${\mathrm{cm}}^2$ is obtained, with an estimated accuracy of 20%. This is somewhat lower than the estimate $\frac{d\sigma }{d\Omega }={10}^{-28\mathrm{}}$ ${\mathrm{cm}}^2$ which has been published recently.

It is demonstrated that, in the presence of collisions and for nonresonant lasers, it is energetically possible to access resonantly excited states and induce a coherence between the states. This situation cannot arise in the absence of collisions if the starting state does not decay. This explains why, when collisions are introduced, a new signal can be generated in a wave-mixing type of experiment. The collisionally induced generation of a coherent signal is intimately related to the process of collisional redistribution. It is shown that all the collisionally induced coherent signals that have been reported up to now involve putting real populations in the excited states. This fact has not always been fully appreciated. No resonance between unpopulated states can exist. The time dependence of these new coherent signals is briefly discussed. In the case of a Raman resonance between equally populated states, it is pointed out that new coherent pathways of equal importance should be considered for explaining the experimental results. A new pressure-induced signal in four-wave mixing is also discussed. It is called "collisionally triggered two-photon quasiresonant coherent signal."

The possibility of a system driven far from equilibrium to exhibit multicritical phenomena is discussed. As an example, the laser oscillating in two modes is shown to possess bicritical and tetracritical points depending on the strength of the coupling between the two modes. The phase diagrams indicating the regions and the nature of the four possible phases for the two-mode laser model are presented. The exponents and the scaling characteristics near the bicritical and tetracritical points are also discussed.

The existence of multistability in a system with a complex order-parameter equation of the form $\dot{\psi }=y-\psi Q\left({\left|\psi \right|}^2\right)$ is examined, with special reference to optical systems such as multiphoton and multimode lasers. It is shown that the neglect of the phase of the order parameter from the dynamical considerations could lead to a different type of multistable behavior. The general polynomial form of $Q$ for the existence of tristability is obtained.

We compute the time-dependent spectrum of fluorescence by two-level atoms after a strong resonant exciting laser pulse is turned off abruptly. The behavior of the "delayed" three-peaked spectrum is shown to be dependent on the natural lifetime of the upper state and on the bandwidth of the interferometer used in the measurement. A prompt increase in the central-peak intensity and an oscillating decay in the two side peaks are predicted to occur immediately after the laser is turned off. These are manifestations of the "undressing" of the atomic states. Our calculation permits consideration of the question of the speed of the undressing and its observation.

A new extended theory of electron transport in dense gases is presented. It is shown that positive and negative density effects can be explained in terms of a single unifying theory. The agreement between theory and experiment is extremely good over a wide range of pressure and temperature in gases with a negative effect, such as He and ${\mathrm{H}}_2$. Some further improvements of the theory in gases with elevated polarizability seem to be necessary for a better quantitative agreement with experimental data, even if the agreement in Ar makes us confident that the proposed theoretical approach can be correct. In the light of our unifying theory, previous theoretical models are analyzed and it is shown that almost all can be obtained under special conditions.