General expressions are derived for the spectral line shapes of resonance absorption and scattering of coherent radiation in collision-broadened gases, taking into account effects of coherent excitation of two or more atoms (or molecules), as steady-state solutions of a hierarchy of master equations described in a previous publication (paper I). Coupling between the coherent motions of the atoms, provided by a Bethe-Salpeter—type effective interaction, in the binary-collision approximation, forms the essential mechanism for introducing cooperative coherent effects into the steady-state spectra. Explicit expressions are given for the effects of two-atom coherence in the binary-collision approximation, in which the Bloch-type dressed-atom self-energy superoperator is modified by the presence of collisions in which both atoms retain memory of their coherent propagation before the collision. The self-energies include the effects of resonance exchange symmetrization in self-broadening, and are renormalized by the coincidence of radiative transitions during the collisions. The impact (near-resonance) and the quasistatic (line-wing) limits of the applied-frequency detunings are discussed. In the quasistatic limit, coherent many-atom excitations become irrelevant; however, interactions of both collision partners with the radiation during the collision accounts for such phenomena as collision-induced absorption or radiative collisions. In the impact limit, the inclusion of the Bethe-Salpeter interactions allows for the appearance of two-atom resonances. Magnitude estimates of these effects are discussed. Effects of higher-rank (many-body) coherences are formally discussed with the help of a diagrammatic method, leading into implicit bootstrap equations that can be solved by iterative or other procedures.

The electronic stopping cross sections for Li projectiles with an energy between 200 and 840 keV have been measured in 49 liquid organic substances, belonging mostly to the basic hydrocarbon and alcohol series. They have been obtained with the inverted Doppler-shift attenuation method. The relative error of the data is in most cases less than 1%. The various sources of error are discussed in detail in order to determine the final reliability of the values.

The experimental values of electronic stopping cross sections of Li projectiles measured in many organic substances are analyzed with regard to the influence of bonding on the stopping cross section. The invalidity of Bragg's rule, especially for low-velocity projectiles, demands a concept for the analysis which goes beyond simply dividing molecular stopping cross sections into the atomic stopping cross sections of the constituents. Two different approaches are discussed. In the first one, the organic molecule is decomposed into characteristic molecular groups and their corresponding contributions to the molecular stopping cross sections are derived by using only symmetry arguments. The influence of bonding is already included in these values and the problematic atomic stopping cross sections are thus avoided. The second approach, which is more restricted, treats the various bonds in a molecule separately with respect to their specific contributions to the molecular stopping cross section. The results obtained with both procedures are tested by using these values to calculate stopping cross sections of more complex organic compounds. The comparison with measured values shows excellent agreement.

An analysis of rotationally inelastic collisions is made in a two-dimensional model. It is assumed that the target is a hard-core ellipsoid, and the properties of the deflection functions and the forbidden transitions are investigated. The existence of the rainbow is predicted and the estimate of the rainbow angle is given. The rules for the forbidden transitions, arising from the geometry of the target, are also discussed.

The scattering amplitude for positronium formation into arbitrary excited $S$ states in positron-helium collisions in which the residual helium ion is left in the ground state, is obtained in a closed form using the first Born approximation and the first-order exchange approximation. Retaining both the post and the prior forms of the interaction potential, cross sections are computed for several incident positron energies in the range 20-2000 eV. For these energies the asymptotic limit of $n^3$ times the cross section as $n\to \infty$ is attained roughly within 0.1% beyond the excited state $16S$.

The cross section for the resonant electron transfer process ${\mathrm{Ba}}^{+}$ + Ba→Ba + ${\mathrm{Ba}}^{+}$ is calculated for collision energies up to 800 keV. Energy curves for the ${}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ molecular states are first obtained using the multiconfiguration valence-bond method. The cross section is then obtained from the energy curves using the two-state impact parameter version of the perturbed stationary states method. The differential cross section is obtained using the eikonal method. Total cross-section values up to approximately $200\pi a_o^2$ are obtained. At low energies the total cross section exhibits rapid, strong interference oscillations of the type commonly considered to be associated with local extrema in the two-state energy difference. The differential cross-section results clearly show that impact-parameter-dependent structural details of the transfer probability are not directly observable.

The extraction of ac Stark shifts and splittings from a semiclassical treatment of multiple wave-atom interactions is considered. Within the rotating-wave and quasistatic approximations, we show that the information can be extracted from the complex Beer's coefficient sensed by a weak tunable probe wave, whose lower level is fully populated and unconnected to the strong fields. This situation leads to a great simplification of the density-matrix equations of motion, from which algorithms are derived for the algebraic construction of the Beer's coefficients appropriate to other cases not treated. Both level-shifted resonance and line-strength information are contained in the Beer's coefficient, many examples of which are given, some for the first time. Generalized sum rules for the transitions are derived along with a connection of this approach to other approaches including dressing transformations.

A signal-flow-graph representation of Schrödinger's equation appropriate to the analysis of multiphoton interactions in the semiclassical limit is described. Within the rotating-wave and quasistatic approximations the equations of motion for the density-matrix elements can be recast into a system of algebraic equations on the basis of which the signal flow graphs are constructed. By introducing selected graph manipulations, the graph can be simplified and direct extraction of information is facilitated by using standard graph algebra. Illustrations are given for typical cases involving three waves and three- or four-level systems for serial, parallel, and parametric interactions. Also, the construction of an ac Stark graph, which is specifically used for the determination of ac Stark shifts, is illustrated. We show that perturbation results for virtual transitions as well as for real transitions can be obtained directly from the graph.

The drastic perturbation of high Rydberg levels in a magnetic field is interpreted as a prototype effect of wave propagation on a ridge with formation of standing waves and with diffraction from radial into angular excitation modes. Analogs of this phenomenon include two-electron excitations into continuum or high Rydberg levels and may well be quite numerous since ridges occur generally on molecular potential surfaces. The Wannier-Peterkop-Rau theory of two-electron detachment at threshold is shown to provide the essential mathematical model for the description of these phenomena in terms of a base set of two eigenmodes that mediate the diffraction process. The apparent limitation of the original theory to an infinitesimal range of coordinates straddling the ridge is lifted. The problem remains of utilizing the eigenmodes as mediators of the coupling among the complete sets of adiabatic modes that seem to afford an adequate description of phenomena away from the ridges, that is, in potential valleys.

We report the measurement of the $n=16-18\mathrm{}$, $n{f}_{\frac{7}{2}}-n{h}_{\frac{11}{2}}$ and $n=17-18\mathrm{}$, $n{f}_{\frac{7}{2}}-n{i}_{\frac{13}{2}}$ intervals in atomic cesium using two- and three-photon microwave spectroscopy techniques coupled with electric field ionization in an atomic beam. We used two techniques to discriminate between the $f$ and higher $l$ states. First, we took advantage of the fact that the higher $l$ states are ionized at lower fields and used selective field ionization. Second, by delaying the field ionization pulse, in time we were able to discriminate between the $f$ states and the longer-lived higher $l$ states. Using this technique, we were also able to measure the $18f_{\frac{7}{2}}-18g_{\frac{9}{2}}$ interval, where the difference in field ionization thresholds is small. From the values of the measured intervals we were able to extract the effective dipole and quadrupole polarizabilities of the ${\mathrm{Cs}}^{+}$ core using only the microwave data. We obtained ${\alpha }_d^{\prime }=15.544\mathrm{}\left(30\right)\mathrm{}{a}_0^3$ and ${\alpha }_q^{\prime }=70.7\mathrm{}\left(29\right)\mathrm{}{a}_0^5$.

Discontinuities corresponding to the simultaneous creation of two and possibly three electronic vacancies were observed in the absorption spectra of germanium. They occur at photon energies approximately equal to the energy required for the synchronous removal of two inner electrons. The magnitude of the observed discontinuities is about 300 ± 50 times smaller than the observed discontinuity at the $K$-absorption edge of the element.

Theoretical line strengths for the $4d^{10}{}_{}{}^1{}_{}{}^{}S-4\mathrm{}{d}^{9}4f{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ resonance transition in the palladium isoelectronic sequence have been computed in three approximations: configuration-averaged Hartree-Fock, term-dependent Hartree-Fock, and many-body perturbation theory. The Hartree-Fock $4f$ state exhibits pronounced term dependence in the intermediate ionization stages III-XV, with the configuration-averaged radial orbital collapsing more rapidly with $Z$ than the $4f{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ term-dependent orbital due to the large repulsive exchange interaction with the $4d^9$ subshell in the latter. The $4d-4f$ oscillator strength is small for low ionization stages, and does not reach a maximum until Ba XI. Contracted orbital many-body perturbation theory calculations confirm that, as expected for this closed-shell ground-state system, most of the correlation effects are concentrated in the $4d^{8}4f^2{}_{}{}^1{}_{}{}^{}S$ configuration mixing with the ground state. As a comparison, Hartree-Fock data are also given for the transition $4d^{10}{}_{}{}^1{}_{}{}^{}S-4\mathrm{}{d}^{9}5p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$. For $Z<\mathrm{}60\mathrm{}$ the $5p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ state is the lowest-lying ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ in the Pd I sequence.

The collision broadening and shift of the hyperfine structure components of the ground-state splitting for the $D_1$ (8943 Å) and $D_2$ (8521 Å) cesium lines by noble gases (He, Ne, Ar, Kr, and Xe) and by light molecular gases (${\mathrm{H}}_2$ and ${\mathrm{N}}_2$) under pressures not greater than 150 Torr and at a temperature of 295 K are investigated. The Lennard-Jones (12-6) interatomic potential constants are calculated for these systems, using the semiclassical theory of Lindholm-Foley (for Cs with Ne, Ar, Kr, Xe, and ${\mathrm{N}}_2$ systems) and the quantum theory of Baranger (for Cs with He and ${\mathrm{H}}_2$ systems), by comparing with our experimental results in fine structure. These potential constants are employed for the determination of the shift and broadening in hyperfine structure, using the hyperfine theory of collision broadening.

The ionization of open-shell electronic systems produces ionic multiplets of various symmetry species. The associated intensity ratios (or branching ratios) are investigated theoretically. Based on three well-defined approximations a method is presented to determine the branching ratios from the one-particle densities in the initial states. This method allows one to take initial-state correlation into account and contains the so-called geometrical branching ratios as a special case. The method is demonstrated for several examples of systems in $\mathrm{LS}$, $J$, and $\mathrm{LSJ}$ symmetry.

A mixture of dense sodium vapor (number density [Na] ∼ ${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$), and buffer gases helium, xenon, and nitrogen is optically pumped to a high degree of spin polarization using a single-frequency single-mode tunable dye laser. The relaxation in the "dark" of the variables $〈S_z〉$ and $〈\overrightarrow{I}·\overrightarrow{S}〉$ is studied as a function of [Na] and buffergas pressures. For lower helium pressures (46-torr helium and 2-torr Xe) the dominant contribution to the relaxation of $〈S_z〉$ in the presence of Xe comes from the "sticking" three-body collisions with He acting as the third body. This is further confirmed by studying the longitudinal magnetic field dependence of the spin-relaxation rate. At higher helium pressures (He 700 torr, and Xe 2 torr) the relaxation of $〈S_z〉$ in the presence of Xe is mainly due to the "sudden" binary collisions between the Na and Xe, and the relaxation rate of $〈S_z〉$ is independent of the longitudinal magnetic field. Significant hyperfine pumping is achieved by proper tuning of the laser. The temperature dependence of the relaxation of $〈\overrightarrow{I}·\overrightarrow{S}〉$ and $〈S_z〉$ is also discussed.

An exact treatment of the space-charge effect in the single-electron analysis of a free-electron laser is presented to calculate its small-signal gain. With the inclusion of the repulsive force between electrons, it is found that the trajectory of an electron can be solved from a generalized equation which includes a space-charge term. The results show the gain is saturated with decreasing growth rate due to high electron density. The radiation frequency is found to increase with the electron density and approach the value at plasma resonance. The condition $\frac{{\omega }_{p}L}{c}=\pi$ clearly defines the boundary between the noninteracting and the collective regime of an electron beam, where ${\omega }_p$ is the plasma frequency, $L$ is the device length, and $c$ is the light velocity in vacuum.

It is demonstrated theoretically in the semiclassical treatment, that bilateral incidence of monochromatic optical waves onto a Fabry-Perot cavity including resonant absorbers leads to bistable output on variation of the relative phase difference between initial phases of two incident beams, as well as of the intensities.

Two models of saturated coherent light amplifier are studied and compared from the statistical point of view. For one of the models the absorption process is not saturated. The first- and second-order moments of the photon distribution exhibit very different behaviors according to the considered model. The reduced second-order moment measuring the fluctuations becomes more important when the absorption process is not saturated.

A highly sensitive method of detection coupled with a laser atomic beam experiment using on-line-produced Fr isotopes, has permitted finding and measuring the first optical resonance line of this element and its wavelength: $\lambda =717.97\mathrm{}\pm 0.01$ nm. A high-resolution optical study has been undertaken, which has led to the determination of the hyperfine structure and isotope shifts for isotopes of mass number 208 to 213.

The conservation laws for coherent resonant propagation are studied, and an interpretation of these laws as conservation of pulse spectral moments is proposed. The nonlinear spectral density is expressed in terms of the scattering data for an initially hyperbolic secant pulse. In this way spectral moments are exactly determined at any distance and are used for a partial description of the propagating pulse. The conservation laws for the three lowest moments are investigated in detail. The evolution of the zero-order moment leads to an explicit formula for the attenuation of the electromagnetic energy. The rate at which the energy is absorbed depends critically on the pulse area. There is an essential difference between propagation of pulse with area smaller than $\pi$ and those with area larger than $\pi$. The evolution of the first moment corresponds to change of the pulse average frequency. The calculated shift of the average frequency due to detuning is compared with the experimental result of Slusher and Gibbs. The second-order moment is a measure of the pulse spectral width. The evolution of the Fourier second-order moment is used to explain the observed spectral narrowing of a $\pi$ pulse and broadening of a $3\pi$ pulse.