Accumulated photon echoes were observed in ${\mathrm{Nd}}^{3+}$-doped silicate glass by using coherent and incoherent light, and it was theoretically and experimentally verified that the time resolution is determined not by the pulse width but by the correlation time of the excitation field. Even by using a cw laser, instead of a mode-locked laser, a subpicosecond time resolution was obtained when it was operated with a broad and smooth spectrum. The broadest output spectrum, and hence the highest time resolution, was attained when the dye laser was pumped by a mode-locked ${\mathrm{Ar}}^{+}$ laser, and their cavity lengths were mismatched by a few μm. In an experiment with a resolution time of 220 fsec, a new very fast decay was observed in the echo decay curve besides a slower decay already reported.

We study one-photon resonant two-photon ionization into an autoionizing Rydberg series for the case of a weak excitation from the ground state to a resonant intermediate state, followed by a strong-field transition to a structured continuum. The dipole strength for the transition into the autoionizing series is thereby modeled by a multichannel-quantum-defect-theory expression taking into account the infinite number of autoionizing Rydberg states. Analytical expressions are derived for the total ionization rate in the limit of extremely overlapping resonances.

The spectrum of $K\alpha$ emission lines resulting from the interaction of a 10-μm laser at 3×${10}^{14}$ W/${\mathrm{cm}}^2$ with aluminum and titanium targets has been temporally resolved with an x-ray streak camera. With Ti targets unshifted $K\alpha$ predominates and the $K\alpha$ yield is observed to peak during the rising edge of the laser pulse. For aluminum targets the complete inner-shell transition spectrum extending up to the He-like resonance line is observed and is consistent with target heating expected from a local hot-electron flux comprising about 10% of the laser intensity during the rising slope of the pulse.

The time-dependent spectrum of $\frac{3}{2}{\omega }_0$ harmonic emission from uniformly illuminated spherical layered targets has been measured. The features of the observed spectra are consistent with theoretical predictions of $\frac{3}{2}{\omega }_0$ emission from plasma waves generated by the two-plasmon decay instability in a hot, expanding plasma.

The effect of modulation of the control parameter on the onset of intermittency is to hasten the onset and to decrease the length of the associated laminar region.

We show that close to the onset of the oscillatory convective instability in binary fluid mixtures the analog of the Benjamin-Feir instability can arise, i.e., the system does not evolve into a regular flow pattern but breaks up into patches which lead to spatially and temporally incoherent behavior.

In unbounded systems with discrete translational symmetry the Pomeau-Manneville scenario turns into a scenario involving intermittent diffusion. The velocity autocorrelation function, its power spectrum $S\left(\omega \right)$, and the mean-square displacements ${\sigma }^2\mathrm{}\left(t\right)\mathrm{}$ are calculated. We find excess noise ($S\sim {\omega }^{-2\mathrm{}}$) at low frequencies and anomalous diffusion (${\sigma }^2\sim t^2$) of transient duration. We explain that the phenomenon can easily be observed in driven Josephson junctions.

We present an exact real-space renormalization-group technique for self-avoiding walks performed on finitely ramified fractals. The exponent $\frac{1}{\nu }$ of the walks is found to be strongly affected by the geometry of the particular fractal. Also, the excluded volume is shown to be relevant for some fractals and irrelevant for others. For the Sierpinski gasket $\frac{1}{\nu }$ is shown to be equal to the fractal dimensionality of the gasket.

Based upon the analysis of electron correlations in hyperspherical coordinates for arbitrary $L$, $S$, and $\pi$ states, a classification scheme for all doubly excited states of two-electron atoms is presented. A new set of internal correlation quantum numbers, $K$, $T$, and $A$, are introduced. Here ($K$,$T$) describe angular correlations and $A=\pm 1,0$ describes radial correlations. These quantum numbers are used to label the first-order wave functions which are approximated as $\Psi =F_{\mu }^n\mathrm{}\left(R\right)\mathrm{}{\Phi }_{\mu }(R;\Omega )$ in terms of hyperspherical coordinates. The channel index $\mu$ is $\mu \equiv |{\mathrm{}(K,T)\mathrm{}}_N^A{}_{}{}^{2S+1}{}_{}{}^{}L_{}^{\pi }{}_{}{}^{}〉$, where $N$ is the dissociation limit of the channel. Rules for constructing the correlation diagram for channel potential $U_{\mu }\mathrm{}\left(R\right)\mathrm{}$ and the labeling of each channel are discussed. By comparing the rotation-averaged surface charge densities, it is shown that channels which have identical ${\mathrm{}(K,T)\mathrm{}}_N^{+,-}$ have isomorphic correlation patterns, irrespective of the overall $L$, $S$, and $\pi$. Such isomorphism is shown to be the underlying origin of the supermultiplet structure of intrashell doubly excited states. In fact, it is shown that such supermultiplet structures actually extend to all states which have $A=+1\mathrm{} or -1\mathrm{}$. A new Grotrian diagram for energy levels grouped according to ${\mathrm{}(K,T)\mathrm{}}^{+}$ and ${\mathrm{}(K,T)\mathrm{}}^{-}$ displays rotor-like structure. Such diagrams can easily reveal missing or misclassified levels. It is also shown that all $A=0\mathrm{}$ states are similar to singly excited states where for a given ${\mathrm{}(K,T)\mathrm{}}_N^0$, the triplet state always has a slightly lower energy than the singlet state. Approximate selection rules for photoabsorption and for $e$-H and $e$-${\mathrm{He}}^{+}$ scatterings are discussed.

The bound-state wave function of a single nonrelativistic particle is written as $F\exp \mathrm{}(-G)\mathrm{}$, where $F$ contains the nodal information and is restricted to be polynomial and $G$ is the negative of the logarithm of the wave-function envelope which contains the spectral information. As a perturbation is turned on, both $F$ and $G$ respond, but the response in $G$ can be absorbed in $F$. A perturbative expansion on $F$ and the energy leads to a hierarchy of inhomogeneous differential equations which resemble Gauss's law with a variable dielectric constant. If the perturbation is of polynomial form, one reasonably expects polynomial solutions for the perturbative corrections to $F$ in this hierarchy. This method is used to obtain the first-order wave-function correction for the hydrogenic $2S$ and $2P_0$ states in a multipole field and their corresponding multipole polarizabilities. In the dipole case, the method is modified to treat degenerate mixing. Then the first-order correction to the wave function for an arbitrary hydrogenic bound state with azimuthal quantum number $m=0\mathrm{}$ in a large-order multipole field where neither degeneracy mixing nor first-order energy shift occurs and its corresponding multipole polarizabilities are calculated in closed forms.

The lowest-order correction in the hyperfine splitting of muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ due to excitation of the effective ${(\mu -\mathrm{He})}^{+}$ nucleus is precisely evaluated numerically. The result is $\Delta {\nu }_1^e=-45.670\mathrm{}\left(8\right)\mathrm{}$ MHz, in agreement with previous approximate analytic calculations. The mass-polarization correction to the hyperfine splitting is found to be $\Delta {\nu }_1^m=0.0785\mathrm{}\left(2\right)\mathrm{}$ MHz. The total perturbation-theory value for the hyperfine splitting is $\Delta \nu =4464.3\mathrm{}\left(1.8\right)\mathrm{}$ MHz, which is consistent with experiments at the Swiss Institute for Nuclear Research and at the Clinton P. Anderson Meson Physics Facility at Los Alamos.

Relativistic calculations for radiative transition rates between atomic inner shells have been made analytically by the use of the Hartree-Fock-Roothaan method. The atomic electrons are taken to be in the single-particle states in the central potential and expressed in terms of Slater-type orbitals. Retardation effects, all multipole contributions of the radiation field, and the effect of finite nuclear size are included. The calculated results are in agreement with the numerical calculations by the relativistic Hartree-Fock and Hartree-Fock-Slater models.

An expression for the functional-derivative sensitivity density of the scattering matrix in parameter space is derived. This expression can be used to assess the effect on scattering observables of varying space-dependent quantities in the Hamiltonian (e.g., the interaction potential or the free-target portion of the Hamiltonian). This work represents the most general formulation of elementary sensitivity analysis for quantum scattering problems, and its use is demonstrated by a few sample calculations.

The final charge states of the scattered ions and the inelastic energy losses have been measured for single collisions of 0.25—3.0-MeV Kr ions with Kr and Xe targets. The charge states of the scattered ions were measured as functions of scattering angle (from 0.8° to 45°) ion energies from 0.25 to 3.0 MeV. The total inelastic energy losses were measured using the scattered- and recoil-particle coincidence technique for 0.4-, 0.6-, and 1.0-MeV ${\mathrm{Kr}}^{+}$-Kr collision energies and from 0.4 to 1.4 MeV for the ${\mathrm{Kr}}^{+}$-Xe combination. The results show the impact-parameter dependence of several inner-shell excitations and confirm the quasimolecular nature of heavy-ion—atom collisions within the framework of the Fano-Lichten model. For the Kr-Kr case, excitations are observed for values of the distance of closest approach, $R_0$, of 0.40, 0.30, and 0.20 Å; and for the Kr-Xe case, excitations are observed at $R_0$ values of 0.28, 0.18, and 0.09 Å. The data show agreement with the molecular-potential calculations of Eichler and co-workers.

Experimental values for the ratio between $2p$-capture and total $2p$-vacancy production cross sections for 30—80-keV protons on Mg has been measured. The fraction is found to vary between 50% and 35% over this energy range and to be in near agreement with theoretical calculations. Separate cross sections for $2p$ capture and ionization are also derived, but are found to deviate substantially from the theoretical values.

Measurements of the charge-changing cross sections ${\sigma }_{g-}$ and ${\sigma }_{g+}$ are reported for 1-25-keV fast $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ atoms incident on a Na-vapor target. The cross section ${\sigma }_{g-}$ falls from 3′${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 1 keV to 3.5′${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 25 keV. The cross section ${\sigma }_{g+}$ rises from 1.1′${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 2 keV to 1.5′${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^{245}$ at 25 keV. Measured values of the equilibrium fractions $F_{-}^{\infty }$ and $F_{+}^{\infty }$ for incident ${\mathrm{H}}^{-}$ ions are also presented.

Experimental cross sections are reported for electron capture and transfer ionization for Ne, Ar, Kr, and Xe projectiles on He for charge states ($q$) between 2 and 13 and for projectile energies between $\left(250\mathrm{} \mathrm{and} 1000 \mathrm{eV}\right)q$. The double-electron capture is found to be typically an order of magnitude weaker than single-electron capture, and to be dominated in most cases by the transfer ionization channel. While gross features of the cross sections can be qualitatively understood, quantitative agreement with available theoretical model calculations is poor.

A method for the rapid and convenient evaluation of the mean excitation energies that appear in excitation-energy moments of the Bethe-Born cross section is described. It consists of an adaptation of a technique introduced by Pekeris and Dalgarno that uses the excitation-energy moments of the dipole-oscillator-strength sums. The approximate procedure proposed here requires only the initial wave function for the target. The average errors in the logarithms of the stopping and straggling mean excitation energies are less than 1% and 2%, respectively, when compared with direct calculations of these quantities for neutral atoms with nuclear charges in the 2-38 range. Certain applications require values for the subshell contributions to the stopping mean excitation energy. The present scheme provides these individual contributions with errors comparable to those observed for the total mean excitation energy.

The foil-induced dissociation of 3.25-MeV C${\mathrm{H}}^{+}$ is investigated by coincident detection of the fragment atoms resulting from this Coulomb explosion. The dissociation energies are deduced for both the explosion in the foil and for the post-foil interactions. The proton-carbon dissociation energies exhibit a linear dependence on the carbon charge state demonstrating a nonvarying charge state during the post-foil interaction. The data for neutral hydrogen in coincidence with carbon ions show a marked dependence of the dissociation energies on the carbon charge states. The post-foil interaction of the neutral atoms is half that of the protons. A model is suggested to explain these results.

Various results concerning molecular x-ray- and electron-scattering intensities are presented. (i) Directional elastic intensities for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ are calculated and a qualitative explanation for the results is given. (ii) The differences between the usual elastic intensities for x-ray and electron scattering from nonvibrating but freely rotating diatomic molecules, and the fully elastic intensities for scattering from the $J=0\mathrm{}$ state are examined for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$. The usual elastic intensities are rigorously shown to be greater than the fully elastic ones and the differences are correctly mimicked by the independent-atom model. (iii) Polarization functions are found to be important in the restricted-Hartree-Fock description of the total and elastic intensities. A counterintuitive ordering of basis-set effects on one- and two-electron properties is found and explained in the case of ${\mathrm{H}}_2$. (iv) It is shown that, in two-electron systems, a quantity closely related to the Coulson-Neilson Coulomb hole function can be extracted from experimental x-ray-scattering intensities. Both these quantities are displayed for ${\mathrm{H}}_2$. (v) An analogous procedure in the many-electron case is shown to yield the intracular projection of the statistical pair-correlation density.