The dipole-dipole-quadrupole (B) and second-dipole (γ) hyperpolarizabilities and the dipole (${\alpha }_1$) and quadrupole (${\alpha }_2$) polarizabilities are calculated for the ground state of the beryllium atom. The results are based on finite-field energies computed using the coupled-cluster double-excitation model (commonly known as CCD), corrected by fourth-order contributions from single and triple excitations computed with CCD amplitudes. The final values are ${\alpha }_1$ =37.30$e^2$$a_0^2$$E_H^{\mathrm{-}1}$, ${\alpha }_2$ =298.8$e^2$$a_0^4$$E_H^{\mathrm{-}r1\mathrm{}}$, B=-2102$e^3$$a_0^4$$E_H^{\mathrm{-}2}$, and γ=3.15 ×${10}^4$$e^4$$a_0^4$$E_H^{\mathrm{-}3}$.

Wave-packet solutions of the Schrödinger equation for the Coulomb potential are obtained that travel along classical elliptic orbits of fixed mean eccentricity and angular momentum. These wave packets are coherent states that have minimal quantum fluctuations in the noncommuting components of the Lenz vector in the plane of the orbit. For large quantum numbers the asymptotic form of the wave packet and the classical equations of the orbit are obtained analytically.

A physically motivated criterion for the validity of the Gaussian approximation for the electric microfield distribution at an arbitrary ion in the general multicomponent classical plasma is presented. The exact second moment is obtained from the Onsager proper energy for a unit dipole at the center of a cavity, of radius equal to the ion-sphere radius, embedded in a uniform conducting fluid. A connection between scaling behaviors of the plasma-mixture thermodynamics and its electric microfield distribution is pointed out.

The lattice structure of bounded Coulomb systems is explored using a simple zero-temperature slab model. For slabs above a certain size infinite-volume behavior (i.e., a bcc lattice) occurs. Below this size surface effects dominate and the lattice type depends on the size, usually taking on an fcc-like symmetry. This state is similar to the lattice observed in recent computer simulations. These results have implications for experiments now underway.

The Hagen-Poiseuille flow of a Lennard-Jones liquid through a cylindrical pore formed by regularly arranged fixed atoms is studied by molecular-dynamics (MD) simulations. Different flow patterns develop depending on the strength of the wall-fluid interaction, the strength of the gravitational-type driving force, the thermodynamic state, and also on the mechanism of heat dissipation. In spite of the high driving forces necessary in MD it is found that up to two molecular layers may stick at the wall which confirms recent experimental findings.

In this Reply, it is shown how our experimental results lead us to the conclusion that the two-step process proposed in the recent Comment by Gillen [Phys. Rev. A 39, 2248 (1989)] cannot explain the ion signals observed for $E_{\mathrm{c}.\mathrm{m}.\mathrm{}\mathrm{\le }50}$ eV, whereas laser-assisted ionization is the only mechanism consistent with our observations in this energy range. The measured amplitude of the signals can be interpreted in terms of a transition-dipole enhancement induced by the collision. Such an enhancement has been ignored in the estimates of Gillen.

Penning electron-energy distributions are calculated for collisions of He(2 ${}_{}{}^1{}_{}{}^{})$ and He(2 ${}_{}{}^3{}_{}{}^{})$ with sodium and potassium atoms. The formulation is in terms of quantum-mechanical wave functions, which are determined using previously published complex potentials for the initial states and available experimental or presently calculated Hartree-Fock potential curves for the final state. Sensitivities to these potentials are tested. The mechanisms for the observed energy structure are analyzed, and the effects of experimental finite energy resolution and collisional velocity spread on the structure are shown.

The previously developed relativistic, two-center, coupled-channel treatment of atomic collisions between high-Z ions has been extended to include pseudostates. By augmenting the atomic basis sets by pseudostates, an approximate representation of the continuum is obtained as well as an improved description of quasimolecular states near the united-atom limit. The problems arising from approximate basis states, specifically in relativistic collisions, are discussed. Numerical calculations for ${\mathrm{U}}^{92+}$+${\mathrm{U}}^{91+}$ at 500 MeV/u are performed with basis sets of up to 36 real and 16 continuum pseudostates. While the presently attainable basis sets are presumably still too small, one can get, nevertheless, reasonable estimates of the cross sections for ionization and K-vacancy production.

Stochastic fields with non-Gaussian Markovian phase or frequency jumplike noise are produced at microwave frequency and used to induce two-photon (TP) processes in a S=(1/2 spin system. The influence of the field statistics on the TP-induced second-order response is experimentally investigated in a system with very short relaxation times, in its stationary state and in the weak-field limit. In the case of frequency-telegraph noise the experimental spectra of the nonlinear response are found to reproduce roughly the spectral profiles of the corresponding driving fields but with a larger width. When the telegraph noise modulates the phase of the field, the relationship between input and output spectra depends on the phase-jump amplitude ${\phi }_0$. For ${\phi }_0$=π/4 the spectrum of the response is much broader than the input one, whereas it is much narrower for ${\phi }_0$=π/2. The experimental results are interpreted using the calculation of the TP-induced second-order response worked out in the preceding paper [Boscaino and Mantegna, Phys. Rev. A 40, 5 (1989)].

We have investigated small-angle electron scattering by highly polar molecules. Recoil experiments are performed at 5 and 20 eV for electrons scattered by LiBr and CsCl, within the shadow of the unscattered molecular beam. Low-angular-range scattering described by the Born approximation for rotating dipoles, combined with different theories for intermediate- and high-angle scattering, are compared with our results. Evaluated total scattering cross sections as well as momentum-transfer and viscosity cross sections are given. A general two-dimensional analysis of the recoil experiment is presented.

The wavelengths of the transition 1s2pAr1s2$p^1$$P_1$→1$s^2$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ in heliumlike potassium, scandium, titanium, vanadium, chromium, and iron have been measured with an experimental precision of Δλ/λ≊1/20 000. The data typically agree within error bars with recent theoretical predictions that include quantum electrodynamical corrections. However, the comparison shows that there are systematic differences between data and predictions, which indicate a need to include additional corrections in the calculations. In particular, it is found that the experimental wavelengths are consistently shorter than the calculated values by amounts which depend on the particular theoretical prediction used in the comparison. Measurements of the wavelengths of Δn≥2 x-ray transitions in heliumlike argon, scandium, titanium, vanadium, chromium, and iron are also presented.

An experiment was constructed to measure the contribution of vacuum polarization [in quantum electrodynamics (QED)] to the 3d-3p energy difference in muonic helium. Major features of the experimental apparatus included design and construction of a pulsed beam of stopping muons with the highest instantaneous intensity available, a laser system producing multijoule pulses from doubly isotopic ${\mathrm{CO}}_2$ gas, a cavity to trap the laser light in 3 atm of helium, and Si(Li) detectors to measure the helium x rays. The number of stimulated x rays accumulated was not sufficient to permit a statistically significant QED measurement, but the results demonstrate the feasibility of laser spectroscopy in a pulsed muon beam. The intensities of separate K x-ray lines in muonic helium were measured at 1 and 3 atm for comparison with recent theories of pressure effects on the muon cascade.

The ${\mathrm{CCl}}_4^{2+}$ ion has been studied using charge-transfer spectroscopy and x-ray-induced Auger-electron spectroscopy. From the kinetic energy distribution of ${\mathrm{H}}^{\mathrm{-}}$ ions arising from double charge transfer of protons impinging on ${\mathrm{CCl}}_4$ gas, three singlet-state energies of ${\mathrm{CCl}}_4^{2+}$ have been measured at 30.4±0.2, 33.0±0.2, and 35.8±0.2 eV. The experimental peaks are narrow, indicating that these doubly ionized states are presumably stable or quasistable. The Cl $L_2$,3VV Auger-electron spectrum exhibits 15 well-defined structures. The lines of the Auger-electron spectrum are narrow, which agrees with the present charge-transfer data, supporting the interpretation in terms of bound or flat potential curves in the double-ionic states. By comparison with recent results from double charge transfer of ${\mathrm{OH}}^{+}$ ions on ${\mathrm{CCl}}_4$ it is shown that all the main features of the Auger spectrum can be associated with singlet or triplet states. The following double-ionization energies have been determined: For triplet states 29.8, 31.4, 33.7, and 34.5 eV; and for the singlet states 30.5, 32.9, 36.1, and 36.5 eV, where all values are given with an accuracy of ±0.1 eV.

The spectrum from Compton-scattered x rays is an inherently broad distribution. This distribution is the sum of several Gaussian-like distributions, which gives the sum its unique shape. The Gaussian-like distributions are the result of convoluting the so-called Compton profile, the spread in the scattered-x-ray energies due to the momentum distributions of the target electrons, with the detector response and the geometrical effects. The distribution is then further modified by the absorption within the sample. A formulation for both qualitatively and quantitatively determining the magnitude of the geometrical contributions is presented. This formulation is based on a recently devised approach to the scattering geometry [Hanson, Gigante, Meron, Phys. Rev. Lett. 61, 135 (1988)]. A methodology for determining the geometrical spread in the energy of the scattered x rays is presented. The results can be conveniently used to optimize scattering geometries for the reduction of the geometry-caused spread.

L Auger-electron emission following selective excitation of autoionizing states in 3.4-MeV/u Na-like Ti ions by He and Ar has been investigated using the technique of 0° electron spectroscopy. The electron emission has been compared to model spectra based on oscillator strengths, transition energies, and transition rates from multiconfigurational Dirac-Fock calculations as well as on collision strengths from the literature. It was found that monopole, dipole, and quadrupole excitation of Auger states with an excited-state configuration 2$p^5$3snl (n=3,4) causes the dominating structure in the spectrum where He was used as an exciter.

Vibronic cross sections for x-ray and Auger decay from short-lived core-hole states in molecules are derived starting from Åberg’s description of atomic x-ray and Auger decay as multichannel-scattering processes [Åberg, Phys. Scr. 21, 495 (1980)]. The derivation includes a scattering-matrix formulation in which intra- and interchannel interactions as well as nonadiabatic corrections are introduced. Computable expressions for x-ray and Auger vibronic spectra are derived assuming the harmonic approximation for multidimensional nuclear motions. Applications for water are carried out using truly ab initio values for all energy and lifetime-related parameters.

Positions and widths of the lowest-lying ${}_{}{}^1{}_{}{}^{}$,3S resonances in helium are presented along with their oscillator strengths to the singly excited ${}_{}{}^1{}_{}{}^{}$,3P ° states (1s-np,n=2,4). The background differential oscillator strength from the P states to the S continuum is also found and is very small. The resonances are described by an expansion of square-integrable functions in hyperspherical coordinates; the continuum is treated by using positive-energy Coulomb functions, and the two are brought together by a scattering variational principle. Computed branching ratios for these states indicate which state might be seen as a satellite line in an ion-atom collision.

The resonance fluorescence spectrum of two atoms near a perfectly conducting metal is investigated. A quantum-mechanical version of the image method, taking into account the dipole-dipole interaction, is adopted to study the excitation spectrum. Within the framework of this approach, each single atom and its corresponding image are kinematically correlated, while dynamically they are actually independent. The effects of the surface are directly exhibited in the decay rates, the frequency shift, and the spectrum. The influence of the surface is found to be large for weak fields but becomes very small for high intensities of the pump field.