Correlation has been treated relativistically by solutions of the pair equation, an inhomogeneous differential equation in two dimensions. The equation is solved within the no–(virtual-)pair approximation and is formally correct to order ${\alpha }^2$ Ry. Continuum dissolution is rigorously avoided, by the use of projection operators. Correlation is treated starting from a suitable choice of a fully relativistic one-particle description of the atom. The solution of the equation involves additional difficulties as compared with the nonrelativistic case, which are discussed. Second-order energies arising from electrostatic and magnetic correlation have been calculated for the 1$s^2$ ground state for a series of heliumlike systems (Z=2–50). The starting point has been either hydrogenlike wave functions or Dirac-Fock orbitals. Comparison has been made with other methods, showing good, sometimes excellent, agreement, and trends in the isoelectronic series are discussed. By iterative solutions of the exact pair equation a nonperturbative treatment of the two-body part of the static Coulomb interaction is obtained. This procedure has been used for s excitations.

Cross sections and rate constants are calculated for collision-induced rotational transitions of compound muonic molecules, which determine relaxation rates important to muon-catalyzed fusion processes. The interaction potential is derived from the ${\mathrm{H}}_2$-${\mathrm{H}}_2$ potential, and the R-matrix propagation method is used to solve the set of coupled collisional equations for the systems ${\mathrm{D}}_2$+[(dtμ)dee], ${\mathrm{D}}_2$+[(ddμ)dee], ${\mathrm{T}}_2$+[(dtμ)dee], ${\mathrm{D}}_2$+[(dtμ)tee], and ${\mathrm{H}}_2$+[(ddμ)pee]. Calculations are also done on ${\mathrm{H}}_2$+HD and ${\mathrm{D}}_2$+HD for comparison with previous work.

The latest information about the ${}_{}{}^5{}_{}{}^{}\mathrm{He}$ nuclear system in terms of R-matrix parameters has been matched to adiabatic dtμ molecular wave functions in order to determine the complex eigenvalues of the molecule. Through the use of the reduced R-matrix formalism, the matching is accomplished by considering only the L=0 dtμ states explicitly. These states are calculated in a series of increasingly more accurate adiabatic approximations that, at least for the lowest vibrational level, appear to be converging to the exact nonadiabatic result. The best complex eigenvalues thus obtained probably have less than 10% uncertainty, and are in reasonably good agreement with those of Bogdanova et al. ( Zh. Eksp. Teor. Fiz. 81, 829 (1981) [Sov. Phys.—JETP 54, 442 (1981)]).

Apparent cross sections are reported for the excitation of Na atoms from the ground 3s level to the 3d level by incident ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2$${\mathrm{}}^{+}$ ${\mathrm{H}}_3$${\mathrm{}}^{+}$, or ${\mathrm{H}}^{\mathrm{-}}$ ions with velocities in the range 0.5×${10}^6$ to 2.2×${10}^6$ m/s. The apparent cross section for ${\mathrm{H}}^{+}$ ions has a maximum value of 4.5×${10}^{\mathrm{-}16}$ ${\mathrm{cm}}^2$ at an incident ion velocity of 1.7×${10}^6$ m/s. At velocities above 1.4×${10}^6$ m/s the apparent cross section for Na(3d)-level excitation by ${\mathrm{H}}^{+}$ ions is the same function of the velocity as the apparent cross section for 3d-level excitation by electrons. The apparent cross section for excitation of Na(3d)-level atoms by incident ${\mathrm{H}}^{\mathrm{-}}$ ions is about 45% below the apparent cross section for excitation by incident ${\mathrm{H}}^{+}$ ions at velocities above 1.7×${10}^6$ m/s. Combination of the apparent Na(3d) cross sections with the apparent Na(3p) cross sections reported earlier gives the direct excitation cross sections of Na(3p) by ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2$${\mathrm{}}^{+}$, ${\mathrm{H}}_3$${\mathrm{}}^{+}$, and ${\mathrm{H}}^{\mathrm{-}}$ impact.

Normalized, absolute differential cross sections (DCS’s) have been measured for the 20 lowest electronic states of xenon. Incident electron energies were 15, 20, 30, and 80 eV and the scattering angles ranged from 5° to 150°. The energy resolution was 40 meV. Absolute elastic DCS’s have been obtained by normalizing the relative values to the recently published absolute elastic DCS’s by Register et al. [J. Phys. B 19, 1685 (1986)]. Elastic-to-inelastic intensity ratios, at different incident energies for the 6s${\left[\right(3/2\mathrm{}]}_1$ state were determined. These ratios were utilized as secondary standards to establish the absolute scale for the other inelastic processes in accordance with intensity ratios of lines in energy-loss spectra. The absolute inelastic DCS’s were extrapolated to 0° and 180° and integrated to yield the integral cross sections (ICS’s). A comparison of the present DCS’s with the only available measurements at 20 eV impact energy shows satisfactory agreement in shape but considerable difference in absolute value.

M-shell x-ray production cross sections are reported for ${}_4{}^9{}_{}{}^{}$${\mathrm{Be}}^{+}$ ions incident upon thin ${}_{59}{}^{}{}_{}{}^{}\mathrm{Pr}$, ${}_{60}{}^{}{}_{}{}^{}\mathrm{Nd}$, ${}_{63}{}^{}{}_{}{}^{}\mathrm{Eu}$, ${}_{66}{}^{}{}_{}{}^{}\mathrm{Dy}$, ${}_{67}{}^{}{}_{}{}^{}\mathrm{Ho}$, ${}_{72}{}^{}{}_{}{}^{}\mathrm{Hf}$, ${}_{74}{}^{}{}_{}{}^{}\mathrm{W}$, ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, ${}_{82}{}^{}{}_{}{}^{}\mathrm{Pb}$, and ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$ targets. Incident-beam energies range from 0.5 to 2.5 MeV (55.6–267 keV/u). The results are compared to the predictions of the first–Born-approximation theory and the perturbed-stationary-state theory with energy-loss, Coulomb-deflection, and relativistic corrections (ECPSSR). The first–Born-approximation theory overpredicts the measured cross sections everywhere, especially at high energies, while the ECPSSR theory tends to underpredict them, especially at low energy. This discrepancy between the measurements and the ECPSSR theory may be due in part to multiple-ionization effects which could change the fluorescence yields from the single-hole values used to convert total ionization to x-ray production cross sections in the theoretical calculations.

Absolute doubly differential electron emission yields were measured as a function of the projectile scattering angle for proton-helium collisions at incident energies of 30, 100, and 300 keV. Coincidence spectra were taken for electron emission angles of 40°, 60°, and 90° at electron energies of 10–500 eV. All investigations were performed at impact parameters small compared to the He 1$s^2$-orbital radius. The experimental data are compared to results of different theoretical models. Large deviations are found especially between the measured values and values calculated by methods based on first-order perturbation theory. These deviations are assigned to polarization effects exceeding pure binding corrections.

We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.

A class of three-dimensional integrals on spatial coordinates of the type occurring in treatments of multiphoton ionization of atoms and of other bound-free transitions is evaluated in closed form for both hydrogenic and Slater-type wave functions. The reported method of evaluation is illustrated with a number of examples, including the multiphoton ionization of hydrogen by a very intense laser field, when the ejected electrons have absorbed more photons than the minimum required to reach the continuum.

The absorption of x rays in atoms assisted by an intense laser field is considered. The general expression for the x-ray absorption cross section (${\sigma }_x$) as a function of the laser field is obtained in the intense-field regime using the Seely and Harris approximation [Phys. Rev. A 7, 1064 (1973)]. We find that in this regime, and when the two photon fields are polarized in the same direction, the cross section ${\sigma }_x$ decreases as ${\varepsilon }^{\mathrm{-}1}$, ɛ being a factor proportional to the intense-field amplitude. When the field is further increased to the limit of superintense fields, ${\sigma }_x$ varies as ${\varepsilon }^{\mathrm{-}3}$. A physical explanation for this behavior is provided.

We report measurements of photoelectron angular distributions via electric quadrupole transitions in cesium atoms using multiphoton excitation techniques. Experimental results are presented for the cases of one-photon resonant, two-photon ionization via the 6d ${\mathrm{}}^2$$D_{3/2}$ and 6d ${\mathrm{}}^2$$D_{5/2}$ electric quadrupole transitions and for one-photon resonant, three-photon ionization via the 5d ${\mathrm{}}^2$ ${\mathrm{D}}_{3/2}$ and 5d ${\mathrm{}}^2$$D_{5/2}$ transitions. The ratios of the total ionization rates for linearly and circularly polarized light have also been measured for the 6d ${\mathrm{}}^2$${\mathrm{D}}_{3/2}$ and 6d ${\mathrm{}}^2$$D_{5/2}$ states. A theoretical analysis and detailed comparison with the experimental results are given.

An analysis is given of the effect of radiative corrections on the threshold behavior of the cross section for the inelastic scattering of a light charged particle by a neutral composite system. Explicit results are obtained for a model problem where the target consists of a proton and antiproton bound under their mutual Coulomb interaction and excited to a 2p state from its 1s ground state by electron impact, but the conclusions drawn are applicable, qualitatively, to a wide range of problems. It is found that when the energy resolution Δɛ of the electron detector is small compared with the kinetic energy K’ of the electron in the final state, the more careful treatment given here, which properly accounts for the rapid variation of the cross section for scattering energies near threshold, leads to only small modifications in the standard form of the radiative correction factor δ. For sufficiently high resolution in energy of a (high-energy) incident beam, the modification could be significant if Δɛ is comparable with K’. The above considerations are applicable not only to scattering cross sections but to endpoints of the energy spectrum of the charged particle in a decay process in which only one charged particle is emitted.

The mechanisms that lead to states with three and four 3d vacancies following L-shell photoionization of metallic Ni have been investigated with synchrotron radiation. Vacancies were created in all three L subshells, in the $L_2$,3 subshells, and in the $L_3$ subshell alone, and the resultant $L_3$-$M_4$,5${\mathrm{M}}_4$,5 Auger spectrum with its satellite structure was measured and analyzed. Auger diagram and satellite energies were computed in terms of a quasiatomic screening model, semiempirical shakeup and shakeoff cross sections were employed, and branching ratios were calculated from Auger transition theory with Hartree-Fock wave functions. Four channels leading to the four–3d-hole final state and three channels leading to the three-hole state, including Auger cascades and shake processes, were clearly identified and their respective roles established, convincingly verifying a model proposed by Mårtensson et al.

The emission anisotropy of selected K molecular-orbital (MO) transitions has been measured by exploiting the cascade relationship between MO x rays emitted in transitions from the (2pσ,${\pi }_x$) MO’s into the 1sσ MO and the characteristic K x ray which follows from the filling of the ensuing vacancy in the projectile or target atoms after their separation. For 40-MeV Ni+Ni collisions the anisotropy is found to exhibit a photon-energy dependence similar to the singles MO x-ray anisotropy but with a striking tenfold increase in overall magnitude. The large positive anisotropy observed for the MO coincidence spectrum, in agreement with theory, thus provides one of the more direct and convincing illustrations of the role played by the MO mechanism in slow ion-atom collisions.

Pion-capture ratios have been measured for fluorides, hydroxides, and tetrahydroborates of alkali metals. The ratios for hydroxides agree with those for fluorides, when OH is taken as a group. However, though it is expected that tetrahydroborates have similar ionic bonding as fluorides and hydroxides, capture ratios of the alkali metal to the ${\mathrm{BH}}_4$ group are enhanced when compared with those of the alkali metal to the F or OH groups. Obtained capture ratios are analyzed with a modified mesomolecular model and the effect of chemical bonding on the capture ratios is discussed.

Vibrationally resolved photoelectron angular distributions have been measured for photoionization of ${\mathrm{H}}_2$ over the range 17 eV≤hν≤39 eV using independent instrumentation at two synchro- tron radiation facilities. The present data greatly extend and add vibrational resolution to earlier variable-wavelength measurements. The average magnitude of the asymmetry parameter continues to lie lower than the best independent-electron calculations. Broad structure is observed for the first time, possibly indicating the effects of channel interaction with dissociative, doubly excited states of ${\mathrm{H}}_2$. Neither the average magnitude nor the gross wavelength-dependent structure vary strongly with the final vibrational channel.

Early results of Agarwal and Jha [Z. Phys. B 35, 391 (1979)] are used to examine the question of quantum jumps in a Raman (Λ) system driven by two coherent fields. We discuss both short-time (${\gamma }_1$t≲1) and long-time (${\gamma }_2$t≊1) behavior of the intensity correlations assuming that the Stokes transition is very weak, ${\gamma }_2$≪${\gamma }_1$. We calculate the counting statistics of the dark periods using the higher-order intensity correlations. The results differ from those obtained using arguments based on population trapping which predict only a very rare ‘‘jump’’ event. The intermittence in fluorescence produced by a coherently driven Λ system is interpreted in terms of an equivalent two-state Markov process.

An analytical study of a dye-laser model which includes quantum white noise and nonwhite pump fluctuations is presented. The extension of an earlier approximation to include quantum noise gives a unified picture of the statistical properties of the laser light for negative pump parameters. These include intensity fluctuations and discontinuous changes of the most probable intensity. An alternative approximation (obtained within the same scheme) is discussed for situations above threshold.

Derbenev and Kondratenko calculated the equilibrium degree of radiative electron polarization in 1973 (Ya. S. Derbenev and A. M. Kondratenko, Zh. Eksp. Teor. Fiz. 64, 1918 (1973) [Sov. Phys.—JETP 37, 968 (1973)]), and more recently Bell and Leinaas did likewise for a more limited model, but following a different approach [J. S. Bell and J. M. Leinaas, Nucl. Phys. B 284, 488 (1987)]. They report a different resonance structure. In this paper the notations, formalisms, and viewpoints of the two sets of authors are compared, and the connection between their treatments is explained. The formula for the polarization, taking into account vertical fluctuations, is derived following the Derbenev-Kondratenko approach and is generalized to strong-focusing machines. It is also combined with the Derbenev-Kondratenko result into a unified formula.

Using accurate and explicitly electron-correlated wave functions, the dynamic hyperpolarizability tensor (γ) components for helium have been calculated. These quantities are relevant to nonlinear optical processes such as the Kerr effect, degenerate four-wave mixing, electric-field-induced second-harmonic generation and third-harmonic generation. For second-harmonic generation at λ=4880 Å the ratio ${\gamma }_{\mathrm{zzzz}}$/${\gamma }_{\mathrm{xxzz}}$ is 2.948, which may be compared with the experimental value of 2.949; we believe this to be indicative of our accuracy in general.