The electron-correlation energies, calculated with the wave functions constrained to the Hartree-Fock density, are computed for the helium series and are compared with the exact (unconstrained) correlation energies. Imposition of the density constraints increases the energies by a surprisingly small amount. Both the l=0 (s) and l=1 (p) limit differences between the constrained and exact energies are demonstrated to scale like the reciprocal of the square of the atomic numbers. The computational results are rationalized by introducing rigorous definitions of the dynamical and nondynamical correlation energies.

A number of resonances, shape as well as Feshbach type, have been observed in atomic systems. It is expected that similar types of resonances exist in muonic systems. Froelich and Szalewicz [Phys. Lett. A 129, 321 (1988)] carried out a calculation for tdμ and obtained two resonances, for J=0 and 1, just above the dμ threshold. Our calculation, carried out with large basis sets and different sets of nonlinear parameters, using the complex-rotation method, shows the existence of Feshbach-type resonances below the n=2 threshold of tμ and dμ. Positions of these resonances are in good agreement with the results of Hara and Ishihara [Phys. Rev. A 40, 4232 (1989)]. The widths of these resonances are calculated.

Positronium wave functions that are approximate solutions to the Breit-Coulomb equation are constructed for the 1 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$, the (L+1) ${}_{}{}^3{}_{}{}^{}$${\mathit{L}}_{\mathit{J}}$, and the non-S ${}_{}{}^1{}_{}{}^{}\mathrm{L}_{\mathrm{L}}^{}{}_{}{}^{}$ states. The energies of these wave functions are accurate up through O(${\mathrm{\alpha }}^4$), giving the correct Coulomb part of the positronium energy levels to this order. Using only first-order perturbation theory, the energy eigenvalues of the Breit-Coulomb equation are calculated to O(${\mathrm{\alpha }}^6$) for these quantum states.

A quantum-fluid density-functional theory (QF DFT) is proposed, yielding a time-dependent (TD) generalized nonlinear Schrödinger equation (GNLSE) as the equation of motion (EOM) for dealing with proton–helium-atom collisions from ‘‘start’’ to ‘‘finish.’’ The EOM contains the Weizsäcker term as the kinetic-energy functional, apart from local exchange and correlation functionals. The GNLSE is numerically solved in cylindrical polar coordinates by a leapfrog-type finite-difference algorithm. Various TD quantities such as difference density (DD), induced-dipole moment (IDM), dipole polarizability tensor component, reaction probability, etc., have been studied to obtain physical insights into the mechanism of the TD collision process. In particular, the DD and the oscillating IDM permit a natural partitioning of the p-He collision process into approach, encounter, and departure regimes. The TD DD profiles reveal that, as a result of the interaction, pσ densities mix substantially into the 1s density of the He atom. Critical comments are made on the usefulness of the QF DFT approach for understanding TD processes.

A generalization of the standard effective Hamiltonian theory is presented, based on the breaking of the one-to-one correspondence between the model and the target spaces. In this way the target space can be smaller than the model space, and problems connected to the presence of intruder states can be solved. An application to the dimer of lithium is given. Moreover, it is shown how the formalism can be translated into an iterative approach, and test computations are presented.

Based on the correspondence principle, a simple semiclassical derivation of a universal formula for the radiative mean lifetime τ(n,l) of hydrogenlike states is presented. (The possibilities of stimulated emission and collisional deexcitation are neglected.) Within the nonrelativistic dipole approximation the mean lifetime for an electron in a state characterized by quantum numbers n and l in the field of a nucleus of charge Z is given by τ(n,l)≊${\mathrm{\tau }}_0$${\mathit{n}}^3$l(l+1)/${\mathit{Z}}^4$, where ${\mathrm{\tau }}_0$= 3ħ/(2${\mathrm{\alpha }}^5$μ${\mathit{c}}^2$)≊93.42×${10}^{\mathrm{-}12}$ s and μ is the reduced mass. The formula is accurate to at least 6% for the lowest states and to a much higher degree of accuracy for highly excited states. The semiclassical result is expected to be valid to leading order in n and l. However, the very simple derivation yields results of an accuracy comparable to several approximate quantum-mechanical and semiclassical results that have been published. The approach is based primarily upon a treatment of the rate of loss of angular momentum, not of energy. A clear physical interpretation of some aspects of the radiative decay process, which is somewhat obscure in the quantum evaluation, emerges naturally from the angular momentum approach.

Differential and integrated elastic, integrated total cross sections as well as various polarization parameters–the spin polarization P and the parameters T and U describing the change in the polarization vector during scattering–for the scattering of electrons and positrons from argon in the energy range of 3–300 eV are calculated using the relativistic Dirac equation. The real part of the projectile-target interaction is represented by a sum of model potentials. The phase shifts for large angular momenta ħl are calculated using the Born approximation. The relativistic calculations for the differential and integrated elastic cross sections obtained using the pure real potential show almost no improvement over those obtained nonrelativistically for positron scattering from argon while similar calculations show some effects, except at low energies (≤5 eV) where relativistic terms are sensitive to the form of potentials used, on the values of the differential cross sections for electron scattering from argon. The polarization parameter P for electron scattering is found to be in good agreement with various calculated and measured values. A few different models of the absorption potential for the inelastic processes are used to calculate the integrated inelastic and the integrated total cross sections for positron and electron scattering from argon. It is noticed that even though the integrated elastic and the integrated total cross sections for the scattering of positrons and electrons calculated using some complex model potential agree well with the corresponding measured values, the differential cross section curves using the same model potentials can differ considerably from each other as well as from the experimental values.

Photoionization cross sections for the 4d, 4f, 5s, 5p, and 6s electrons and angular-distribution asymmetry parameters for the 4d, 4f, and 5p electrons of atomic europium at photon energies near the 4${\mathit{d}}^{10}$4${\mathit{f}}^7$→4${\mathit{d}}^9$4${\mathit{f}}^8$ resonance have been calculated by use of many-body perturbation theory. Interactions among ionization channels were included in the calculation, and the results are compared with experiments and other calculations.

An ${\mathit{L}}^2$ approach to the coupled-channel optical method is studied. The investigation is done for electron-hydrogen elastic scattering at projectile energies of 30, 50, 100, and 200 eV. Weak-coupling, free-particle Green’s function, and no exchange in Q space are approximations used to calculate the polarization potential. This model problem is solved exactly using actual hydrogen discrete and continuum functions. The convergence of an ${\mathit{L}}^2$ approach with the Laguerre basis to the exact result is investigated. It is found that a basis of ten Laguerre functions is sufficient for convergence of approximately 5% in the polarization potential matrix elements, and 2% in the differential cross sections for nonlarge angles. The convergence is faster for smaller energies. In general, the convergence to the exact result is slow.

An optical-optical double resonance procedure is used to compare the relative populations of e/f spin components of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$(v=7) rotational manifold resulting from the collision-induced electronic transitions in ${\mathrm{N}}_2^{+}$ for the cases of large and small energy gaps. Rotational levels of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{ui}}^{}{}_{}{}^{}$(v=3 or 4) vibrational state of ${\mathrm{N}}_2^{+}$ are selectively populated with a pump laser. Transitions to rotational levels of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$(v=7) level due to collisions with bath gas helium atoms at room temperature are monitored by scanning the lines of the B-X(5,7) band with a second, probe laser. The relaxation pathways A(v=3)→X(v=7) and A(v=4)→X(v=7) traverse energy gaps (ΔE) of ∼0 and ∼1760 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively. Perturbation of the rotational levels of the ${\mathit{B}}^2$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$(v=5) state by the ${\mathit{A}}^2$${\mathrm{\Pi }}_{\mathrm{u}1/2\mathrm{}}$(v=17) manifold allows for the e/f, spin-rotation splitting of the lines of the B-X(5,7) probe laser scan to be resolved. The effects of these perturbations on the relative intensities of the B-X(5,7) lines have been taken into account. The intensity patterns for collision-induced transitions across the two widely different energy gaps are nearly identical, indicating that the propensities for this case have an insignificant energy-gap dependence. These detailed propensities from selectively excited rotational levels of the A(v=4 or 3) level to the individual, nearly degenerate rotational levels of the X(v=7) manifold are compared with theoretical models for inelastic scattering between ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }$ and ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }$ electronic states.

Direct radiative recombination (RR) cross sections ${\mathrm{\sigma }}^{\mathrm{RR}}$ and rate coefficients ${\mathrm{\alpha }}^{\mathrm{RR}}$ are presented for all ions using the scaling property of the cross section in the parameter η=${\mathit{Z}}_{\mathrm{eff}}$/(${\mathit{ka}}_0$). The RR cross section is defined simply in terms of two parameters, η and the number of electrons N in the target ion. The RR rate coefficient ${\mathrm{\alpha }}^{\mathrm{RR}}$/${\mathit{Z}}_{\mathrm{eff}}$ in turn depends on two parameters, the scaled temperature (FTHETA=${\mathit{k}}_{\mathit{B}}$T/${\mathit{Z}}_{\mathrm{eff}}^2$) and N. An empirical formula for the effective charge ${\mathit{Z}}_{\mathrm{eff}}$ is constructed, which is weakly dependent on the electron energy ${\mathit{k}}^2$. The cross-section values can also be used in analyzing high-energy ion-atom collisions with radiative electron capture.

As shown many years ago by Bloch and Nordsieck [Phys. Rev. 52, 54 (1937)] and Nordsieck [Phys. Rev. 52, 59 (1937)], the cross section for scattering with the emission of an arbitrary number of soft photons is finite and can be expressed in terms of the cross section for scattering in the absence of the radiation field. The model used by Bloch and Nordsieck included only soft-photon modes of the field, with maximum frequency ${\mathrm{\omega }}_{\mathit{s}}$. They argued that corrections to their sum rule would be expressed in terms of two small parameters, ${\mathit{r}}_0$${\mathrm{\omega }}_{\mathit{s}}$/c and ħ${\mathrm{\omega }}_{\mathit{s}}$/ν, where ${\mathit{r}}_0$ is the classical electron radius and ν is the scattering energy. Corrections of first order were obtained previously by the author [Phys. Rev. A 21, 1939 (1980)], in the context of a nonrelativistic formulation of the scattering problem. Here all corrections of second order are derived. As in the earlier versions, the corrected cross section for scattering in the radiation field, summed over final states of the field, is determined from a knowledge of the field-free cross section. Use of the unitarity property (the optical theorem) is found to be a simplifying technical device for this calculation, as indicated by the cancellation of divergences in the scattering amplitude in the forward direction. It is shown that in the dipole approximation the term in the electron-field interaction that is quadratic in the vector potential, while contributing to an energy-level shift, has no effect, to second order, on the final form of the sum rule.

In a new extension of the Dirac-Fock method, calculations have been performed on the 80 electrons of mercury (in 22 nlj orbitals) plus one continuum electron of negative energy less than -${\mathit{mc}}^2$. The asymptotic form of the numerical wave function of the negative-energy electron determines the phase shifts for the elastic scattering of positrons on Hg. The self-consistent-field calculations include the usual exchange interaction between electrons. The exchange between the bound Hg electrons and the negative-energy continuum electron represents the positron-electron annihilation-creation process. Such effects are usually computed in quantum electrodynamics to some order of approximation in a perturbation expansion. We believe ours is the first Dirac-Fock calculation of this effect, but we find its influence on the elastic positron scattering to be negligible.

A variational approach to the problem of scattering in a low-frequency laser field is adopted, with trial functions chosen to be of the type originally introduced by Kroll and Watson [Phys. Rev. A 8, 804 (1973)], who used them nonvariationally. The variational calculation leads to a low-frequency approximation that includes higher-order correction terms of a relatively simple form. This provides the basis for an analysis of the accuracy of the approximation as the strength of the external field varies over a wide range of values. The cross-section sum rule is shown, for the case of a linearly polarized monochromatic field of moderate intensity, to be more accurate than had previously been realized by virtue of the cancellation of higher-order correction terms in the transition amplitude. The approach is shown to be applicable to elastic and inelastic electron-atom scattering in a multimode laser field with arbitrary polarization properties; it represents a natural generalization of the standard Kohn-type variational procedure frequently employed for field-free scattering problems, reducing to it in the absence of the field. The dressing of the target by the field, an effect which is known to have a significant influence on the scattering cross section in certain circumstances, is not accounted for in the construction of the trial function, but is properly included as part of the variational correction.

The response of relativistic ${\mathrm{H}}^{\mathrm{-}}$ ions to thin carbon foils was investigated for beam energies ranging from 226 to 800 MeV. For the foil thicknesses studied, ranging from 15 to 300 μg/${\mathrm{cm}}^2$, an appreciable fraction of the ${\mathrm{H}}^{\mathrm{-}}$ beam survives intact, some ${\mathrm{H}}^{\mathrm{-}}$ ions are stripped down to protons, and the remainder is distributed over the states of ${\mathrm{H}}^0$. This experiment is different from the low-energy studies in that the projectile velocity is comparable to the speed of light, leading to an interaction time typically less than a femtosecond. The present results challenge the theoretical understanding of the interaction mechanisms. An electron spectrometer was used to selectively field ionize the Rydberg states 9<n<17 at beam energies of 581 and 800 MeV. The yield of low-lying states was measured by Doppler tuning a Nd:YAG (where YAG represents yttrium aluminum garnet) laser to excite transitions to a Rydberg state that was then field ionized and detected. Data are presented for production of n=2,3 at 226 MeV, n=2,3 at 500 MeV, n=2,3,4 at 581 MeV, n=2 at 716 MeV, and n=1,2,3,4,5 at 800 MeV. A simple model is developed to fit the yield of each state as a function of foil thickness. Although the simple model is successful in predicting the general features, the data are suggestive of a more complex structure, in the yield of a state as a function of the foil thickness. The optimum thickness to produce a given state increases with the principal quantum number of the state, suggesting an excitation process that is at least partially stepwise. The results of a Monte Carlo simulation are compared with the experimental data to estimate the distribution of the excited states coming out of a foil.

Measurements of velocity-changing collision (VCC) kernels are obtained using velocity-selective optical pumping. This is the first measurement of the shape of an elastic VCC kernel over the full thermal range of velocity changes. Since ground-state collisions are studied (5${\mathit{s}}_{1/2}$ Rb and He, Ne, Ar, Kr, or Xe), very low buffer-gas pressures can be used, and therefore pressure broadening (dephasing collisions) does not obscure the effects of VCC’s. The data are deconvolved to eliminate the effects of the natural linewidth and are then extrapolated with respect to buffer-gas pressure to determine the single-collision limit. For small initial velocities, the measured kernels are consistent with a hard-sphere model for large velocity changes, but differ significantly for small velocity changes. The measured VCC kernels for large initial velocities and large velocity changes do not exhibit this agreement with the hard-sphere kernel. This implies that information about the inter- atomic potential can be obtained from a measurement of VCC kernels. We also show the inadequacy of the much-used Keilson-Storer kernel [J. Appl. Math. 10, 243 (1952)].

The closed analytic form for bound-state transitions due to projectile impact is found in the intermediate representation. The coordinate is obtained by evaluating the remaining two integrals in the general multicenter integral derived previously [J. C. Straton, Phys. Rev. A 41, 71 (1990)]. Evaluating the remaining time integral depends upon relating a sum of modified Bessel functions of the second kind KN+1/2(z) to a simple polynomial in 1/z. The results of Van Den Bos and De Heer [Physica 34, 333 (1967)] are shown to be missing a phase factor of (-i)(l′+l).

We have formulated the quantum inverse problem for an alternative version of the nonlinear Schrödinger equation (NLS), which is a variant of the derivative NLS (DNLS) equation. While the DNLS equation is nonultralocal and cannot be formulated as a problem of the quantum inverse scattering method, our equation is ultralocal, and hence it is possible to construct the quantum R matrix and the commutation rules for the scattering data. Next we have constructed the algebraic Bethe ansatz, from which the eigenvalue equation for the excited states is derived. This eigenvalue equation admits stringlike configurations, and the density of states corresponding to real and complex eigenvalues is explicitly derived in the thermodynamic limit.

Electron-impact double ionization of helium is investigated theoretically for the case of high incident energies (5–10 keV). An ab initio calculation is proposed, which includes almost full correlation in the initial state and partial correlations in the final state. The results of this model are compared with those given by other theories in the framework of the wave-function approach. We show that the correlations in the final state must be taken into account for the evaluation of the angular distributions.

Electron energy spectra and total electron yields are studied to provide information on the neutralization of 24-keV ${\mathrm{N}}^{\mathit{q}+}$ ions (q=2,4,6) incident at grazing angles on a Cu(100) surface. A computer simulation of the neutralization is presented that assumes resonant neutralization of the ions leading to highly excited ‘‘hollow’’ atoms. Deexcitation of these atoms is assumed to take place by purely intra-atomic Auger transitions. The results of this simulation are not in agreement with our experimental observations. A modified simulation, assuming again resonant neutralization of the ions followed by faster deexcitation processes, and, in addition, fast Auger deexcitation directly into the L shell, shows a much better agreement with the experimental observations.