Electrons can have a given smooth density distribution $\rho \mathrm{}\left(r\right),$ even if their Coulomb interaction is scaled to infinity. This strong-interaction limit of density-functional theory provides essential information on the correlation energy of real electron systems. The simple concept of strictly correlated electrons (SCE) is analyzed here as a model for that limit. SCE is solved exactly for any one-dimensional (1D) N-electron density and, in particular, for any 3D spherical two-electron system, such as the helium atom. Both the SCE interaction energy and the SCE external potential, which are obtained here as density functionals, obey all the relations known for the corresponding quantities in the unknown true strong-interaction limit. At large but finite interaction, the electrons are still strongly correlated, performing zero-point oscillations about the SCE limit.

The theory of the contracted Schrödinger equation (CSE) [D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998)] is connected with traditional methods of electronic structure including configuration-interaction (CI) and coupled-cluster (CC) theory. We derive a transition contracted Schrödinger equation (TCSE) which depends on the wave function $\psi$ as well as another N-particle function $\chi$ through the two-, three-, and four-particle reduced transition matrices (RTMs). By reconstructing the 3 and 4 RTMs approximately from the 2-RTM, the indeterminacy of the equation may be removed. The choice of the reconstruction and the function $\chi$ determines whether one obtains the CI, CC, or CSE theory. Through cumulant theory and Grassmann algebra we derive reconstruction formulas for the 3- and 4-RTMs which generalize both the reduced density matrix (RDM) cumulant expansions as well as the exponential ansatz for the CC wave function. This produces a fresh approach to CC theory through RTMs. Two theoretical differences between the CC and the CSE theories are established for energetically nondegenerate states: (i) while the CSE has a single exact solution when the 3- and 4-RDMs are N-representable, the CC equations with N-representable 3- and 4-RTMs have a family of solutions. Thus, N-representability conditions offer a medium for improving the CSE solution but not the CC solution, and (ii) while the 2-RDM for an electronic Hamiltonian reconstructs to unique N-representable 3- and 4-RDMs, the 2-RTM builds to a family of N-representable 3- and 4-RTMs. Hence, renormalized reconstructions beyond the cumulant expansion may be developed for the 2-RDM but not for the 2-RTM without explicit use of the Hamiltonian. In the applications we implement our recently developed reconstruction formula for the 3-RDM which extends beyond the cumulant approximation. Calculations compare the 3-RDM and 3-RTM reconstructions for the molecules LiH, ${\mathrm{BeH}}_2,$ ${\mathrm{BH}}_3,$ and ${\mathrm{H}}_2\mathrm{O}$ as well as for systems with more general two-particle interactions. The TCSE offers a unified approach to electronic structure.

In this paper we discuss the hyperfine structure and isotope shift of the xenon atom. The study was performed using a semiconductor diode laser mounted in an extended-cavity configuration and emitting in the near-infrared range of spectrum. Doppler-free spectra of four transitions between 820 and 830 nm were obtained by using either a saturation spectroscopy technique in a cell or a laser-induced fluorescence technique on a collimated atomic metastable beam. The hyperfine coupling constants of ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$ were determined for the levels ${1s}_5,$ ${1s}_4,$ ${1s}_2,$ ${2p}_2,$ ${2p}_4,$ and ${2p}_6$ (Paschen notation). Moreover, a systematic study of the isotope shift was performed for the ${1s}_3\to {2p}_4$ $(\lambda =820.8\mathrm{}\mathrm{nm})$ and ${1s}_5\to {2p}_6$ (λ=823.3 nm) transitions for which all the stable isotopes ${}^{128–131}\mathrm{Xe},$ ${}^{132}\mathrm{Xe},$ ${}^{134}\mathrm{Xe},$ and ${}^{136}\mathrm{Xe}$ were fully resolved.

Threshold scattering properties of ${}^{39}\mathrm{K}$ atoms are extracted from a line-shape analysis of photoassociation data. Specifically, we consider the rovibrational levels ${(v}^{\prime }=0\mathrm{}–6)$ populated in the photoassociation process $\mathrm{K}\mathrm{}\left(4S\right)+\mathrm{K}\mathrm{}\left(4S\right)+ħ\overrightarrow{\omega }{\mathrm{K}}_2^{*}\left[0_g^{-}{(v}^{\prime }{,J}^{\prime }\right)].$ The measured spectra exhibit several general trends, including large $J^{\prime }=2\mathrm{}$ linewidths, large relative $J^{\prime }=4\mathrm{}$ peak intensities, and odd rotational lines which are weak or missing. The even $J^{\prime }$ features signal the presence of a d-wave shape resonance in the ground-state collisions. The combination of spectral features allows us to place the following limits on the ground-state singlet and triplet scattering lengths, $a_s{=140\mathrm{}}_{-9}^{+6\mathrm{}}$ a.u. and $a_t=-17-{0.045(C}_6-C_6)\pm 25$ a.u., $C_6=3800\mathrm{}$ a.u.

We report threshold scattering properties for ${}^{39}\mathrm{K}\mathrm{}(f=1\mathrm{})\mathrm{}$ atoms obtained from analysis of experimental photoassociation spectra of the purely long-range ${}^{39}{\mathrm{K}}_2\hspace{0.5em}{1}_u$ state. The existence of hyperfine structure in the excited ${\mathrm{K}}_2\hspace{0.5em}{1}_u$ state and a knowledge of the Hamiltonian structure for two colliding ground state alkali atoms enables us to obtain information on the sign and magnitudes of certain scattering lengths for ground state collisions. Analysis of the experimental photoassociation line shapes shows that the ${}^{39}\mathrm{K}$ scattering lengths are between $-3.2$ and $+0.8\mathrm{}\mathrm{nm}(-{60a}_0$ and ${+15a}_0,$ where ${1a}_0=1\mathrm{}\mathrm{a}.\mathrm{u}.\mathrm{}=0.052\mathrm{}9177\mathrm{nm})$ for the $a{}^3{\Sigma }_u^{+}$ molecular state, between +4.8 and +12 nm ${(+90a}_0$ and ${+230a}_0)$ for the $X^1{\Sigma }_g^{+}$ state, and between $-7.9$ and $+1.1\mathrm{}\mathrm{nm}\hspace{0.5em}(-{150a}_0$ and ${+20a}_0)$ for collisions of two $f=1,m=-1$ atoms.

The parity-odd perturbation operator for the inelastic electron-nucleon scattering by weak neutral currents (exchange of virtual $Z^0$ bosons) has been implemented into a fully relativistic four-component Dirac-Hartree-Fock scheme. Dirac-Hartree-Fock electronic structure calculations on ${\mathrm{H}}_2{\mathrm{O}}_2,$ ${\mathrm{H}}_2{\mathrm{S}}_2,$ ${\mathrm{H}}_2{\mathrm{Se}}_2,$ ${\mathrm{H}}_2{\mathrm{Te}}_2,$ and ${\mathrm{H}}_2{\mathrm{Po}}_2$ provides a demonstration of the higher than $Z^5$ scaling of the parity-violating energy shift $(Z$ is the nuclear charge) in chiral molecules. To our knowledge, the calculations for ${\mathrm{H}}_2{\mathrm{Te}}_2$ and ${\mathrm{H}}_2{\mathrm{Po}}_2$ are the first for molecules containing heavy elements from period 5 or 6 of the Periodic Table, and the parity-violating energy shifts are some of the highest reported in any ab initio study. It has been shown that special care is needed in the basis set expansion of the wave function because of the coupling between the large and small components of the Dirac wave function through the ${\gamma }^5$ matrix. Estimates of the remaining errors in the calculations have been given. A comparison with the calculated parity-violating energy shift of ${\mathrm{H}}_2\mathrm{TeO}$ have confirmed the importance of the single-center theorem, which states that the parity-violating energy shift is suppressed in molecules containing only a single heavy atomic center. Due to the close correspondence between parity-violating energy shifts and observable parity-odd properties, our results have important consequences for the current search for an experimental confirmation of parity-odd effects in molecular physics: (i) The experiments should be performed on molecules containing heavy (period 5 or 6) elements. (ii) Molecules with more than one heavy atomic center will be extremely favorable due to the single-center theorem.

Coupled-state calculations are presented for $\mathrm{Ps}\mathrm{}\left(1s\right)+\mathrm{He}{(1\mathrm{}}^{1}S)$ scattering in the energy range 0–40 eV. Up to 22 Ps states are employed but only one He state is retained. Pseudostates are used to represent the Ps continuum. First Born estimates of cross sections in which the He is excited or ionized are found to be negligible in the chosen energy range. Calculation shows that ionization of the Ps is the main process at the higher energies. Comparison is made with available experimental measurements of the total cross section and with other theories. At low energies there is not only serious conflict between different experiments but also between the different theoretical approximations. In particular, the calculations of Biswas and Adhikari [Phys. Rev. A 59, 363 (1999)] and Peach (unpublished) predict a much smaller elastic cross section at low energies than that obtained in the present work. The relative merits of the different approximations are discussed.

In this work, a bound-state formalism appropriate for the study of positronium is presented. The formalism is based on a three-dimensional “quasipotential” equation derived from the Bethe-Salpeter equation. A reference kernel is proposed that contains the main physics of the nonrelativistic Coulomb bound state, and for which the quasipotential equation can be solved exactly. A perturbation theory for energy levels and decay rates based on this reference problem is described.

Removal energies and hyperfine constants of the lowest four $ns,$ ${\mathrm{np}}_{1/2},$ and ${\mathrm{np}}_{3/2}$ states in Na, K, Rb, and Cs are calculated; removal energies of the $n=7\mathrm{}–10$ states and hyperfine constants of the $n=7\mathrm{}$ and 8 states in Fr are also calculated. The calculations are based on the relativistic single-double (SD) approximation in which single and double excitations of Dirac-Hartree-Fock wave functions are included to all orders in perturbation theory. Using SD wave functions, accurate values of removal energies, electric-dipole matrix elements, and static polarizabilities are obtained; however, SD wave functions give poor values of the magnetic-dipole hyperfine constants for heavy atoms. To obtain accurate values of the hyperfine constants for heavy atoms, we include triple excitations partially in the wave functions. The present calculations provide the basis for reevaluating parity nonconserving amplitudes in Cs and Fr.

The C $1s$ x-ray absorption spectrum of ${\mathrm{CF}}_4$ molecules is theoretically investigated by calculating the line shape quantum mechanically based upon a vibronic model. It is found that the main peak with a broad width is attributed to the transition of the C $1s$ core electron to the antibonding valence orbitals which are coupled with the $\mathrm{C}—\mathrm{F}$ bond-stretching modes through the Jahn-Teller and the quasi-Jahn-Teller interactions. It is also clarified that the sharp asymmetric absorption line at the higher-energy side of the main band comes from the transition to the Rydberg states, where the interference effect between the Rydberg states and the vibronic state of the antibonding molecular orbitals leads to the asymmetric structure.

Experimental and theoretical lifetimes ${\tau }_{v^{\prime }{N}^{\prime }}$ for $e{}^3{\Sigma }_u^{+}$ and $d{}^3{\Pi }_u^{-}$ states of molecular hydrogen and deuterium are presented in a wide range of vibrational $v^{\prime }$ and rotational $N^{\prime }$ quantum numbers. Lifetimes have been measured by a delayed coincidence method following electron-impact excitation from the ground state. The cascade effects on the lifetimes measured were estimated to be negligible through a detailed analysis. Predissociative rates were estimated by the Fermi golden rule based on adiabatic rovibronic wave functions and radial coupling matrix elements $B\left(R\right)\mathrm{}$ for the $e{}^3{\Sigma }_u^{+}\sim b{}^3{\Sigma }_u^{+}$ and $d{}^3{\Pi }_u^{-}\sim c{}^3{\Pi }_u^{-}$ pairs of interacting states. The radiative lifetimes of both excited states were evaluated by the theoretical $e{}^3{\Sigma }_u^{+}-a{}^3{\Sigma }_g^{+}$ and $d{}^3{\Pi }_u–a{}^3{\Sigma }_g^{+}$ transition dipole moment functions $d\left(R\right)\mathrm{}$ and adiabatic rovibronic wave functions of the states involved. The electronic matrix elements $B\left(R\right)\mathrm{}$ and $d\left(R\right)\mathrm{}$ were obtained by direct ab initio calculations as well as within the framework of quantum defect theory. The ab initio $B\left(R\right)\mathrm{}$ functions were calculated by the finite-difference method and by the analytical Sidis formula, which were based on the full configuration-interaction electronic wave functions. At small and medium internuclear distances the quantum defect matrix elements agree well with their ab initio counterparts. The predissociative rates for both $e{}^3{\Sigma }_u^{+}{(v}^{\prime }>~0)$ and $d{}^3{\Pi }_u^{-}{(v}^{\prime }>~4)$ states of hydrogen were found to increase sharply as the $v^{\prime }$ value of the predissociated level increases, and become compatible with the radiative decay rate. The predissociation effect in the deuterium was negligible for both states studied; hence their experimental lifetimes correspond to the radiative decay channel only. A sum of the theoretical radiative and predissociative rates was in good agreement with the experimental results for the $e{}^3{\Sigma }_u^{+}$ state but slightly overestimated for the $d{}^3{\Pi }_u^{-}$ state. Reasons for the remaining discrepancies are discussed and suggestions for further improvements are given.

We have investigated electron capture and excitation in collisions of ${\mathrm{Si}}^{2+}$ ions with He atoms in the collision energy range from 0.02–6 keV/u based on a molecular representation. Molecular states are determined by using the multireference single- and double-excitation configuration-interaction method. We have considered electron capture and excitation both by the ground singlet and metastable triplet ${\mathrm{Si}}^{2+}$ ions. The capture cross section by the ground singlet ${\mathrm{Si}}^{2+}$ ion increases with increasing collision energy and reaches a value of $\sim 1.5\times {10}^{-16}{\mathrm{cm}}^2,$ while that by the metastable triplet ion is found to be large with a magnitude of $4\times {10}^{-16}{\mathrm{cm}}^2$ at the highest energy studied. Weak but conspicuous oscillatory structures are found for both cases, which are due to multichannel interference. The present rate coefficient for the ground singlet ${\mathrm{Si}}^{2+}$ ion impact is found to be much smaller than those of the $[{\mathrm{Si}}^{4+}+\mathrm{H}\mathrm{e}]$ system studied earlier.

The relativistic multichannel theory has been applied to calculations of cross sections of dielectronic recombination on ${\mathrm{He}}^{+}.$ A first-order approximation is adopted for the radiative process. A correction based on isolated resonance approximation is used for the very narrow resonances among the ${2lnl}^{\prime }$ states to include the radiation width. Twelve partial cross sections are calculated for both the ${2lnl}^{\prime }$ and ${3lnl}^{\prime }$ resonance states with $n<~5.$ The convolved cross sections for the $n<~3$ states are in good agreement with those of the observations. A quantitative discrepancy for the $n=4\mathrm{}$ and $n=5\mathrm{}$ states may be attributed to the l dependence of the field ionization and the radiative decay during the time of flight.

We performed both single- and coupled-channel scattering calculations of the photoionization of HCN at a photon energy range of 40–1000 eV. Based upon the present results, we predict that HCN is a system for which the inner-valence photoionization is characterized by a complete breakdown of the quasiparticle picture of photoionization. We find that there is no inner valence main line and that the intensity from photoionization from the inner valence 3σ orbital is split into two prominent satellites and two weaker satellites. These four satellites occur at binding energies of approximately 27.0, 29.5, 31.0, and 33.0 eV, and are almost solely of inner valence origin. We identify these satellites as being of inner-valence origin as a consequence of the theoretically predicted high-energy convergence of the photoionization cross-section rations to the ratio of corresponding spectroscopic intensity factors. Additionally, we find that there is one mixed provenance satellite that occurs on the shoulder of the highest binding energy $\left(4\mathrm{}{\sigma }^{-1}\right)$ line at 22.5 eV, i.e., lower than the expected energy range for satellites. The existence of this satellite is another result of the breakdown of the quasiparticle picture. On a phenomenological basis, all four of the inner-valence-derived satellites appear to be dynamically correlated shake-up states.

The outgoing scattering state describing two electrons in the continuum of a Coulomb charge is investigated. Boundary, simple, and double conditions are used to construct ab initio wave functions. Simple conditions describe the limits when the Coulomb charges are switched off, and double conditions take into account the cases when two out of three particles are close and have low relative velocity. A base to expand the double continuum—here called the $\Lambda$ base—is introduced. All the components of the three-body wave function in this base have the appropriate Coulomb conditions and are versatile enough to build up simple as well as double conditions.

Relative differential cross sections, at $0°,$ for electron-impact excitation of the $E{}^3{\Sigma }_g^{+}$ state of the nitrogen molecule have been measured in the near-threshold energy region. A high-resolution crossed-beam double trochoidal electron spectrometer is used and the cross section is measured directly, by inelastically scattered electrons detection. Measurements are placed on the absolute scale by simultaneous measurement of this process and vibrational excitation of the $v=8\mathrm{}$ level of the ground state of ${\mathrm{N}}_2,$ via the ${}^2{\Pi }_g$ resonance. Integral cross sections are obtained by using relative angular distributions from previous measurements, for energies of 11.94 and 12.14 eV. Obtained results are compared with other available data.

Using a classical method, cross sections in $A^{q+}+(\mathrm{H},{\mathrm{H}}_2)\hspace{0.5em}(q=1,\dots ,8)$ collisions are obtained for impact energy ranges $9\hspace{0.5em}{\mathrm{keV}\mathrm{}\mathrm{amu}}^{-1}–6.4\hspace{0.5em}{\mathrm{MeV}\mathrm{}\mathrm{amu}}^{-1}$ (ionization), $–600\hspace{0.5em}{\mathrm{KeV}\mathrm{}\mathrm{amu}}^{-1}$ (electron capture). For bare ion impact on H, comparison to experiment and to the results of accurate semiclassical calculations shows that total and partial cross sections, as well as transition probabilities, obtained with the classical trajectory Monte Carlo approach, are more accurate than usually assumed. From the characteristics of the mechanisms, we are led to use our data as estimates for the case of dressed-ion impact at the higher nuclear velocities. We successfully apply a very simple model for ${\mathrm{H}}_2$ targets, in which the relevant quantities are the charge of the projectile and the vertical ionization potential of the molecule. For practical purposes, we give scaling laws to benchmark $({\mathrm{H}}^{+},{\mathrm{He}}^{2+})$ cases, and for ionization we relate them, at higher $v,$ to the behavior of the transition probabilities.

Two exactly soluble two-state curve crossing models, with potential matrices formed by a linear combination of time-independent terms and (I) inversely proportional $\left(\sim t^{-1}\right)$ or (II) exponential time-dependent terms, are considered here. It is shown that the two models are related to each other by a simple transformation of the time variable. These models can be further transformed to a simpler one (the “reduced” model), in which the two crossing potentials are a constant (horizontal) one and an inversely proportional time-dependent one, and the interaction coupling them is time-independent. Analysis of the exact solution of the reduced model discloses that the nonadiabatic transition probability saturates at increasingly large coupling strengths without vanishing (in contradiction of the linear Landau-Zener theory and various adiabatic theories). Similar saturation can also occur in more general models, within certain ranges of the potential parameters involved.

The low-energy (0–6-eV) behavior of positrons scattering from gaseous ${\mathrm{C}}_{60}$ molecules is examined through a computational study which employs a nonempirical modeling of all the relevant interaction forces (static, correlation, and polarization potentials). There is uncertainty concerning the most appropriate correlation-polarization potential to use in the study of positron-molecule scattering. Here we have considered two such potentials which are representative of the potentials which have been proposed for this purpose. The coupled quantum scattering equations are solved in the body-fixed frame of reference, and the fixed-nuclei approximation is used to decouple the nuclear motion during the collision. The elastic integral cross sections without positronium formation exhibit strong one-particle resonances in the very-low-energy region up to $\sim 4$ eV. The low-angular-momentum scattering components are shown to be the dominant contributions to trapped state wave functions. The existence of resonances in positron scattering from molecules is unusual. In the system studied here there are two types of resonances. First there are angular-momentum barrier resonances with the positron trapped outside of the ${\mathrm{C}}_{60}$ cage. Second, there are resonances of low angular momentum $(l<~2)$ with the positron trapped inside of the ${\mathrm{C}}_{60}$ cage by the repulsive interaction between the positron and the nuclei. The possibility of the experimental observation of these resonances is also discussed.

We demonstrate that much simpler techniques can reproduce the results of the full Breit-Pauli R-matrix method to include relativistic effects in photoionization calculations. To allow for the fine-structure splitting of channels in the photoionization of ${\mathrm{Fe}}^{16+},$ we have performed three sets of calculations. The first combined an $\mathrm{LS}$ R-matrix calculation with an $\mathrm{LS}-\mathrm{JK}$ frame transformation, using multichannel quantum defect theory. The second used a relativistic random phase approximation based on the Dirac equation. Both methods give resonant photoionization results nearly identical to those from a third calculation using the full Breit-Pauli R-matrix method. An accurate treatment of fine-structure splitting in ${\mathrm{Fe}}^{16+}$ is necessary to realistically include the ${2p}^5{(}^2{P}_{1/2})nl$ resonances which dominate the low-energy photoionization cross section; consequently, in the inverse process of photorecombination, the low-temperature rate coefficient is dominated by the ${2p}^5{(}^2{P}_{1/2})nl$ dielectronic recombination resonances.