Autoionization and Electronic Correlation in Atoms

CASSCF study of the relation between the Fe charge and the Mössbauer isomer shift

The photofragmentation of the He79Br2 van der Waals complex is studied for the transition from the ground to the excited electronic state B and where the Br2 subunit is also excited to the neighborhood of the v0=45 vibrational state. At this vibrational level the bromine molecule is close to its dissociation limit and the Δv=−1 channel is closed for dissociation of the complex. In a previous work it was suggested that energy in the HeBr2(B, v0=45) quasibound state may be internally redistributed (exciting van der Waals modes at the expense of the bromine excitation) prior to dissociation. Such mechanisms are more deeply studied in this work by means of the stabilization method, which works with square-integrable wave functions and is an appropriate approach to perform quasibound state analysis. Stabilization total cross sections compare fairly well with close-coupling ones, where the proper asymptotic behaviour of the continuum wave functions is taken into account. By inspection of the quasibound state wave functions, it is seen that energy is redistributed to several excited states belonging to the v0−1 manifold. In addition, it is shown that such excited states also carry oscillator strength in the transition from the ground electronic state and thus interference effects in the excitation process are significant. HeBr2 near the halogen dissociation limit is found to be a rather strongly coupled system where the quasibound states involved can only approximately be assigned to quantum numbers corresponding to interhalogen and van der Waals vibrational excitations.

Bound electron states in highly charged ions are strongly influenced by the effects of relativity and quantum electrodynamics (QED). These effects induce shifts of the binding energies as well as corrections to observables related to atomic processes. In this work a numerical procedure is described and implemented in which the QED effects are treated as corrections to relativistic bound-state wavefunctions. This approach, which is based on the recently developed covariant evolution-operator formalism, allows for a merging of QED with the standard methods of many-body perturbation theory. In particular, it enables an evaluation of the combined effect of QED and electron correlation in few-electron systems. Numerical results for this effect are presented for the ground state energy of heliumlike ions. A detailed analysis of the contribution from the electron self-energy is carried out in both the Feynman and Coulomb gauge. It is found that the Feynman gauge suffers from large numerical cancellations and aquires significant contributions from terms involving multiple interactions with the nuclear potential (the so-called many-potential terms), while the Coulomb gauge is well suited for an approximate treatment based on terms involving only freely propagating electrons (the zero-potential terms). With the help of QED-corrected wavefunctions it is also possible to compute corrections to observables in basic atomic processes. In this work some of the one-loop QED corrections (those derivable from perturbed wavefunctions and energies) to the differential cross section and distribution of polarization in radiative recombination of initially bare uranium nuclei are evaluated, as well as the corresponding corrections to the ratio of the electric dipole and magnetic quadrupole transition amplitudes in the 2p3/2 → 1s radiative decay of hydrogenlike uranium. The results from these calculations are all of the expected magnitude, namely on the order of the fine-structure contant.

We have computed the partial and total autoionization widths with interchannel coupling for the ${}^{3}{P}^{o}$ Wannier-ridge resonances of ${\mathrm{H}}^{\ensuremath{-}}$ below the $n=3$, 4, 5, 6, and 7 hydrogenic thresholds. The complex eigenvalue Schr\"odinger equations are solved using square-integrable wave functions with numerical and analytic real and complex orbitals. Trends regarding the decay dynamics and the excitation of high-orbital-angular-momentum electrons near threshold are established.

Total (elastic + inelastic) differential photon-scattering cross sections have been measured for ${\mathrm{H}}_{2}$ gas over a range of $2.5\ensuremath{\le}S=(\frac{4\ensuremath{\pi}}{\ensuremath{\lambda}})sin(\frac{\ensuremath{\theta}}{2})\ensuremath{\le}6.7$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and for He over $3\ensuremath{\le}S\ensuremath{\le}11.2$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, using an x-ray beam in the Stanford Synchrotron Radiation Laboratory. Absolute measured cross sections agree with theory within the probable errors. Relative cross sections (normalized to theory at large $S$) agree to better than 1% with theoretical values calculated from wave functions that include the effect of electron-electron Coulomb correlation, but the data deviate significantly from theoretical independent-particle (e.g., Hartree-Fock) results. The ratios of measured absolute He cross sections to those of ${\mathrm{H}}_{2}$, at any given $S$, also agree to better than 1% with theoretical He-to-${\mathrm{H}}_{2}$ cross-section ratios computed from correlated wave functions. It appears that photon scattering constitutes a very promising tool for probing electron correlation in light atoms and molecules. The degree of polarization of the synchrotron radiation beam has been measured by rotating the scattering plane about the beam axis; results are compared with theory.

In Z-dependent perturbation theory, the lowest-order wave functions for a polyatomic molecule are not only independent of the nuclear charges, but also of the total number of nuclear centers and electrons in the molecule. The complexity of the problem is then determined by the highest order retained in the calculation. Choosing the simplest possible unperturbed Hamiltonian, we describe an n-electron, m-center polyatomic molecule as n ‘‘hydrogenic’’ electrons on a single center perturbed by electron–electron and electron–nucleus Coulomb interactions. With this H0, the first-order wave function for any polyatomic molecule will be a sum of products of hydrogenic orbitals with either two-electron, one-center or one-electron, two-center first-order wave functions. These first-order wave functions are obtained from calculations on He-like and H+2-like systems. Similarly, the nth-order wave function decouples so that the most complex terms are just the nth-order wave functions of all the p-electron, q-center subsystems (p+q=n+2) contained in the molecule. We illustrate applications of this method with some results, complete through third order in the energy, for H+3-like molecules. These are compared with accurate variational results available in the literature. We conclude that, through this order, this perturbation approach is capable of yielding results comparable in accuracy to variational calculations of moderate complexity. The ease and efficiency with which such results can be obtained suggests that this method would be useful for generating detailed potential energy surfaces for polyatomic molecules.

An analysis of wave functions in a generalized two-state model for a series of even–even nuclei is presented here. With minimal assumptions, necessary and sufficient conditions for consistency in obtaining these from data on (p,t) and (t,p) cross-section ratios are exhibited.

The photoionization cross section of the hydrogen negative ion is computed using a discrete-basis-set expansion to represent both the ground and continuum states of the system. This discrete-basis-set representation is used to construct an approximation to the dynamic polarizability, which in turn is used in an analytical continuation procedure for complex values of the frequency. This discretization of the continuum makes the method potentially applicable to larger systems, and a study of the basis-set dependence is made. The final results are in good agreement with more elaborate calculations and with experimental results. The dynamic polarizability in the normal dispersion region is also computed. I. INTRODUCTION The photoionization cross section of the hydrogen negative ion has been the subject of several calculations since Wildt' first suggested that it could be responsible for the visible and infrared opacity in the atmosphere of cooler late spectral type stars. Ghandrasekhar' and his co-workers pioneered these studies in a series of papers investigating the dependence of the cross section on the accuracy of the bound-state wave function. They also investigated the effect of the central field approximation for the free state. ' The importance of,taking into account exchange effects in the free wave function was first investigated by John' using the Hart-Herzberg 20-parameter wave function for the ground state and the 1sexchange approximation continuum function. A number of subsequent calculations have appeared. Geltman' employed the 70-parameter bound-state wave function of Schwartz and variationally determined symmetrized continuum functions, containing terms corresponding to excited states of the hydrogen atom. This allowed him to treat both correlation and distortion of the residual hydrogen atom. Doughty et al. ' employed a close-coupling approach for using a Hartree-Pock eigenfunction expansion for the continuum states which included up to 3d atomic orbitals of the hydrogen atom. Bell and Kingston' used the method of polarized orbitals to obtain a representation of the continuum. More recently Ajmera and Ghung' used the variational method of Kohn-Feshbach to obtain free-state wave functions. A recent review of the photodetachment of H was given by Risley. ' While many of the above calculations have produced good results for H, they are generally not easily extended to large systems, first because such highly accurate wave functions are not available for systems with more electrons, and secondly because the generation of continuum functions by the methods used above becomes very cumbersome '0 Our interest is in developing a method w'hich could be equally applied to larger systems. Thus we use highly accurate wave functions and methods practicable for polyatomic molecules, and w'e avoid

The effects of atomic and molecular electron correlation and Gaunt interaction on the transition energies between the D-5(0) and F-7(1,2) levels, arising from the (4)f(6) State of the europium ion, have been studied for the ion and for the [EuO6](9-) cluster as it is found in the Ba2GdNbO6 crystal. The calculations were performed using the MOLFDIR program package. The results are compared to work previously done by Visser et al. in which correlation effects had not been taken into account. The effect of the Gaunt interaction is found to be small. An important contribution to the correlation energy emerges from the configuration represented by the double excitations from 4d to 4f. This in agreement with work performed by Jankowski and Sokolowski on Pr3+. The results are now in better agreement with experiment but are still not satisfactory. (C) 1995 John Wiley & Sons, Inc.

The first two members of the cyclic polyene homologous series are studied over a wide range of the coupling constant using the Hubbard and Pariser–Parr–Pople model Hamiltonians. The full and various limited configuration interaction (CI) correlation energies and wave functions are calculated exploiting the unitary group approach. The formalism for the cluster analysis of the exact wave function expressed through the unitary group formalism electronic Gelfand states is developed and applied to the full CI wave functions of the cyclic polyene models studied. It is shown that the connected tetraexcited clusters become essential in the fully correlated limit and that their contribution also significantly increases with electron number even for the coupling constant corresponding to the spectroscopic parametrization of the model Hamiltonians used.

A 12 C+four-nucleon (4N ) five-body model is applied for the ground and first excited states of 16 O. The 4N configurations are selected in a wide Hilbert space under the fulfillment of the Pauli principle excluding the occupied orbits in 12 C. The energies of both the states are obtained in excellent agreement with experiment. Analysis of the wave functions indicates a spatially localized alpha-particle-like cluster structure for the excited state and a shell-model-like delocalized structure for the ground state. The difficulty of describing the cluster structure by a standard shell model approach is discussed by calculating components of the harmonic-oscillator quanta in the wave functions.

In an earlier study of benzene, Small and Head-Gordon found that the spin-coupled generalized valence bond (SCGVB) wave function for the π system predicted a distorted (non-D6h ) geometry, one with alternating CC bond lengths. However, the variations in the energy were very small and the predictions were made using a very small basis set (STO-3G). We re-examined this prediction using a much larger basis set (aug-cc-pVTZ) to determine the dependence of the energy of benzene on the distortion angle, ΔθCXC (ΔθCXC = 0° corresponds to the D6h structure). We also found a distorted geometry with the optimum ΔθCXC being 0.31° with an energy 0.040 kcal mol-1 lower than that for the D6h structure. In the optimum geometry, adjacent CC bond lengths are 1.3861 Å and 1.4004 Å. Analysis of the SCGVB wave function led us to conclude that the cause of the unusual non-D6h geometry predicted by the SCGVB calculations seems to be a result of the interaction between the Kekulé and Dewar components of the full SCGVB wave function. The addition of doubly ionic configurations to the SCGVB wave function leads to the prediction of a D6h geometry for benzene and a dependence on ΔθCXC essentially the same as that predicted by the complete active space self-consistent field wave function.

We report the study of the spectral properties of a quasiperiodic superlattice within a tight binding model. Numerical work is carried out using the transfer matrix method. An approximate analytical scheme is used to obtain expressions for the band gaps which explain all the features obtained numerically. Due to the fact that blocks of atoms are repeated quasiperiodically, the gaps are shown to vanish at specific energies. These states have much the same behaviour as the extended states but the amplitude is a quasiperiodic function of the site index. The total number of such extended states are estimated. Since it is known that other states in quasiperiodic systems are critical, these states are expected to exhibit a cross-over behaviour to the critical states as a function of the energy. Multifractal analysis of the quasiperiodic wave function show that it has the same signature as the extended wave function. We briefly comment on the cross-over behaviour.

Ab initio calculations including electron correlation are reported for the water and methylene molecules as a function of geometry. A large contracted gaussian basis set is used and the multiconfiguration wave functions, optimized by the iterative natural orbital procedure, include 277 and 617 configurations for H2O and CH2 respectively. The method of selecting configurations, yielding “first-order” wave functions, is discussed in some detail. For H2O, the SCF geometry is r=0,942 A, θ=105,8°, the correlated result is r=0,968 A, θ=103,2°, and the experimental r=0,957 A, θ=104,5°. The water stretching force constants, in millidynes/A, are 8,72 (SCF), 8,75 (CI), and 8,4 (experiment). Bending force constants are 0,88 (SCF), 0,83 (CI), and 0,76 (experiment). For methylene the SCF geometry is r=1,072 A, θ=129,5°, while the result from first-order wave functions is r=1,088 A, θ=134°. The predicted CH2 force constants are 6,16 (SCF) and 6,13 (CI) for stretching and 0,44 (SCF) and 0,33 (CI) for bending.

A review of the theory of electron momentum spectroscopy (EMS) based on the single (multiple) electron impact ionization of a quantum target (atom, molecule, thin film) is presented. Numerous examples are considered which demonstrate the advantages of EMS for interpreting the momentum distributions of the ejected electrons compared to other methods used for direct studies of the many-body wave function of a target. In particular, it is shown that EMS provides considerable progress in the quantum chemistry of molecules and gives a better understanding of processes leading to rearrangement of their outer electron orbitals upon their adiabatic approach. In addition, EMS allows one to study in detail the band structure and form of one-electron wave functions for both crystalline and amorphous thin films. The possibility of direct 'portraying' of electron correlations in atoms using the double ionization technique is also considered.