Many-body Perturbation Theory Approach Research Articles

Investigation of transitions between metastable levels of the first excited configuration of palladium-like tungsten

Spectroscopy in the wavelength region of 330 nm to 400 nm for highly charged tungsten was performed using the High Temperature Super Conducting Electron Beam Ion Trap (SH-HtscEBIT) at Fudan University. Three lines from palladium-like tungsten (W28+) were identified as transitions between metastable levels in the first excited configuration ([Kr]4d94f). A second-order relativistic many-body perturbation theory approach and a simple collisional radiative model were used to theoretically study the fine structure levels of the 4d94f configuration. The calculated results show qualitative agreement with experiment. We conclude that some levels in the 4d94f excited configuration have extremely long lifetimes and may exhibit extraordinarily high populations, possibly leading to indirect ionization in, for example, fusion plasmas.

Signatures of electron-magnon interaction in charge and spin currents through magnetic tunnel junctions: A nonequilibrium many-body perturbation theory approach

We develop a numerically exact scheme for resumming certain classes of Feynman diagrams in the self-consistent perturbative expansion for the electron and magnon self-energies in the nonequilibrium Green function formalism applied to a coupled electron-magnon (e-m) system driven out of equilibrium by the applied finite bias voltage. Our scheme operates with the electronic and magnonic GFs and the corresponding self-energies viewed as matrices in the Keldysh space, rather than conventionally extracting their retarded and lesser components, which greatly simplifies translation of diagrams into compact mathematical expressions and their computational implementation. This is employed to understand the effect of inelastic e-m scattering on charge and spin current vs bias voltage ${V}_{b}$ in F/I/F (F-ferromagnet; I-insulating barrier) magnetic tunnel junctions (MTJs), which are modeled on a quasi-one-dimensional (quasi-1D) tight-binding lattice for the electronic subsystem and quasi-1D Heisenberg model for the magnonic subsystem. For this purpose, we evaluate the Fock diagram for the electronic self-energy and the electron-hole polarization bubble diagram for the magnonic self-energy. The respective electronic and magnonic GF lines within these diagrams are the fully interacting ones, thereby requiring to solve the ensuing coupled system of nonlinear integral equations self-consistently. Despite using the quasi-1D model and treating e-m interaction in many-body fashion only within a small active region consisting of few lattice sites around the F/I interface, our analysis captures essential features of the so-called zero-bias anomaly observed [V. Drewello, J. Schmalhorst, A. Thomas, and G. Reiss, Phys. Rev. B 77, 014440 (2008)] in both MgO- and ${\mathrm{AlO}}_{x}\ensuremath{-}$based realistic 3D MTJs where the second derivative ${d}^{2}I/d{V}_{b}^{2}$ (i.e., inelastic electron tunneling spectrum) of charge current exhibits sharp peaks of opposite sign on either side ${V}_{b}=0$. We show that this is closely related to a substantially modified magnonic density of states (DOS) after the e-m interaction is turned on---the magnonic bandwidth over which DOS is nonzero becomes broadened, thereby making e-m scattering at arbitrary small bias voltage possible, while DOS also acquires peaks (on the top of a continuous background) signifying the formation of quasibound states of magnons dressed by the cloud of electron-hole pair excitations. We also demonstrate that the sum of electronic spin currents in all of the semi-infinite leads attached to the active region quantifies the loss of spin angular momentum carried away from the active region by the magnonic spin current.

Measurement and calculation of L-shell transitions in M-shell iron ions

We have made high-resolution measurements of the iron L-shell emission near 15 Å using the EBIT-I electron beam ion trap at Livermore that exhibit L-shell transitions from autoionizing levels in Fe13+, Fe14+ and Fe15+ ions. The observed L-shell iron spectra were modeled using the flexible atomic code augmented with transition energies produced by calculations based on the relativistic multi-reference Møller–Plesset (MRMP) perturbation theory, allowing us to identify multiple M-shell iron lines. Our measured values for the Fe XV emission lines are in excellent agreement with a recent measurement using the BESSY-II synchrotron but the present measurements have somewhat higher accuracy. Our MRMP calculations are compared to earlier calculations using the many-body perturbation theory approach, and we find good agreement for some but not all transitions.

Excitons at the (001) surface of anatase: Spatial behavior and optical signatures

Within an ab initio study, based on the application of Many-Body Perturbation Theory approaches on top of ground-state Density Functional Theory calculations, we study the optical behavior of the TiO2 anatase (001) surface. We focus on the (1 × 1) and the (1 × 4) reconstructions, both experimentally observed, which reveal a different optical response and an anisotropy, in the (001) plane, not present in the bulk phase. The determination of the spatial behavior of the electron-hole photoexcited couple provides a possible explanation of the observed enhanced photocatalytic activity of TiO2 anatase nanostructures with a high percentage of (001)-(1 × 1) exposed facets.

Multi-reference many-body perturbation theory and coupled cluster developments

Multi-reference methods for the description of quasi-degenerate ground states and excited states of many-electron systems have been one of the main objectives of scientific activity at the Quantum Theory Project (QTP) University of Florida in Gainesville. The pioneering works by Dr. Per-Olov Löwdin on the partitioning technique, and important contributions to the development of multi-reference methods made by Dr. Monkhorst and Dr. Bartlett must be mentioned here. Dr. Bartlett, his group and its visitors have been especially active in this field. In this paper we describe some of the multi-reference developments, problems that have been faced and solved as well as those which still require solving. The focus is on multi-reference many-body perturbation theory and coupled-cluster approaches. We present recent advances and future perspectives in the development of these methods. Special attention is paid to two multi-reference approaches that seem very promising and have been either initiated or developed at QTP.

Relativistic Many-Body Perturbation Theory approach to electron-ion recombination of He- and Be-like systems

We report on efforts to perform fully correlated calculations of effective three-body systems with a Rel-ativistic Many-Body Perturbation Theory approach. A preliminary version of the program is used on resonances in Ge27+, formed in collisions of electrons with Be-like Ge28+. We will show a comparison between experimental and calculated spectra, including both dielectronic and trielectronic recombination resonances. Results for some pure three electron systems will also be shown.

Electron correlation and properties of many-electron systems

Different computational methods of quantum chemistry, which are currently employed in accurate calculations of atomic and molecular properties, are discussed and their advantages and disadvantages are investigated in calculations of electric properties of Be, FH, and H2O. A complete fourth-order many-body perturbation theory (MBPT) approach based on the coupled Hartree–Fock (CHF) solution for the perturbed problem reveals that in several cases the fourth-order correlation correction to the CHF result is dominated by those terms which involve triply substituted intermediate states. Moreover, in some cases a complete fourth-order MBPT result appears to be inferior to those obtained in approximate MBPT treatments which involve only certain classes of intermediate states. Hence, a complete fourth-order MBPT approach may not be sufficient for accurate predictions of atomic and molecular properties. The applicability of the complete active space (CAS) SCF method is studied in calculations of electric properties of FH. Although this method offers some advantages over the MBPT approach, its usefulness may be limited by the requirement of rather large active orbital spaces which have to be used in order to achieve sufficiently high accuracy. The CAS SCF results can be improved by using multireference CI methods with reference functions built of the CAS SCF natural orbitals. A good performance of the MBPT method limited to singly and doubly substituted intermediate states suggests that reasonable results can also be obtained in similar configuration interaction (CI) calculations, provided the latter are corrected for the erratic treatment of unlinked clusters. It is shown that the unlinked cluster corrections due to Davidson and Siegbahn result in reasonable estimates of the total correlation contribution to different properties. Because of its fairly routine character the CI method limited to single and double substitutions may in this way provide useful data with relatively small computational effort.

Energies of 1s 22l q (1 ⩽ q ⩽ 8) states for Z ⩽ 60 with a combined configuration interaction and many-body perturbation theory approach

Using a combined configuration interaction and many-body perturbation theory approach, we calculate the level energies of 1s 22l q (1 ⩽ q ⩽ 8) states for ions with Z ⩽ 60. Comparison with experimental results wherever available indicates that the calculated energies are accurate to within a few 1000 cm −1 for all ions except for near-neutral systems which are less than 2–3 times ionized. The ground state ionization energies of these ions are also reported and compared with experimental values.

Wavelengths of 2l→3l′ Transitions in L‐Shell Ions of Iron and Nickel: A Combined Configuration Interaction and Many‐Body Perturbation Theory Approach

Using a combined configuration interaction and many-body perturbation theory approach, we calculate the level energies of 1s22lq and 1s22lq-13l' (1 ≤ q ≤ 8) complexes in iron and nickel ions. Comparison of 1s22lq energies with experimental results shows that the calculation is accurate to within ~0.15 eV for these levels. The accuracy of 1s22lq-13l' energies can be slightly worse, at ~0.5 eV. The theoretical wavelengths of 2→3 transitions of iron ions are compared with the published experimental measurements, and discrepancies are found to be mostly within ±10 mA. Similar accuracy is expected for wavelengths of nickel ions. Such accuracy is a significant improvement over that obtainable with standard configuration interaction methods. A complete table of 2l → 3l' transition wavelengths of all L-shell ions of iron and nickel is presented.

N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium ( D 0) structure, and the normal-mode ( D −1) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose–Einstein condensate with a repulsive hard-core potential.

An ab inito study of NMR isotropic shielding bond length derivatives in phosphorus compounds

Ab initio calculations of the effect of bond length modifications on phosphorus nuclear magnetic resonance (NMR) shieldings have been carried out. Moderately large basis sets have been employed in the gauge including atomic orbital (GIAO) approach at the Hartree–Fock, second-order Møller–Plesset (MP2), and estimated infinite order many-body perturbation theory (EMPI) approaches employing MP2(fc)/6-31+G(d) geometries. The EMPI approach yields better shielding derivatives than does Hartree–Fock (HF) or MP2, and correlation is found to be important in the shielding derivatives when it is also important in the isotropic shielding itself. The computed phosphorus shielding bond length derivatives, ∂ σ/∂ R, in the homologous series H 2PXH n parallel those found for other nuclei. Trends for ∂ σ/∂ R for the X atom in the same series reproduce the behavior predicted for a universal shielding surface for second-row atoms but not for the corresponding first-row species.

Thermodynamics of quantum Hall ferromagnets.

The two-dimensional interacting electron gas at Landau level filling factor $\nu =1$ and temperature $T=0$ is a strong ferromagnet; all spins are completely aligned by arbitrarily weak Zeeman coupling. We report on a theoretical study of its thermodynamic properties using a many-body perturbation theory approach and concentrating on the recently measured temperature dependence of the spin magnetization. We discuss the interplay of collective and single-particle aspects of the physics and the opportunities for progress in our understanding of itinerant electron ferromagnetism presented by quantum Hall ferromagnets.

Relativistic and QED effects in highly charged ions

We review the recent progress in calculations of high- Z many-electron ions. The relativistic many-body perturbation theory approach is discussed together with the recent development of calculations of two-particle effects beyond it. Theoretical results for several ionic systems are compared with experiments. We discuss also the treatment of effects which vanish in the non-relativistic limit, especially concerning the bound state corrections to the electron g-factor.

The effect of virtual positronium formation on positron-atom scattering

A new method is proposed to calculate the contribution of virtual Ps formation to elastic positron-atom scattering. The calculations were performed using the many-body perturbation theory approach. It is shown that for the scattering of positrons by hydrogen and helium atoms, the virtual Ps formation contribution is about 30% and 20% of the total correlation potential, respectively. Good agreement was obtained with the results of precise variational calculations and with experimental data.

Theory of many-electron atoms

The theory of many-electron atoms is treated first from a many-body perturbation theory approach, and then in terms of Furry representation QED. The connection between the two approaches is shown to allow the precise definition of QED effects, and it is shown that the spectroscopy of highly charged ions provides an ideal way to study these effects. One-photon Feynman diagrams are evaluated for sodiumlike platinum in a non-Coulomb potential, and shown to give good agreement with experiment. The role of two-photon diagrams and the importance of their complete evaluation is discussed.

Diagrammatic many-body perturbation expansion for atoms and molecules: VI: Experiments in vector processing and parallel processing for second-order energy calculations

The efficient evaluation of the second-order expression in the many-body perturbation theory expansion for the correlation energy on vector processing and parallel processing computers is discussed. It is argued that the linked diagram theorem not only leads to the well known theoretical advantages of the many-body perturbation theory approach which allows the calculation of correlation energies for large (i.e. extended molecules or species containing heavy atoms) systems but also decouples the many-electron problem allowing efficient implementation on parallel processing machines. Furthermore, the computation associated with each of the resulting subproblems is very well suited to vector processing machines. Timing tests are reported for the CRAY 1 and CDC Cyber 205 vector processors, for a 1 processor implementation on the CRAY X-MP/48 and the ETA-10E, and for a 4 processor implementation on the Cray X-MP/48.

Electric properties of the chloride ion

The dipole (α), quadrupole (C), and dipole-quadrupole (B) polarizabilities and the dipole hyperpolarizability (γ) of the chloride ion have been calculated by using the many-body perturbation theory approach and a series of large polarized GTO/CGTO basis sets. The complete fourth-order treatment of the electron correlation effects with a basis set comprising the s, p, d, f, and g functions gives: α=38.01 a.u., C=211.5 a.u., B=−5.14×103 a.u., and γ=128. 5×103 a.u. as compared to the corresponding SCF values (α=31.49 a.u., C=158.9 a.u., B=−2.92×103 a.u., γ=57.7×103 a.u.). The quenching of polarizabilities of the Cl− ion in solutions and ionic crystals is discussed.

Multipole polarizabilities of Ar

The four lowest multipole polarizabilities of Ar have been calculated by using the complete fourth-order many-body perturbation theory approach and a large GTO/CGTO basis set including a number of diffuse and polarization functions. The present results for the dipole polarizability (α =11.23 au), quadrupole polarizability ( C= 26.79 au), dipole-quadrupole polarizability ( B = -164.3), and the dipole hyperpolarizability (γ =1329 au) are compared with other theoretical data and experimental values.

Perturbation theory of the electron correlation effects for atomic and molecular properties. VII. Complete fourth-order MBPT study of the dipole moment and dipole polarizability of H2O

The dipole moment and dipole polarizability tensor of the water molecule are calculated by using a complete fourth-order many-body perturbation theory (MBPT) approach based on the coupled Hartree-Fock (CHF) solution for the one-electron perturbation problem. The CHF-based MBPT calculations reveal that the fourth-order correlation corrections involving triple and single substitutions in the reference HF determinant are by no means negligible. On the contrary they represent the two largest in magnitude fourth-order terms. The present study reveals that good results obtained with several approximate fourth-order MBPT schemes follow from some mutual cancellations between the neglected lower and higher-order contributions. Among these approximate MBPT approaches particular attention is given to the CHF-based MBPT treatment which involves only singly and doubly substituted states (SD-MBPT) and which provides a reasonable agreement with both the experimental data and more accurate theoretical values.

Configuration interaction and perturbation study of the electron correlation contribution to the dipole polarizability of beryllium

Correlation corrections to the dipole polarizability of the beryllium atom are calculated by using the configuration interaction method and the fourth-order many-body perturbation theory approach, both limited to single and double excitations with respect to the ground state determinant. The role of the frozen-core approximation is investigated. It is concluded that the dipole polarizability of Be is certainly lower than the recommended literature value.