Three-Body and One-Body Channels of the Auger Core-Valence-Valence decay: Simplified Approach

We propose a computationally simple model of Auger and APECS line shapes from open-band solids. Part of the intensity comes from the decay of unscreened core-holes and is obtained by the two-body Green's function $G^{(2)}_{\omega}$, as in the case of filled bands. The rest of the intensity arises from screened core-holes and is derived using a variational description of the relaxed ground state; this involves the two-holes-one-electron propagator $G_{\omega}$, which also contains one-hole contributions. For many transition metals, the two-hole Green's function $G^{(2)}_{\omega}$ can be well described by the Ladder Approximation, but the three-body Green's function poses serious further problems. To calculate $G_{\omega}$, treating electrons and holes on equal footing, we propose a practical approach to sum the series to all orders. We achieve that by formally rewriting the problem in terms of a fictitious three-body interaction. Our method grants non-negative densities of states, explains the apparent negative-U behavior of the spectra of early transition metals and interpolates well between weak and strong coupling, as we demonstrate by test model calculations.Comment: AMS-LaTeX file, 23 pages, 8 eps and 3 ps figures embedded in the text with epsfig.sty and float.sty, submitted to Phys. Rev.

Antiferromagnetism of the 2D Hubbard Model at Half Filling: Analytic Ground State at Weak Coupling

We introduce a local formalism to deal with the Hubbard model on a N times N square lattice (for even N) in terms of eigenstates of number operators, having well defined point symmetry. For U -> 0, the low lying shells of the kinetic energy are filled in the ground state. At half filling, using the 2N-2 one-body states of the partially occupied shell S_{hf}, we build a set of (2N-2 N-1)^{2} degenerate unperturbed ground states with S_{z}=0 which are then resolved by the Hubbard interaction \hat{W}=U\sum_{r}\hat{n}_{r\ua}\hat{n}_{r\da}. In S_{hf} we study the many-body eigenstates of the kinetic energy with vanishing eigenvalue of the Hubbard repulsion (W=0 states). In the S_{z}=0 sector, this is a N times degenerate multiplet. From the singlet component one obtains the ground state of the Hubbard model for U=0^{+}, which is unique in agreement with a theorem by Lieb. The wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. We show that the total momentum vanishes, while the point symmetry is s or d for even or odd N/2, respectively.Comment: 13 pages, no figure

W=0 pairing in Hubbard and related models of low-dimensional superconductors

Lattice Hamiltonians with on-site interaction $W$ have W=0 solutions, that is, many-body {\em singlet} eigenstates without double occupation. In particular, W=0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W=0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO$_{2}$ planes of cuprate superconductors, armchair Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W=0 pairs quantize the magnetic flux like superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W=0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the $4\times 4$ Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W=0 pairing mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed Matte

The global and persistent millennial-scale variability in the thermoluminescence profiles of shallow and deep Mediterranean sea cores

In this paper we present the thermoluminescence (TL) profile in the last 7500 y, measured in the upper part of the deep Tyrrhenian sea core CT85-5. This core was dated with tephroanalysis and radiocarbon techniques: a constant sedimentation rate (10 cm/ky) was found up to 200 cm. The sampling interval adopted for obtaining the TL profile is 2.5 mm, corresponding to 25 y. Using different spectral-analysis methods, we show the presence of a millennial-scale variability, corresponding to an average period of about 1315 y. This oscillation has been noted also in other climatic indices measured in North Atlantic sea sediment cores and in the Greenland GISP2 ice core. This result indicates that this millennial oscillation is the expression of climate changes of worldwide extent. We show that this millennial periodicity persisted during the last deglaciation. The transition to Holocene was determined in our core by the oxygen isotope ratio d 18O measured in Globigerina bulloides. The fact that the observed TL changes do not have a local character is also suggested by the excellent agreement between this deep sea TL profile of the uppermost part of the core and the TL profile measured in the shallow Ionian sea GT89-3 core over the last 2500 y, with a time resolution of 3.096 y

Correlated Nanoscopic Josephson Junctions

We discuss correlated lattice models with a time-dependent potential across a barrier and show how to implement a Josephson-junction-like behavior. The pairing occurs by a correlation effect enhanced by the symmetry of the system. In order to produce the effect we need a mild distortion which causes avoided crossings in the many-body spectrum. The Josephson-like response involves a quasi-adiabatic evolution in the time-dependent field. Besides, we observe an inverse-Josephson (Shapiro) current by applying an AC bias; a supercurrent in the absence of electromotive force can also be excited. The qualitative arguments are supported by explicit exact solutions in prototype 5-atom clusters with on-site repulsion. These basic units are then combined in ring-shaped systems, where one of the units sits at a higher potential and works as a barrier. In this case the solution is found by mapping the low-energy Hamiltonian into an effective anisotropic Heisenberg chain. Once again, we present evidence for a superconducting flux quantization, i.e. a Josephson-junction-like behavior suggesting the build-up of an effective order parameter already in few-electron systems. Some general implications for the quantum theory of transport are also briefly discussed, stressing the nontrivial occurrence of asymptotic current oscillations for long times in the presence of bound states.Comment: 12 pages, 2 figures, to appear in J. Phys. - Cond. Ma

The sunspot cycle recorded in the thermoluminescence profile of the GT89/3 Ionian sea core

We measured the thermoluminescence (TL) depth profile of the GT89O3 shallow-water Ionian sea core. This profile has been transformed into a time series using the accurate sedimentation rate previously determined by radiometric and tephroanalysis methods. The TL measurements were performed in samples of equal thickness of 2 mm, corresponding to a time interval of 3.096 y. The TL time series spans A1800 y. The DFT power spectral densities in the decadal periodicity range of this TL series show significant periodicities at 10.7, 11.3 and 12 y closely similar to the periodicities present in the sunspot number series. These results confirm that the TL signal in recent sea sediments faithfully records the solar variability, as we previously proposed

On the ab initio calculation of CVV Auger spectra in closed-shell systems

We propose an ab initio method to evaluate the core-valence-valence (CVV) Auger spectrum of systems with filled valence bands. The method is based on the Cini-Sawatzky theory, and aims at estimating the parameters by first-principles calculations in the framework of density-functional theory (DFT). Photoemission energies and the interaction energy for the two holes in the final state are evaluated by performing DFT simulations for the system with varied population of electronic levels. Transition matrix elements are taken from atomic results. The approach takes into account the non-sphericity of the density of states of the emitting atom, spin-orbit interaction in core and valence, and non quadratic terms in the total energy expansion with respect to fractional occupation numbers. It is tested on two benchmark systems, Zn and Cu metals, leading in both cases to L23M45M45 Auger peaks within 2 eV from the experimental ones. Detailed analysis is presented on the relative weight of the various contributions considered in our method, providing the basis for future development. Especially problematic is the evaluation of the hole-hole interaction for systems with broad valence bands: our method underestimates its value in Cu, while we obtain excellent results for this quantity in Zn.Comment: 20 pages, 5 figures, 4 table

22 year cycle in the planktonic 18 of a shallow-water Ionian sea core

The d18 O profile of Globigerinoides ruber was measured in the GT90/3 Ionian sea core between 1205 and 1898 AD. The high temporal resolution of 3.87 y allowed us to determine the presence in the time series of an 11 y component with an amplitude of 0.07‰, at significance level of 99% (by Monte Carlo singular spectrum analysis, MC-SSA). Here we focus attention on the 22 y periodicity in the time series and we show that SSA principal components (PCs) 15 and 16 carry this oscillation, in phase with the Hale solar cycle, obtained by inverting the odd cycles of the sunspot number series. This result shows that the even and odd Schwabe cycles do not have the same influence on this climatic record

On the half-life of 44Ti by results in meteorites

Measurements of the 44Ti half-life display a large spread ranging from 46.4 to 66.6 years. The activity of this radioisotope measured in eight meteorites (chondrites) fell in the time interval 1883-1992 and calculated at the time of fall by the different values of T1O2 shows that the shorter values are not reliable, if it is assumed that the average cosmic-ray intensity has remained the same during the past two centuries. The low activity of the cosmogenic isotope 44Ti has been determined by means of a selective Ge-NaI (Tl) g-spectrometer with a very low background (about 1 count per day in the g-peak at 1157 keV of 44Sc in equilibrium with its parent 44Ti). The high stability of this system allows long-lasting runs (A107 s ), in order to achieve the standard deviation of counting up to A10%. PACS 94.40.Vf – Cosmic-ray effects in meteorites and terrestrial matter