The Screen representation of spin networks. Images of 6j symbols and semiclassical features

This article presents and discusses in detail the results of extensive exact calculations of the most basic ingredients of spin networks, the Racah coefficients (or Wigner 6j symbols), exhibiting their salient features when considered as a function of two variables - a natural choice due to their origin as elements of a square orthogonal matrix - and illustrated by use of a projection on a square "screen" introduced recently. On these screens, shown are images which provide a systematic classification of features previously introduced to represent the caustic and ridge curves (which delimit the boundaries between oscillatory and evanescent behaviour according to the asymptotic analysis of semiclassical approaches). Particular relevance is given to the surprising role of the intriguing symmetries discovered long ago by Regge and recently revisited; from their use, together with other newly discovered properties and in conjunction with the traditional combinatorial ones, a picture emerges of the amplitudes and phases of these discrete wavefunctions, of interest in wide areas as building blocks of basic and applied quantum mechanics.Comment: 16 pages, 13 figures, presented at ICCSA 2013 13th International Conference on Computational Science and Applicatio

Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective

A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of the symmetric coupling in spin network approaches: here, crucial to our presentation are an appreciation of the role of the Racah sum rule and the simplification arising from the use of Regge symmetry. The projective geometry approach permits the introduction of a symmetric representation of a network of seven spins or angular momenta. Results of extensive computational investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International Conference on Computational Science and Application

Stability of Jahn-Teller distortion ordering in LaMn1-x ScxO3

We have investigated the role of Mn3+ Jahn-Teller distortion in driving ferromagnetism in the LaMn1-xScxO3 series. The replacement of Mn by Sc in LaMnO3 decreases the orthorhombic distortion of the Pbnm cell, but the unit cell remains distorted even in the LaScO3 sample. The analysis of the x-ray diffraction patterns indicates a continuous evolution from the typical Jahn-Teller distorted octahedron in LaMnO3 into a nearly regular one in LaScO3. Surprisingly, x-ray absorption spectroscopy measurements at the Mn and Sc K edges reveal the stability of both Jahn-Teller distorted MnO6 octahedron and nearly regular ScO6 octahedron along the whole Sc-substituted series. Moreover, the structure is described as a random distribution of Jahn-Teller distorted MnO6 octahedra spatially ordered as in LaMnO3 and nearly regular ScO6 octahedra. This result contrasts with the pseudocubic phase and the appearance of regular MnO6 octahedra in LaMn1-xGaxO3 for x>0.5. Thus the occurrence of Jahn-Teller distortion strongly depends on the distorted orthorhombic crystallographic structure of the matrix in which the Mn3+ atom is allocated. Besides, a ferromagnetic ground state is observed for x>0.5 in both series independently of the presence (or not) of Jahn-Teller distortions around Mn3+, which discards either the spin flipping or the vibronic superexchange models proposed for the ferromagnetism in LaMn1-xBxO3 (B=Sc or Ga).The authors thank ESRF, ALBA, and Elettra Synchrotrons for granting beam time. Financial support from the Spanish MINECO (Projects No. MAT2012-38213-C02-01 and No. MAT2011-23791) and the Diputacion General de Aragón (CAMRADS) are acknowledged.Peer Reviewe

The two-dimensional hydrogen atom revisited

The bound state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This "accidental" degeneracy is due to the existence of a two-dimensional analogue of the quantum-mechanical Runge-Lenz vector. Reformulating the problem in momentum space leads to an integral form of the Schroedinger equation. This equation is solved by projecting the two-dimensional momentum space onto the surface of a three-dimensional sphere. The eigenfunctions are then expanded in terms of spherical harmonics, and this leads to an integral relation in terms of special functions which has not previously been tabulated. The dynamical symmetry of the problem is also considered, and it is shown that the two components of the Runge-Lenz vector in real space correspond to the generators of infinitesimal rotations about the respective coordinate axes in momentum space.Comment: 10 pages, no figures, RevTex

Boundary Conditions on Internal Three-Body Wave Functions

For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.

Dependence of the Jahn-Teller distortion in LaMn1-xScxO3 on the isovalent Mn-site substitution

We investigated the relative importance of removing the Mn3+ Jahn-Teller distortion in driving ferromagnetism in LaMn1-xScxO3 combining x-ray powder diffraction and x-ray absorption spectroscopy at the Mn and Sc K-edges. By increasing the Sc content, the orthorhombic distortion of the Pbnm cell in LaMnO3 decreases but the unit-cell remains slightly distorted in LaScO3. Besides, the nearly tetragonal-distorted MO6 in LaMnO3 continuously evolves into a nearly regular one in LaScO3. On the other hand, x-ray absorption spectra show that the MnO6 octahedron remains Jahn-Teller distorted and the ScO6 octahedron is nearly regular along the whole series. Moreover, the ordering of the Mn3+ Jahn-Teller distortion is not disrupted in the ab plane for any Sc concentration. This contrasts with the Gasubstituted compounds, where a regular MnO6 is found for x > 0.5. However, both LaMn0.5Sc0.5O3 and LaMn0.5Ga0.5O3 show ferromagnetic behavior independently of the presence (or not) of Jahn-Teller distorted Mn3+. Thus, our results point to the Mn-sublattice dilution as the main effect in driving ferromagnetism in these manganites over local structure effects previously proposed by the spin flipping or the vibronic superexchange models

Heavy metals concentrations and speciation of Pb and Ni in airborne particulate matter over two residential sites in Greater Cairo - reflection from synchrotron radiation

Synchrotron radiation-based techniques [X-ray absorption near-edge structure (XANES) and X-ray fluorescence (XRF)] combined with inductively coupled plasma-mass spectrometry (ICP-MS) were used for the assessment of heavy metals concentrations as well as lead (Pb) and nickel (Ni) speciation in airborne particulate matter (PM10) over two residential sites in Greater Cairo. Nineteen 24 h high-volume samples collected at Giza (G) Square and Helwan (H) University (Egypt) were selected for this study. Mean concentrations of heavy metals in PM10 at both sites were found to have the same descending order of Pb > Cu > Ni > Cd > Co > As, of which concentrations of Pb, Cu, Ni and Cd in H samples were higher than those in G samples. For Pb, synchrotron-based XRF results were in good agreement with concentrations obtained by ICP-MS. The XANES spectra of PM10 at the Pb L 2-edge and Ni K-edge were compared with those of Pb and Ni in model standard compounds to provide information on the potential oxidation states as well as the chemical forms of those elements. The data show that Pb has similar chemical environments in both series G and H with the predominance of Pb2+oxidation state. Nickel was found as Ni(OH)2, NiO and Ni metal in the analyzed samples. However, the content of Ni in the background filter shows a very strong interference with that of the collected PM10. Carcinogenic and non-carcinogenic risks resulting from the inhalation of the studied heavy metals were assessed for children and adult residents and were found below the safe limits, at both sites

Combining synchrotron radiation techniques for the analysis of gold coins from the Roman Empire

Four gold coins minted in the V century have been studied with non-destructive synchrotron radiation techniques, namely X-Ray Fluorescence (XRF) and X-ray Absorption Near Edge Spectroscopy (XANES). XRF data analyzed coupling standard and statistical methods were used to distinguish the composition of the alloy constituting the coins from that of successive deposits processes. Our analysis presents a quantification of the trace elements present in the metallic alloy providing interesting details for historical insight. Furthermore, on the basis of the XRF maps, some regions of interest were selected for XANES at the K-edge of Fe. Our analysis of the Fe spectra points out two main phases which can be related to Fe oxides naturally present in soil. From the relative abundance of these oxides, information on the site where the coins were found can be obtained, providing additional information on their fate across the centuries