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.

Double photoionization of propylene oxide: a coincidence study of the ejection of a pair of valence-shell electrons

Propylene oxide, a favorite target of experimental and theoretical studies of circular dichroism, was recently discovered in interstellar space, further amplifying the attention to its role in the current debate on protobiological homochirality. In the present work, a photoelectron-photoion-photoion coincidence technique, using an ion-imaging detector and tunable synchrotron radiation in the 18.0-37.0 eV energy range, permits us (i) to observe six double ionization fragmentation channels, their relative yields being accounted for about two-thirds by the couple (C2H4+, CH2O+) and one-fifth by (C2H3+, CH3O+); (ii) to measure thresholds for their openings as a function of photon energy; and (iii) to unravel a pronounced bimodality for a kinetic-energy-released distribution, fingerprint of competitive non-adiabatic mechanisms

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

Whole-nanoparticle atomistic modelling of the schwertmannite structure from total scattering data

Schwertmannite is a poorly crystalline nanometric iron sulfate oxyhydroxide. This mineral shows a structural variability under different environments. Because of that, the determination of its structure and, consequently, of its physical–chemical properties is quite challenging. This article presents a detailed structural investigation of the structure of schwertmannite conducted under different approaches: X-ray absorption spectroscopy, Rietveld refinement, and a combined reverse Monte Carlo and Debye function analysis of the whole nanoparticle structure. The schwertmannite model presented here is, to the auhors' knowledge, the most complete model so far reported.This work has been supported by a grant from Labex OSUG@2020 (Investissements d'avenir - ANR10 LABX56). SC was partially funded by a 'Nano Espagne' fellowship (Campus France)

Ion chemistry in the early universe: revisiting the role of HeH+ with new quantum calculations

The role of HeH+ has been newly assessed with the aid of newly calculated rates which use entirely ab initio methods, thereby allowing us to compute more accurately the relevant abundances within the global chemical network of the early universe. A comparison with the similar role of the ionic molecule LiH+ is also presented. Quantum calculations have been carried out for the gas-phase reaction of HeH+ with H atoms with our new in-house code, based on the negative imaginary potential method. Integral cross sections and reactive rate coefficients obtained under the general conditions of early universe chemistry are presented and discussed. With the new reaction rate, the abundance of HeH+ in the early universe is more than one order of magnitude larger than in previous studies. Our more accurate findings further buttress the possibility to detect cosmological signatures of HeH+.Comment: Astronomy and Astrophysics, in pres

Raising the COx Methanation Activity of a Ru/γ-Al2O3 Catalyst by Activated Modification of Metal–Support Interactions

Ru/Al2O3 is a highly stable, but less active catalyst for methanation reactions. Herein we report an effective approach to significantly improve its performance in the methanation of CO2/H2 mixtures. Highly active and stable Ru/γ-Al2O3 catalysts were prepared by high-temperature treatment in the reductive reaction gas. Operando/in situ spectroscopy and STEM imaging reveals that the strongly improved activity, by factors of 5 and 14 for CO and CO2 methanation, is accompanied by a flattening of the Ru nanoparticles and the formation of highly basic hydroxylated alumina sites. We propose a modification of the metal–support interactions (MSIs) as the origin of the increased activity, caused by modification of the Al2O3 surface in the reductive atmosphere and an increased thermal mobility of the Ru nanoparticles, allowing their transfer to modified surface sites

Quantum three-body system in D dimensions

The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schr\"{o}dinger equation is reduced to the generalized radial equations satisfied by the generalized radial functions with a given total orbital angular momentum denoted by a Young diagram $[\mu,\nu,0,...,0]$ for the SO(D) group. Only three internal variables are involved in the functions and equations. The number of both the functions and the equations for the given angular momentum is finite and equal to $(\mu-\nu+1)$.Comment: 16 pages, no figure, RevTex, Accepted by J. Math. Phy

Local structure modification in lithium rich layered Li-Mn-O cathode material

X-ray absorption spectroscopy (XAS) is applied to study the local geometry of Co, Ni, and Mn sites in a new high voltage cathode for lithium batteries. The material is a solid solution between Li$_{2}$MnO$_{3}$ and Li$_{(x)}$Mn$_{0.4}$Ni$_{0.4}$Co$_{0.2}$O$_{2}$. The XAS technique has permitted to check the local atomic structure and charge associated with the metals in a series of electrodes with different lithium concentration x, obtained during the first charge operation, and compared to the first discharge and a successive charge. The ex-situ XAS investigation on the initial activation of the cathode material (first charge) can be described by two separated reaction of LiMO$_{2}$ (M = Ni and Co) and Li$_{2}$MnO$_{3}$. The strength and limitations of the EXAFS approach in these materials is underlined