Next‐to‐next‐to‐leading order post‐Newtonian spin‐orbit Hamiltonian for self‐gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin‐orbit Hamiltonian for two self‐gravitating spinning compact objects. If at least one of the objects is rapidly rotating, then the corresponding interaction is comparable in strength to a 3.5PN effect. The result in the present paper in fact completes the knowledge of the post‐Newtonian Hamiltonian for binary spinning black holes up to and including 3.5PN. The Hamiltonian is checked via known results for the test‐spin case and via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.     

Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

The next‐to‐next‐to‐leading order post‐Newtonian spin‐orbit and spin(1)‐spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt‐Deser‐Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter‐only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short‐range behavior of the integrands around the sources. The Hamiltonian of a test‐spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post‐Newtonian approximate) Poincaré algebra are applied. Along the way a self‐contained overview for the computation of the 3PN ADM point‐mass Hamiltonian is provided, too.     

High‐resolution stimulated Raman spectroscopy and analysis of the ν1/ν5 (C–H) stretching dyad of C2H4

The high‐resolution stimulated Raman spectra of the ν₁/ν₅ C–H stretching bands of C₂H₄ have been recorded and analyzed by means of the tensorial formalism developed in Dijon for X₂Y₄ asymmetric‐top molecules. A total of 689 lines (428 for ν₅ and 261 for ν₁) were assigned and fitted as a dyad including Coriolis coupling constants. We obtained a global root mean square deviation of 4.39 × 10^{− 3} cm^{− 1} (4.61 × 10^{− 3} cm^{− 1} for ν₁, 4.25 × 10^{− 3} cm^{− 1} for ν₅). The nearby 2ν₂ band, extrapolated from ν₂, was included in the analysis. However, no interaction parameter involving it could be fitted. The analysis is quite satisfactory, although some parts of ν₅ are not very well reproduced, probably indicating some yet unidentified resonances. This region is indeed quite dense, with many interacting dark states that cannot be included at present. Copyright © 2012 John Wiley & Sons, Ltd.     

Facile Synthesis of Gd(OH)3‐Doped Fe3O4 Nanoparticles for Dual‐Mode T1‐ and T2‐Weighted Magnetic Resonance Imaging Applications

The facile hydrothermal synthesis of polyethyleneimine (PEI)‐coated iron oxide (Fe₃O₄) nanoparticles (NPs) doped with Gd(OH)₃ (Fe₃O₄‐Gd(OH)₃‐PEI NPs) for dual mode T₁‐ and T₂‐weighted magnetic resonance (MR) imaging applications is reported. In this approach, Fe₃O₄‐Gd(OH)₃‐PEI NPs are synthesized via a hydrothermal method in the presence of branched PEI and Gd(III) ions. The PEI coating onto the particle surfaces enables further modification of poly(ethylene glycol) (PEG) in order to render the particles with good water dispersibility and improved biocompatibility. The formed Fe₃O₄‐Gd(OH)₃‐PEI‐PEG NPs have a Gd/Fe molar ratio of 0.25:1 and a mean particle size of 14.4 nm and display a relatively high r₂ (151.37 × 10^?3m ^?1 s^?1) and r₁ (5.63 × 10^?3m ^?1 s^?1) relaxivity, affording their uses as a unique contrast agent for T₁‐ and T₂‐weighted MR imaging of rat livers after mesenteric vein injection of the particles and the mouse liver after intravenous injection of the particles, respectively. The developed Fe₃O₄‐Gd(OH)₃‐PEI‐PEG NPs may hold great promise to be used as a contrast agent for dual mode T₁‐ and T₂‐weighted self‐confirmation MR imaging of different biological systems.