We use $$ \mathcal{N} $$ N = 8 supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at $$ \mathcal{O} $$ O (G3) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known D-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by Bern et. al. in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.

Experiments are described in which a direct comparison was made between a conventional 2 kW water‐cooled sealed‐tube X‐ray source and a 30 W air‐cooled microfocus source with focusing multilayer optics, using the same goniometer, detector, radiation (Mo Kα), crystals and software. The beam characteristics of the two sources were analyzed and the quality of the resulting data sets compared. The Incoatec Microfocus Source (IµS) gave a narrow approximately Gaussian‐shaped primary beam profile, whereas the Bruker AXS sealed‐tube source, equipped with a graphite monochromator and a monocapillary collimator, had a broader beam with an approximate intensity plateau. Both sources were mounted on the same Bruker D8 goniometer with a SMART APEX II CCD detector and Bruker Kryoflex low‐temperature device. Switching between sources simply required changing the software zero setting of the 2θ circle and could be performed in a few minutes, so it was possible to use the same crystal for both sources without changing its temperature or orientation. A representative cross section of compounds (organic, organometallic and salt) with and without heavy atoms was investigated. For each compound, two data sets, one from a small and one from a large crystal, were collected using each source. In another experiment, the data quality was compared for crystals of the same compound that had been chosen so that they had dimensions similar to the width of the beam. The data were processed and the structures refined using standard Bruker and SHELX software. The experiments show that the IµS gives superior data for small crystals whereas the diffracted intensities were comparable for the large crystals. Appropriate scaling is particularly important for the IµS data.

No abstract

Although CCD instruments are now widely used in single-crystal diffraction, they have not been employed so extensively in crystallographic studies at high pressure. This paper describes some practical experience in the application of one CCD instrument, the Bruker±Nonius SMART APEX (a ®xed-1 instrument). Centring a sample in a pressure cell is complicated by the restrictions on viewing the sample imposed by the body of the cell. The data collection strategy is de®ned by the requirements that (i) the incident beam must illuminate the sample and (ii) no more than 80% of the detector should be shaded by the body of the pressure cell. High-pressure diffraction images are contaminated by powder lines from the gasket and backing-disk materials, which form part of the pressure cell, and very intense spots from the diamond anvils. Procedures for the selection of spots for indexing are described. Integration routines attempt to harvest intensity data from regions of the detector that are shaded by the body of the pressure cell, and a procedure for generating dynamic masks is described. Shading also reduces the volume of reciprocal space that can be sampled, although this can be increased by performing data collections at more than one pressure-cell setting. Corrections for absorption are carried out in a two-stage procedure comprising an analytical correction for absorption by the cell, followed by a second multi-scan correction. Data sets collected at high pressure often contain some signi®cant outliers; these can be identi®ed during merging using a robust resistant weighting scheme, as described by Blessing [J.

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and $$ \mathcal{N} $$ N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $$ \mathcal{O} $$ O (G3) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

No abstract

The synthesis of the highly encapsulating pyrazolylborate ligand hydrotris(3-p-cumenyl-5-methylpyrazolyl)borate (L = Tp(Cum,Me)) and of its zinc hydroxide complex L.Zn-OH (1) are described. 1 is converted by H(2)S into the hydrosulfide complex L.Zn-SH (2). Both 1 and 2 seem to be contaminated with traces of the isomeric species 1' and 2' containing L' with one 3-methyl-5-p-cumenyl substituent. Thermal condensations of 1' and 2 yield the molecular zinc oxide and sulfide complexes L'.Zn-O-Zn.L' (3') and L.Zn-S-Zn.L (4). The hydroxide complex 1 has been found to react readily with cumulated double-bonded species: CO(2) is incorporated in alcoholic solutions to form the alkylcarbonate complexes L.Zn-OCOOR (5). Similarly, CS(2) in ethanol forms the O-ethyl dithiocarbonate complex L.Zn-SC(S)OEt (6). SO(2) is converted to a bridging sulfito ligand in L.Zn-O-SO-O-Zn.L (7), and phenyl isothiocyanate is bound as a thiocarbamidato ligand in L.Zn-SC(O)NHPh (8). Complexes 1, 2, 2', 3', 4, 5, and 6 have been confirmed by structure determinations and complexes 7 and 8 by spectral data.

No abstract