Dynamics of supercooled water in highly compacted clays studied by neutron scattering

The freezing behavior of water confined in compacted charged and uncharged clays (montmorillonite in Na-and Ca-forms, illite in Na-and Ca-forms, kaolinite and pyrophyllite) was investigated by neutron scattering. Firstly, the amount of frozen (immobile) water was measured as a function of temperature at the IN16 backscattering spectrometer, Institute Laue-Langevin (ILL). Water in uncharged, partly hydrophobic (kaolinite) and fully hydrophobic (pyrophyllite) clays exhibited a similar freezing and melting behavior to that of bulk water. In contrast, water in charged clays which are hydrophilic could be significantly supercooled. To observe the water dynamics in these clays, further experiments were performed using quasielastic neutron scattering. At temperatures of 250, 260 and 270 K the diffusive motion of water could still be observed, but with a strong reduction in the water mobility as compared with the values obtained above 273 K. The diffusion coefficients followed a non-Arrhenius temperature dependence well described by the Vogel-Fulcher-Tammann and the fractional power relations. The fits revealed that Na-and Ca-montmorillonite and Ca-illite have similar Vogel-Fulcher-Tammann temperatures (T-VFT, often referred to as the glass transition temperature) of similar to 120 K and similar temperatures at which the water undergoes the 'strong-fragile' transition, T-s similar to 210 K. On the other hand, Na-illite had significantly larger values of T-VFT similar to 180 K and T-s similar to 240 K. Surprisingly, Ca-illite has a similar freezing behavior of water to that of montmorillonites, even though it has a rather different structure. We attribute this to the stronger hydration of Ca ions as compared with the Na ions occurring in the illite clays.

Water–montmorillonite systems: Neutron scattering and tracer throughdiffusion studies

Designs for deep geological respositories of nuclear waste include bentonite as a hydraulic and chemisorption buffer material to protect the biosphere from leakage of radionuclides. Bentonite is chosen because it is a cheap, naturally occurring material with the required properties. It consists essentially of montmorillonite, a swelling clay mineral. Upon contact with groundwater such clays can seal the repository by incorporating water in the interlayers of their crystalline structure. The intercalated water exhibits significantly different properties to bulk water in the surrounding interparticle pores, such as lower diffusion coefficients (González Sánchez et. al. 2008). This doctoral thesis presents water distribution and diffusion behavior on various time and space scales in montmorillonite. Experimental results are presented for Na- and Cs-montmorillonite samples with a range of bulk dry densities (0.8 to 1.7 g/cm3). The experimental methods employed were neutron scattering (backscattering, diffraction, time-of-flight), adsorption measurements (water, nitrogen) and tracer-through diffusion. For the tracer experiments the samples were fully saturated via the liquid phase under volume-constrained conditions. In contrast, for the neutron scattering experiments, the samples were hydrated via the vapor phase and subsequently compacted, leaving a significant fraction of interparticle pores unfilled with water. Owing to these differences in saturation, the water contents of the samples for neutron scattering were characterized by gravimetry whereas those for the tracer experiments were obtained from the bulk dry density. The amount of surface water in interlayer pores could be successfully discriminated from the amount of bulk-like water in interparticle pores in Na- and Csmontmorillonite using neutron spectroscopy. For the first time in the literature, the distribution of water between these two pore environments was deciphered as a function of gravimetric water content. The amount was compared to a geometrical estimation of the amount of interlayer and interparticle water determined by neutron diffraction and adsorption measurements. The relative abundances of the 1 to 4 molecular water layers in the interlayer were determined from the area ratios of the (001)-diffraction peaks. Depending on the characterization method, different fractions of surface water and interlayer water were obtained. Only surface and interlayer water exists in amontmorillonite with water contents up to 0.18 g/g according to spectroscopic measurements and up to 0.32 g/g according to geometrical estimations, respectively. At higher water contents, bulk-like and interparticle water also exists. The amounts increase monotonically, but not linearly, from zero to 0.33 g/g for bulk-like water and to 0.43 g/g for interparticle water. It was found that water most likely redistributes between the surface and interlayer sites during the spectroscopic measurements and therefore the reported fraction is relevant only below about -10 ºC (Anderson, 1967). The redistribution effect can explain the discrepancy in fractions between the methods. In a novel approach the fractions of water in different pore environments were treated as a fixed parameter to derive local diffusion coefficients for water from quasielastic neutron scattering data, in particular for samples with high water contents. Local diffusion coefficients were obtained for the 1 to 4 molecular water layers in the interlayer of 0.5·10–9, 0.9·10–9, 1.5·10–9 and 1.4·10–9 m²/s, respectively, taking account of the different water fractions (molecular water layer, bulk-like water). The diffusive transport of 22Na and HTO through Na-montmorillonite was measured on the laboratory experimental scale (i.e. cm, days) by tracer through-diffusion experiments. We confirmed that diffusion of HTO is independent of the ionic strength of the external solution in contact with the clay sample but dependent on the bulk dry density. In contrast, the diffusion of 22Na was found to depend on both the ionic strength of the pore solution and on the bulk dry density. The ratio of the pore and surface diffusion could be experimentally determined for 22Na from the dependence of the diffusion coefficient on the ionic strength. Activation energies were derived from the temperaturedependent diffusion coefficients via the Arrhenius relation. In samples with high bulk dry density the activation energies are slightly higher than those of bulk water whereas in low density samples they are lower. The activation energies as a function of ionic strengths of the pore solutions are similar for 22Na and HTO. The facts that (i) the slope of the logarithmic effective diffusion coefficients as a function of the logarithmic ionic strength is less than unity for low bulk dry densities and (ii) two water populations can be observed for high gravimetric water contents (low bulk dry densities) support the interlayer and interparticle porosity model proposed by Glaus et al. (2007), Bourg et al. (2006, 2007) and Gimmi and Kosakowski (2011).

Analyzing diffuse scattering with supercomputers

Two new approaches to quantitatively analyze diffuse diffraction intensities from faulted layer stacking are reported. The parameters of a probability-based growth model are determined with two iterative global optimization methods: a genetic algorithm (GA) and particle swarm optimization (PSO). The results are compared with those from a third global optimization method, a differential evolution (DE) algorithm [Storn & Price (1997). J. Global Optim. 11, 341–359]. The algorithm efficiencies in the early and late stages of iteration are compared. The accuracy of the optimized parameters improves with increasing size of the simulated crystal volume. The wall clock time for computing quite large crystal volumes can be kept within reasonable limits by the parallel calculation of many crystals (clones) generated for each model parameter set on a super- or grid computer. The faulted layer stacking in single crystals of trigonal three-pointedstar- shaped tris(bicylco[2.1.1]hexeno)benzene molecules serves as an example for the numerical computations. Based on numerical values of seven model parameters (reference parameters), nearly noise-free reference intensities of 14 diffuse streaks were simulated from 1280 clones, each consisting of 96 000 layers (reference crystal). The parameters derived from the reference intensities with GA, PSO and DE were compared with the original reference parameters as a function of the simulated total crystal volume. The statistical distribution of structural motifs in the simulated crystals is in good agreement with that in the reference crystal. The results found with the growth model for layer stacking disorder are applicable to other disorder types and modeling techniques, Monte Carlo in particular.

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion–photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for γ⁎γ⁎→ππ.

Dispersive approach to hadronic light-by-light scattering

Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from ππ intermediate states to the partial waves for the process γ * γ * → ππ. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects

We show how to avoid unnecessary and uncontrolled assumptions usually made in the literature about soft SU(3) flavor symmetry breaking in determining the two-flavor nucleon matrix elements relevant for direct detection of weakly interacting massive particles (WIMPs). Based on SU(2) chiral perturbation theory, we provide expressions for the proton and neutron scalar couplings fp,nu and fp,nd with the pion-nucleon σ term as the only free parameter, which should be used in the analysis of direct detection experiments. This approach for the first time allows for an accurate assessment of hadronic uncertainties in spin-independent WIMP-nucleon scattering and for a reliable calculation of isospin-violating effects. We find that the traditional determinations of Vfpu−fnu and fpd−fnd are off by a factor of 2.

The multiple-scattering series in few-nucleon systems

We discuss under which circumstances the resummation of the multiple-scattering series is justified from an EFT point of view. The application to πd and K̅d scattering is briefly discussed.

Roy-Steiner equations for piN scattering

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

Dispersive approach to hadronic light-by-light scattering and the muon ɡ − 2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (ɡ − 2)μ come from hadronic contributions. In particular, it can be expected that in a few years the subleading hadronic light-by-light (HLbL) contribution will dominate the theory uncertainty. We present a dispersive description of the HLbL tensor. This new, model-independent approach opens up an avenue towards a data-driven determination of the HLbL contribution to the (ɡ − 2)μ.

Virtual photon-photon scattering

Based on analyticity, unitarity, and Lorentz invariance the contribution from hadronic vacuum polarization to the anomalous magnetic moment of the muon is directly related to the cross section of e+e− → hadrons. We review the main difficulties that impede such an approach for light-by-light scattering and identify the required ingredients from experiment. Amongst those, the most critical one is the scattering of two virtual photons into meson pairs. We analyze the analytic structure of the process γ*γ* → ππ and show that the usual Muskhelishvili–Omnès representation can be amended in such a way as to remain valid even in the presence of anomalous thresholds.

First πK atom lifetime and πK scattering length measurements

The results of a search for hydrogen-like atoms consisting of π∓K±π∓K± mesons are presented. Evidence for πK atom production by 24 GeV/c protons from CERN PS interacting with a nickel target has been seen in terms of characteristic πK pairs from their breakup in the same target (178±49178±49) as well as in terms of produced πK atoms (653±42653±42). Using these results, the analysis yields a first value for the πK atom lifetime of View the MathML sourceτ=(2.5−1.8+3.0) fs and a first measurement of the S-wave isospin-odd πK scattering length View the MathML source|a0−|=13|a1/2−a3/2|=(0.11−0.04+0.09)Mπ−1 (aIaI for isospin I).

Measurement of the total cross section from elastic scattering in pp collisions at √s=7TeV with the ATLAS detector

A measurement of the total pp cross section at the LHC at √s = 7 TeV is presented. In a special run with high-β* beam optics, an integrated luminosity of 80 μb−1 was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable t . The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the |t | range from 0.01 GeV2 to 0.1 GeV2 to extrapolate to |t | →0, the total cross section, σtot(pp→X), is measured via the optical theorem to be: σtot(pp→X) = 95.35± 0.38 (stat.)± 1.25 (exp.)± 0.37 (extr.) mb, where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to |t | → 0. In addition, the slope of the elastic cross section at small |t | is determined to be B = 19.73 ±0.14 (stat.) ±0.26 (syst.) GeV−2.

Dispersion relation for hadronic light-by-light scattering: theoretical foundations

In this paper we make a further step towards a dispersive description of the hadronic light-by-light (HLbL) tensor, which should ultimately lead to a data-driven evaluation of its contribution to (g − 2) μ . We first provide a Lorentz decomposition of the HLbL tensor performed according to the general recipe by Bardeen, Tung, and Tarrach, generalizing and extending our previous approach, which was constructed in terms of a basis of helicity amplitudes. Such a tensor decomposition has several advantages: the role of gauge invariance and crossing symmetry becomes fully transparent; the scalar coefficient functions are free of kinematic singularities and zeros, and thus fulfill a Mandelstam double-dispersive representation; and the explicit relation for the HLbL contribution to (g − 2) μ in terms of the coefficient functions simplifies substantially. We demonstrate explicitly that the dispersive approach defines both the pion-pole and the pion-loop contribution unambiguously and in a model-independent way. The pion loop, dispersively defined as pion-box topology, is proven to coincide exactly with the one-loop scalar QED amplitude, multiplied by the appropriate pion vector form factors.