XAFS spectroscopy. I. Extracting the fine structure from the absorption spectra

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing parameter and the method for raising of stability with respect to k_min variation; (ii) interpolation spline with the varied knots; (iii) the line obtained from bayesian smoothing. This methods considers various prior information and includes a natural way to determine the errors of XAFS extraction. Particular attention has been given to the estimation of uncertainties in XAFS data. Experimental noise is shown to be essentially smaller than the errors of the background approximation, and it is the latter that determines the variances of structural parameters in subsequent fitting.Comment: 16 pages, 7 figures, for freeware XAFS analysis program, see http://www.crosswinds.net/~klmn/viper.htm

Deconvolution problems in x-ray absorption fine structure

A Bayesian method application to the deconvolution of EXAFS spectra is considered. It is shown that for purposes of EXAFS spectroscopy, from the infinitely large number of Bayesian solutions it is possible to determine an optimal range of solutions, any one from which is appropriate. Since this removes the requirement for the uniqueness of solution, it becomes possible to exclude the instrumental broadening and the lifetime broadening from EXAFS spectra. In addition, we propose several approaches to the determination of optimal Bayesian regularization parameter. The Bayesian deconvolution is compared with the deconvolution which uses the Fourier transform and optimal Wiener filtering. It is shown that XPS spectra could be in principle used for extraction of a one-electron absorptance. The amplitude correction factors obtained after deconvolution are considered and discussed.Comment: 6 two-column pages, 5 eps figures; submitted to J. Phys.: Appl. Phy

A next-generation inverse-geometry spallation-driven ultracold neutron source

The physics model of a next-generation spallation-driven high-current ultracold neutron (UCN) source capable of delivering an extracted UCN rate of around an-order-of-magnitude higher than the strongest proposed sources, and around three-orders-of-magnitude higher than existing sources, is presented. This UCN-current-optimized source would dramatically improve cutting-edge UCN measurements that are currently statistically limited. A novel "Inverse Geometry" design is used with 40 L of superfluid $^4$He (He-II), which acts as a converter of cold neutrons (CNs) to UCNs, cooled with state-of-the-art sub-cooled cryogenic technology to $\sim$1.6 K. Our design is optimized for a 100 W maximum heat load constraint on the He-II and its vessel. In our geometry, the spallation target is wrapped symmetrically around the UCN converter to permit raster scanning the proton beam over a relatively large volume of tungsten spallation target to reduce the demand on the cooling requirements, which makes it reasonable to assume that water edge-cooling only is sufficient. Our design is refined in several steps to reach $P_{UCN}=2.1\times10^9\,/$s under our other restriction of 1 MW maximum available proton beam power. We then study effects of the He-II scattering kernel as well as reductions in $P_{UCN}$ due to pressurization to reach $P_{UCN}=1.8\times10^9\,/$s. Finally, we provide a design for the UCN extraction system that takes into account the required He-II heat transport properties and implementation of a He-II containment foil that allows UCN transmission. We estimate a total useful UCN current from our source of $R_{use}=5\times10^8\,/$s from a 18 cm diameter guide 5 m from the source. Under a conservative "no return" approximation, this rate can produce an extracted density of $>1\times10^4\,/$cm$^3$ in $<$1000~L external experimental volumes with a $^{58}$Ni (335 neV) cut-off potential.Comment: Submitted to Journal of Applied Physic

M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by grt_1, up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) E_n operads may be expressed through the cohomology of a suitable graph complex. Our methods also give a second proof of a result of H. Furusho, stating that the pentagon equation for grt_1-elements implies the hexagon equation

New Understanding of Ultra-Cold Neutron Production in Solid Deuterium

Our recent neutron scattering measurements of phonons and other quasi-particle excitations in solid deuterium (sD$_2$) and the extraction of the density of states for phonons and rotational transitions in sD2 have led us to a new understanding of the production of ultra-cold neutrons (UCN) in sD2. This new picture is somehow different to earlier published results for sD2. The cross section for UCN production in sD2 has been determined by using the density of states G1(E) in combination with the incoherent approximation and by a direct calibration of our measured neutron cross sections with the known cross section of the J=1 -> 0 rotational transition in deuterium. Both methods deliver new data on this cross section and agree quite well with direct measurements of this energy averaged UCN production cross section.Comment: 4 pages, 6 figure

Production of Ultra-Cold-Neutrons in Solid \alpha-Oxygen

Our recent neutron scattering measurements of phonons and magnons in solid \alpha-oxygen have led us to a new understanding of the production mechanismen of ultra-cold-neutrons (UCN) in this super-thermal converter. The UCN production in solid \alpha-oxygen is dominated by the excitation of phonons. The contribution of magnons to UCN production becomes only slightly important above E >10 meV and at E >4 meV. Solid \alpha-oxygen is in comparison to solid deuterium less effcient in the down-scattering of thermal or cold neutrons into the UCN energy regime.Comment: 4 pages, 5 figuer

Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems