A review of the Yorkshire and Humber regional waste strategy

Managing waste has become a primary issue for regional planners. This article reports on the institutional process underpinning the region’s strategy and the stages in its production. It emphasises that there has been a watering down of the target for household waste production without appropriate explanation

Nuclear Reactions from Lattice QCD

One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three- nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD provides the only reliable option for performing calculations of some of the low- energy hadronic observables. With the aim of bridging the gap between lattice QCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from Lattice QCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path planned to move forward in the upcoming years.Comment: 35 pages, 13 figures, 1 table, review article for the "Nuclear Reactions from Lattice QCD" workshop hosted by the Institute for Nuclear Theory on March 2013; version 2 includes updated references and extended discussion of previous wor

Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion

The spectrum of a system with multiple channels composed of two hadrons with nonzero total momentum is determined in a finite cubic volume with periodic boundary conditions using effective field theory methods. The results presented are accurate up to exponentially suppressed corrections in the volume due to the finite range of hadronic interactions. The formalism allows one to determine the phase shifts and mixing parameters of pipi-KK isosinglet coupled channels directly from Lattice Quantum Chromodynamics. We show that the extension to more than two channels is straightforward and present the result for three channels. From the energy quantization condition, the volume dependence of electroweak matrix elements of two-hadron processes is extracted. In the non-relativistic case, we pay close attention to processes that mix the 1S0-3S1 two-nucleon states, e.g. proton-proton fusion (pp -> d+ e^+ + nu_e), and show how to determine the transition amplitude of such processes directly from lattice QCD.Comment: 20 pages, 3 figure

Two-Nucleon Systems in a Finite Volume: (II) 3S1-3D1 Coupled Channels and the Deuteron

The energy spectra of two nucleons in a cubic volume provide access to the two phase shifts and one mixing angle that define the S-matrix in the 3S1-3D1 coupled channels containing the deuteron. With the aid of recently derived energy quantization conditions for such systems, and the known scattering parameters, these spectra are predicted for a range of volumes. It is found that extractions of the infinite-volume deuteron binding energy and leading scattering parameters, including the S-D mixing angle at the deuteron pole, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with 10 fm <~ L <~ 14 fm. The viability of extracting the asymptotic D/S ratio of the deuteron wavefunction from Lattice QCD calculations is discussed.Comment: 31 pages, 17 figure

Two-Baryon Systems with Twisted Boundary Conditions

We explore the use of twisted boundary conditions in extracting the nucleon mass and the binding energy of two-baryon systems, such as the deuteron, from Lattice QCD calculations. Averaging the results of calculations performed with periodic and anti-periodic boundary conditions imposed upon the light-quark fields, or other pair-wise averages, improves the volume dependence of the deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L. However, a twist angle of pi/2 in each of the spatial directions improves the volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging the binding energy with a random sampling of twist angles improves the volume dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest lattice volumes. Using the experimentally determined phase shifts and mixing angles, we determine the expected energies of the deuteron states over a range of cubic lattice volumes for a selection of twisted boundary conditions.Comment: 20 pages, 3 figure