Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations

L\"uscher's method is routinely used to determine meson-meson, meson-baryon and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from Lattice QCD calculations - presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase-shifts describing meson-meson scattering in partial-waves with angular-momentum l<=6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase-shifts from Lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial-waves.Comment: 79 pages, 41 figure

Nucleon-Nucleon Scattering in a Harmonic Potential

The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it might be possible to determine the amplitudes for the scattering of complex systems, such as n-d, n-t or n-alpha, from the energy-eigenvalues confined to finite volumes using ab-initio bound-state techniques.Comment: 19 pages, 13 figure

Cometary implications of the internal energy distributions of the C2 and C3 radicals produced in the photolysis of the C2H and C3H2

The C2 and C3 radicals are prominent emission in the visible region of cometary spectra. Observational evidence exists that suggests these radicals are formed as granddaughter fragments in the photolysis of more stable molecules. Likely candidates for these parent molecules ar C2H2, C3H4 (allene), and CH3C2H (propyne). Recent laboratory studies were performed on all of these parent molecules and they indicate that they can indeed produce the observed cometary radicals. In the case of C2H2, the laboratory evidence suggest that C2 is formed via the following mechanisms: (1) C2H2 + photon(193 nm) yields C2H + H; and (2) C2H + photon(193 nm) yields C2 + H. Evidence is presented to show that the C2 radical produced in the second reaction occurs in a variety of electronic, vibrational, and rotational states. It is argued that this is a result of conical intersections in the potential energy curves and the density of states associated with these curves. Since this is a property of the C2H radical similar initial product state distributions are expected to occur in comets. This means that any models of the C2 emission may have to start off with rotationally excited C2 radicals in both the singlet and the triplet manifolds. When C3H4 (allene) and CH3C2H (propyne) were photolyzed, the C3 radical is formed. In the allene case, laboratory evidence shows that the C3 radical is formed via the following mechanism: (1) C3H4 + photon(193 nm) yields C3H2 + H2; and (2) C3H2 + photon(193 nm) yields C3 + H2. More C3 is formed in the case of allene than in the propyne case, even though the absorption cross section for propyne is a factor of 2 larger. This suggests that competing dissociation pathways are present during the photolysis of propyne that are not available to allene. The observed quantum state distributions of the C3 product were the same for both parent molecules, indicating that the same intermediate state is involved. These observations can be understood if the excited propyne formed in the initial absorption step isomerizes to excited allene before it dissociates to the same daughter compound. This postulate was tested by comparing RRKM calculations of the isomerization rate of excited propyne versus the decomposition rate to other products

Formulation of gradient multiaxial fatigue criteria

International audienceA formulation of gradient fatigue criteria is proposed in the context of multiaxial high-cycle fatigue (HCF) of metallic materials. The notable dependence of fatigue limit on some common factors not taken into account in classical fatigue criteria, is analyzed and modeled. Three interconnected factors, the size, stress gradient and loading effects, are here investigated. A new class of fatigue criteria extended from classical ones with stress gradient terms introduced not only in the normal stress but also in the shear stress components, is formulated. Such a formulation allows to capture gradient effects and related “size” effects, as well as to cover a wide range of loading mode, then can model both phenomena “Smaller is Stronger” and “Higher Gradient is Stronger”. Gradient versions of some classical fatigue criteria such as Crossland and Dang Van are provided as illustrations

Planets opening dust gaps in gas disks

We investigate the interaction of gas and dust in a protoplanetary disk in the presence of a massive planet using a new two-fluid hydrodynamics code. In view of future observations of planet-forming disks we focus on the condition for gap formation in the dust fluid. While only planets more massive than 1 Jupiter mass (MJ) open up a gap in the gas disk, we find that a planet of 0.1 MJ already creates a gap in the dust disk. This makes it easier to find lower-mass planets orbiting in their protoplanetary disk if there is a significant population of mm-sized particles.Comment: 5 pages, 3 figures, accepted for publication in A&A Letter