Reactions induced by 9^9Be in a four-body continuum-discretized coupled-channels framework

We investigate the elastic scattering of $^9$Be on $^{208}$Pb at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.Comment: 2 pages, 1 figure. Proceedings of the International Scientific Meeting on Nuclear Physics, RABIDA15, La R\'abida (Spain), June 1-5, 201

Analytical transformed harmonic oscillator basis for three-body nuclei of astrophysical interest: Application to 6He

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6He (4He + n + n) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as 9Be and 12C, for which actual three-body continuum calculations are very involved.Comment: Accepted in Phys. Rev.

Radiative capture reaction for 17^{17}Ne formation within a full three-body model

Background: The breakout from the hot Carbon-Nitrogen-Oxigen (CNO) cycles can trigger the rp-process in type I x-ray bursts. In this environment, a competition between $^{15}\text{O}(\alpha,\gamma){^{19}\text{Ne}}$ and the two-proton capture reaction $^{15}\text{O}(2p,\gamma){^{17}\text{Ne}}$ is expected. Purpose: Determine the three-body radiative capture reaction rate for ${^{17}\text{Ne}}$ formation including sequential and direct, resonant and non-resonant contributions on an equal footing. Method: Two different discretization methods have been applied to generate $^{17}$Ne states in a full three-body model: the analytical transformed harmonic oscillator method and the hyperspherical adiabatic expansion method. The binary $p$--$^{15}$O interaction has been adjusted to reproduce the known spectrum of the unbound $^{16}$F nucleus. The dominant $E1$ contributions to the $^{15}\text{O}(2p,\gamma){^{17}\text{Ne}}$ reaction rate have been calculated from the inverse photodissociation process. Results: Three-body calculations provide a reliable description of $^{17}$Ne states. The agreement with the available experimental data on $^{17}$Ne is discussed. It is shown that the $^{15}\text{O}(2p,\gamma){^{17}\text{Ne}}$ reaction rates computed within the two methods agree in a broad range of temperatures. The present calculations are compared with a previous theoretical estimation of the reaction rate. Conclusions: It is found that the full three-body model provides a reaction rate several orders of magnitude larger than the only previous estimation. The implications for the rp-process in type I x-ray bursts should be investigated.Comment: 10 pages, 10 figures. Corrected versio

The continuum description with pseudo-state wave functions

Benchmark calculations are performed aiming to test the use of two different pseudo-state bases on the the Multiple Scattering expansion of the total Transition amplitude (MST) scattering framework. Calculated differential cross sections for p-6He inelastic scattering at 717 MeV/u show a good agreement between the observables calculated in the two bases. This result gives extra confidence on the pseudo-state representation of continuum states to describe inelastic/breakup scattering.Comment: 4 pages, 2 figures. Published in Physical Review

Simultaneous analysis of elastic scattering and transfer/breakup channels for the 6He+208Pb reaction at energies near the Coulomb barrier

The elastic and alpha-production channels for the 6He+208Pb reaction are investigated at energies around the Coulomb barrier (E_{lab}=14, 16, 18, 22, and 27 MeV). The effect of the two-neutron transfer channels on the elastic scattering has been studied within the Coupled-Reaction-Channels (CRC) method. We find that the explicit inclusion of these channels allows a simultaneous description of the elastic data and the inclusive alpha cross sections at backward angles. Three-body Continuum-Discretized Coupled-Channels (CDCC) calculations are found to reproduce the elastic data, but not the transfer/breakup data. The trivially-equivalent local polarization potential (TELP) derived from the CRC and CDCC calculations are found to explain the features found in previous phenomenological optical model calculations for this system.Comment: 7 pages, 6 figures (replaced with updated version

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Blade loss transient dynamics analysis, volume 1. Task 1: Survey and perspective

An analytical technique was developed to predict the behavior of a rotor system subjected to sudden unbalance. The technique is implemented in the Turbine Engine Transient Rotor Analysis (TETRA) computer program using the component element method. The analysis was particularly aimed toward blade-loss phenomena in gas turbine engines. A dual-rotor, casing, and pylon structure can be modeled by the computer program. Blade tip rubs, Coriolis forces, and mechanical clearances are included. The analytical system was verified by modeling and simulating actual test conditions for a rig test as well as a full-engine, blade-release demonstration

Classical Tensors and Quantum Entanglement II: Mixed States

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.Comment: 23 pages, 4 figure