Origin of Borromean systems

The complex energies of the three-body resonances for one infinitely heavy particle and two non-interacting light particles are the sum of the two contributing two-body complex resonance energies. The bound state of a Borromean system originates from a resonance when the third interaction is introduced, a finite mass is allowed and proper angular momentum coupling is included. The relative importance of these contributions are investigated and the resulting structure of Borromean systems are traced back to the two-body continuum properties. The $0^+$ and $2^+$ states in $^{6}$He result from neutron-core p-states and the ground and first excited state of $^{11}$Li originate from neutron-core $s^2$ and $sp$-states.Comment: Physics Letters B, in pres

Momentum distributions and reaction mechanisms for breakup of two--neutron halos

A theoretical model able to describe fragmentation reactions of three--body halo nuclei on different targets, from light to heavy, is used to compute neutron and core momentum distributions. Both Coulomb and nuclear interactions are simultaneously included. We specify the different reaction mechanisms related to various processes. The method is applied to fragmentation of $^6$He and $^{11}$Li on C and Pb. We find good agreement with the available experimental results.Comment: 10 pages, 3 figures, Phys.Lett.B in pres

Three-body structure of the low-lying 17^{17}Ne-states

The Borromean nucleus $^{17}$Ne ($^{15}$O$+ p + p$) is investigated by using the hyperspheric adiabatic expansion for a a three-body system. The measured size of $^{15}$O and the low-lying resonances of $^{16}$F ($^{15}$O$+ p$) are first used as constraints to determine both central and spin-dependent two-body interactions. Then, the ground state structure of $^{17}$Ne is found to be an almost equal mixture of $s^2$ and $d^2$ proton-$^{15}$O relative states, the two lowest excited states have about 80% of $sd$-mixed components, and for the next two excited three-body states the proton-$^{15}$O relative s-states do not contribute. The spatial extension is as in ordinary nuclei. The widths of the resonances are estimated by the WKB transmission through the adiabatic potentials and found in agreement with the established experimental limits. We compare with experimental information and previous works.Comment: 29 pages, 7 postscript figures, to be published in Nuclear Physics

The Desirable Organizational Structure for Evolutionary Firms in Static Landscapes

In addition to the common analysis of the Kauffman NK model where the value of K and the structure of interaction is given, the aim of this paper is to study what would be the values of these two parameters if they were endogenized. Thus, a model is proposed where firms and business schools coordinate to search for high peaks in their respective landscapes using evolutionary algorithms. The main result coming out from the analysis of the model is that agents, using evolutionary algorithms, attempt to simplify the problems of coordination and this, over time, produces the existence in the economy of agents using many different strategies. (JEL-code: C61, C63, D21, D23

On the congruence subgroup problem for branch groups

We answer a question of Bartholdi, Siegenthaler and Zalesskii, showing that the congruence subgroup problem for branch groups is independent of the branch action on a tree. We prove that the congruence topology of a branch group is determined by the group; specifically, by its structure graph, an object first introduced by Wilson. We also give a more natural definition of this graph.Comment: 9 pages, no figures; minor changes in accordance with referee report, exposition improve

Isospin mixing and energy distributions in three-body decay

The structure of the second 2$^+$ resonance in $^{6}$Li is investigated with special emphasis on its isospin 0 components. The wave functions are computed in a three-body model ($\alpha$+$n$+$p$) using the hyperspherical adiabatic expansion method combined with complex scaling. In the decay into three free particles the symmetry conserving short-range interaction dominates at short distance whereas the symmetry breaking Coulomb interaction dominates at intermediate and large distances resulting in substantial isospin mixing. We predict the mixing and the energy distributions of the fragments after decay. Computations are consistent with available experiments. We conjecture that nuclear three-body decays frequently produce such large isospin mixing at large distance where the energy distributions. are determined.Comment: 5 pages, 4 figures, to be published in Physics Letters

Resonances in three-body systems with short and long-range interactions

The complex scaling method permits calculations of few-body resonances with the correct asymptotic behaviour using a simple box boundary condition at a sufficiently large distance. This is also valid for systems involving more than one charged particle. We first apply the method on two-body systems. Three-body systems are then investigated by use of the (complex scaled) hyperspheric adiabatic expansion method. The case of the 2$^+$ resonance in $^6$Be and $^6$Li is considered. Radial wave functions are obtained showing the correct asymptotic behaviour at intermediate values of the hyperradii, where wave functions can be computed fully numerically.Comment: invited talk at the 18th International Conference on Few-Body Problems in Physics, Santos-S.Paulo, August 21-26, 200

A Comparative Analysis of Self-Rectifying Turbines for the Mutriku Oscillating Water Column Energy Plant

Oscillating Water Column (OWC) based devices are arising as one of the most promising technologies for wave energy harnessing. However, the most widely used turbine comprising its power take-off (PTO) module, the Wells turbine, presents some drawbacks that require special attention. Notwithstanding different control strategies are being followed to overcome these issues; the use of other self-rectifying turbines could directly achieve this goal at the expense of some extra construction, maintenance, and operation costs. However, these newly developed turbines in turn show diverse behaviours that should be compared for each case. This paper aims to analyse this comparison for the Mutriku wave energy power plant.This work was supported by the MINECO through the Research Project DPI2015-70075-R (MINECO/FEDER, UE) and in part by the University of the Basque Country (UPV/EHU) through PPG17/33. The authors would like to thank the collaboration of the Basque Energy Agency (EVE) through Agreement UPV/EHUEVE23/6/2011, the Spanish National Fusion Laboratory (EURATOM-CIEMAT) through Agreement UPV/EHUCIEMAT08/190, and EUSKAMPUSCampus of International Excellence

Origin of three-body resonances

We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the $S$-matrix. For one infinitely heavy core and two non-interacting light particles, the complex energies of the three-body poles are the sum of the two two-body complex pole-energies. These generic relations are modified by center-of-mass effects which alone can produce a Borromean system. We show how the three-body states evolve in $^6$He, $^6$Li, and $^6$Be when the nucleon-nucleon interaction is continuously switched on. The schematic model is able to reproduce the main properties in their spectra. Realistic calculations for these nuclei are shown in detail for comparison. The implications of a core with non-zero spin are investigated and illustrated for $^{17}$Ne ($^{15}$O+p+p). Dimensionless units allow predictions for systems of different scales.Comment: 15 pages, 7 figure