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

Anatomy of three-body decay I. Schematic models

Sequential three-body decay proceeds via spatially confined quasi-stationary two-body configurations. Direct three-body decay populates the three-body continuum without intermediate steps. The relative importance of these decay modes is discussed in a schematic model employing only Coulomb or centrifugal barrier potentials. Decisive dimensionless charge, mass and energy ratios are derived. Sequential decay is usually favored for charged particles. Small charge and small mass of high energy is preferably emitted first. Without Coulomb potential the sequential decay is favored except when both resonance energy and intermediate two-body energy are large.Comment: To be published in Nuclear Physics

Momentum distributions of particles from three-body halo fragmentation: Final state interactions

4 págs.; 3 figs.; 1 tab. ; PACS number (s): 25.60.2t, 21.45.1v, 21.60.Gx, 27.20.1nMomentum distributions of particles from nuclear breakup of fast three-body halos are calculated consistently, and applied to Li-11. The same two-body interactions between the three particles are used to calculate the ground state structure and the final state of the reaction processes. We reproduce the available momentum distributions from Li-11 fragmentation, together with the size and energy of Li-11, with a neutron-core relative state containing ap-state admixture of 20%-30%. The available fragmentation data strongly suggest an s state in Li-10 at about 50 keV and indicate a p state around 500 keV. ©1996 American Physical SocietyOne of us (E.G.) acknowledges support from the European Union through the Human Capital and Mobility program Contract No. ERBCHBGCT930320Peer Reviewe

Three-body bremsstrahlung and the rotational character of the 12C spectrum

22 págs.; 11 figs.; 6 tabs.; PACS number(s): 23.20.−g, 21.60.Gx, 21.45.−v, 27.20.+nThe electric quadrupole transitions between 0+,2+, and 4+ states in C12 are investigated in a 3α model. The three-body wave functions are obtained by means of the hyperspherical adiabatic expansion method, and the continuum is discretized by imposing a box boundary condition. Corresponding expressions for the continuum three-body (3α) bremsstrahlung and photon dissociation cross sections are derived and computed for two different α−α potentials. The available experimental energy dependence is reproduced and a series of other cross sections are predicted. The transition strengths are defined and derived from the cross sections, and compared to schematic rotational model predictions. The computed properties of the C12 resonances suggest that the two lowest bands are made, respectively, by the states {0+1,2+1,4+2} and {0+2,2+2,4+1}. The transitions between the states in the first band are consistent with the rotational pattern corresponding to three alphas in an equilateral triangular structure. For the second band, the transitions are also consistent with a rotational pattern, but with the three alphas in an aligned arrangement. ©2015 American Physical SocietyThis work was partly supported by funds provided by DGI of MINECO (Spain) under Contract No. FIS2011-23565.Peer Reviewe

Comment on "New modes of halo excitations in the 6He nucleus"

We try to explain the differences in the 6He dipole strength function in refs. [1] and [2]. We perform the full basis calculation of the strength function with the same renormalized interaction as in [1] and show that the size of the basis, needed for converged calculations of the 6He continuum spectrum, is much larger than that for the discrete spectrum. The renormalized interaction of [1] therefore cannot be used for the continuum spectrum calculations with the same basis as for the ground state.Comment: 2 pages, 3 figure

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

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

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

Cluster sum rules for three-body systems with angular-momentum dependent interactions

10 págs.; 3 figs.; 2 tabs.; 1 apéndice ; PACS number(s): 21.45.−v, 11.55.Hx, 23.20.−g, 31.15.xjWe derive general expressions for non-energy-weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum rule is usually determined by the kinetic energy operator, but we demonstrate that it has similar additional contributions from the angular momentum and parity dependence of two- and three-body potentials frequently used in three-body calculations. The importance of the different contributions is illustrated with the dipole excitations in He6. The results are compared with the available experimental data. © 2008 The American Physical Society.This work was partly supported by funds provided by DGI of MEC (Spain) under contract no. FIS2005-00640. One of us (R.D.) acknowledges support by a predoctoral I3P fellowship from CSIC and the European Social Fund.Peer Reviewe

Three-Body Halos. II. from Two- to Three-Body Asymptotics

The large distance behavior of weakly bound three-body systems is investigated. The Schr\"{o}dinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The resulting coupled set of effective radial equations are then derived. Both two- and three-body asymptotic behavior are possible and their relative importance is studied for systems where subsystems may be bound. The system of two nucleons outside a core is studied numerically in detail and the character of possible halo structure is pointed out and investigated.Comment: 16 pages, compressed and uuencoded PosrScript file, IFA-94/3