Predictions are made for the structure of a second 2 ϩ resonance, the soft dipole mode and unnatural parity modes in the 6 He continuum. We use a structure model which describes the system as a three-body ␣ϩNϩN cluster structure, giving the experimentally known properties of 6 He and 6 Li, and use the distortedwave impulse approximation ͑DWIA͒ reaction theory appropriate for dilute matter. The presence of both resonant and nonresonant structures in the halo excitation continuum is shown to be manifest in chargeexchange reactions as well as inelastic scattering with single nucleons. ͓S0556-2813͑97͒50302-5͔PACS number͑s͒: 21.45.ϩv, 21.60.Gx, 24.30.Gd, 27.20.ϩn The known spectrum of 6 He contains only the 0 ϩ bound state and the well known 2 ϩ (E*ϭ1.8 MeV͒ three-body resonance, and then a desert in the three-body ␣ϩnϩn continuum up to the 3 H ϩ 3 H threshold at about 13 MeV ͓1͔. While for 11 Li a response ͑E1 strength͒ function has been reconstructed from exclusive experiments ͓2,3͔, such information is still lacking for 6 He. Except for momentum distributions from fragmentation experiments with 6 He beams ͓4-6͔, the only data are from charge-exchange reactions with 6 Li to the 6 He continuum, but with poor statistics and limited angles ͓7-9͔.The recent developments of radioactive nuclear beam techniques and of dynamic approaches to three-body continuum theory ͓10͔ make it possible to investigate to what extent our knowledge of the lightest Borromean halo nucleus 6 He is complete. What are the specific features of the continuum of a system with a halo ground state? Below we give predictions of a second 2 ϩ three-body resonance that may be accessible in experiment, and also ͑a much less pronounced͒ 1 ϩ resonance. The so-called ''soft dipole mode'' suggested in ͓11,12͔ still needs clarification ͓13͔. According to existing three-body models it is not a simple binary core -point dineutron resonance, neither in 11 Li nor probably in 6 He, but although this seems now widely accepted, further tests within these three-body models are desirable. It shows no three-body pole structure, as discussed, e.g., in ͓14͔, and therefore it is still an open question whether the ''soft dipole mode'' is just a dynamical enhancement arising from final state interactions in the direct excitation of the three-body continuum. It is now possible for experiments to tell whether the three-body frameworks are adequate, since these models are shown in the present paper to give rise to other soft modes of other multipolarities. Such modes were suggested in ͓15͔, but need both theoretical and experimental clarification. We believe that the predictions given below are reliable as guide for future experiments, and that the observation of the dipole and other modes predicted here would support the validity of three-body models and their representation of the ''soft dipole mode'' as not being a genuine three-body resonance.The nucleus 6 He has in past years been used as a reference case, with the most reliable information on the binary core-n interac...

The general properties of intrinsic energy correlations in the three-body continuum of Borromean halo nuclei are considered. A model that describes the system as a three-body α + n + n cluster structure and reproduces the experimentally known properties of 6 He and 6 Li is used to study low-lying resonances and soft modes. The intrinsic correlated structure of the 6 He continuum reveals a unique structure for three-body 2 + 1 , 2 + 2 , and 1 + 1 resonances and a lack of resonant structure in soft dipole and monopole modes.

Four-body distorted wave theory appropriate for nucleon-nucleus reactions leading to 3-body continuum excitations of two-neutron Borromean halo nuclei is developed. The peculiarities of the halo bound state and 3-body continuum are fully taken into account by using the method of hyperspherical harmonics. The procedure is applied for A = 6 test-bench nuclei; thus we report detailed studies of inclusive cross sections for inelastic 6 He(p,p ′ ) 6 He * and charge-exchange 6 Li(n,p) 6 He * reactions at nucleon energy 50 MeV. The theoretical low-energy spectra exhibit two resonance-like structures. The first (narrow) is the excitation of the well-known 2 + three-body resonance. The second (broad) bump is a composition of overlapping soft modes of multipolarities 1 − , 2 + , 1 + , 0 + whose relative weights depend on transferred momentum and reaction type. Inelastic scattering is the most selective tool for studying the soft dipole excitation mode.Recent success in developing experimental methods for dripline nuclei, that in particular allow exploration of halo phenomena in light nuclei, has put on the agenda a need for appropriate theoretical methods which take into account the peculiarities of weakly bound and spatially extended systems. For Borromean two-neutron halo nuclei ( 6 He, 11 Li, etc.) an understanding of the essential halo structure has been obtained in the framework of 3-body models [1]. Reactions involving these nuclei present however, at least a 4-body problem. The direct solution of 4-body systems is extremely difficult, and approximate methods are required. For high energy elastic scattering and relativistic fragmentation of Borromean halo nuclei, a 4-body Glauber method has been developed [2,3]. For Coulomb breakup or electromagnetic dissociation (EMD) the first order (Alder-Winther) perturbation theory or an equivalent semiclassical treatment [4] has been used, but with exact 3-body continuum wave functions [5][6][7]. Also for the (anti)neutrino induced reactions on 6 Li populating the 6 He and 6 Be 3-body continua, have proper final state wave functions recently been used [8].The most reliable information on properties of halo nuclei, especially for the low-lying part of excitation spectra, is experimentally obtainable by intermediate energy elastic and inelastic scattering and charge-exchange reactions. The distorted wave theory is the most common way to analyse such processes [9], but for halo systems their spatial granularity as well as peculiarities of their quantum structure have to be taken into account. The 3-body interaction dynamics defines the low-lying part of excitation spectra, in particular the soft modes of Borromean systems, and has to be treated properly. Until now, only the hyperspherical harmonics (HH) method [10] is able to provide a formulation of the scattering theory to the 3-body Borromean continuum. The Faddeev equations technique [11] has been developed to investigate breakup of 3-nucleon systems, but has hitherto not been applied to investigate the continuum in Borromean...

Spatial correlations in the three-body continuum of Borromean (having no bound binary subsystems) threebody systems are discussed. The hyperspherical harmonics method is used to investigate low-lying resonances and the soft dipole mode in the two-neutron halo nucleus 6 He, which has only the ␣ + n + n continuum for excitation energies below 13 MeV. The spatial correlations reveal characteristic structures for true three-body resonances, a moderate amplification in the interior region for above-barrier resonances and long-range correlations in the cases of three-body 1 − virtual and 0 + continuum states.

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Energy correlations in transitions from the bound state to the three-body continuum of Borromean halo nuclei are considered. A core+n + n three-body cluster model which reproduces the experimentally known properties of 6 He and 11 Li has been used to study the low-lying resonances and soft modes. An analysis of the correlated responses in 6 He shows that in the case of the narrow three-body 2 + 1 resonance the transition energy correlations are the same as in the intrinsic correlated structure in 3 → 3 scattering. They differ significantly for wide 2 + 2 , 1 + 1 resonances, and also for the soft dipole and monopole modes, where, due to the transition operators, the intertwining of the ground state and the three-body continuum plays a significant role.

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