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Using the cluster orbital shell model of the 4 He+n+n three-body system, we investigate lowlying resonance states described by the P-shell configurations of two valence neutrons in "He. Applying the complex scaling method, we calculate resonance energies and decay widths (lifetimes) of excited o+, 1 + and z+ states. In addition to the first excited z+ state, which has experimentally been observed and reproduced well by this model, we predict the second z+ (£..,=3.43 MeV, r=4.75 MeV), the first 1+ (£..,=3.75 MeV, r=6.39 MeV) and the second o+ (E.r=4.69 MeV, r=9.45 MeV) three-body resonance states. § 1. IntroductionThe purpose of this paper is to present a theoretical study of the low-lying three-body resonance states in 6 He, which are described within the p-shell configurations of two valence neutrons around the 4 He-core nucleus. On the basis of our previous work, I> we attempt to extend our knowledge of the excitation mechanism and spectroscopic properties of excited resonance states in 6 He, which is typical among neutron-rich nuclei.In a previous paper/> we investigated the weak binding mechanism bringing about the exotic neutron halo or skin structure of 6 He 2 > by using a developed 4 He+ n + n three-body model. To understand the weak binding, we emphasized the importance of the neutron-neutron correlation in addition to the mean field correlation. It was shown that both correlations are adequately described by the so-called hybrid-TV model, in which the extended cluster model (ECM) 3 > is combined with the cluster orbital shell model (COSM). 4 > Furthermore, we employed the more reliable 4 He-n interaction to fit observed 4 He+ n phase shift data including higher partial waves. The calculated binding energy 0.784 MeV of the 4 He+ n+ n model reproduces well the experimental value 0.975 MeV.In addition to the successful result of the binding energy, we investigated excited states of 6 He. The 2+ state is observed as a resonance state with resonance energy 0.822±0.025 MeV and width 0.113±0.020 MeV. 5 > This excited state is a genuine three-body resonance state above the three-body threshold but below the two-body threshold. To study such a three-body resonance state, we have applied the complex scaling method 6 > to the 4 He+ n+ n system, which is a very powerful method to determine resonance energies and widths of many-body systems with correct boundary conditions. 7 H> By this method, we predicted the 2+ resonance state at the resonance energy 1.03 MeV and with the width 0.260 MeV. The excitation energy 1.81 MeV with respect to the theoretical ground state energy is in very good agreement with the experimental value 1.80 MeV.

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