Theoretical Predictions of Low-Lying Three-Body Resonance States in 6He

Abstract

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.

Dipole excited states in 11Li with complex scaling

“…The same method has also been applied to study the continuum structure of 9 Be and 9 B [28] assuming these nuclei as three-body systems made by two α-particles and a neutron and a proton, respectively. Application to the two-neutron halo nucleus 6 He can be found in [29][30][31], and in [32] the case of 10 He is considered. When available, the agreement with the experimental data is satisfactory.…”

Origin of three-body resonances

“…This problem is solved by applying the complex scaling method [25,27,28,29,30], where the Jacobi coordinates x i and y i are rotated into the complex plane by an arbitrary angle θ (x i → x i e iθ , y i → y i e iθ ). This means that only the hyperradius ρ is rotated (ρ → ρe iθ ), while the five hyperangles {Ω i } remain unchanged.…”

Study of resonances in exotic drip-line nuclei by the use of super-symmetric quantum mechanics

“…In the nuclear landscape, one may find some of the observed one-neutron halo nuclei-17 B, 19 C; two-neutron halo nuclei- 6 He, 11 Li, 11,14 Be; one-proton halo nuclei-8 B, 26 P, 20 C; two-proton halo nuclei- 17 Ne, 27 S and also four-neutron halo nuclei- 14 Be, 19 B, etc [1] [2] [3] [4] [5] [6] [7] [8]. Due to low-density envelope surrounding the dense core, halo-nuclei have unusually large RMS matter radii (larger than the liquid-drop model prediction of R A ∝ A 1/3 ) as reported by Audi et al 2003 [9], Acharya et al 2013 [10].…”

“…Till now, much scientific research has been conducted to study the structure of this exciting nuclear species. Tanaka et al 2010 [6] observed of a large reaction cross-section in the drip-line nucleus 22 C, Kobayashi et al 2012 [7] conducted research on one-and two-neutron removal reactions using the most neutron-rich carbon isotopes, Gaudefroy et al 2012 [11] carried a direct mass measurements of 19 B, 22 C, 29 F, 31 Ne, 34 Na and some other light exotic nuclei. Togano et al, 2016 [12] studied interaction cross-section of the two-neutron halo nucleus 22 C. In the literature review, it is noted that for the investigation of the structure of the 2n-halo nuclei three main theoretical approaches are used-i) the microscopic model approach where the valence neutrons are supposed to move around the conglomerate of other nucleons (protons and neutrons) without having any stable core, Sääf et al [13]; ii) the three-body cluster model in which the valence nucleons are assumed to move around the structureless inert core, and iii) the microscopic cluster model in which the valence nucleons move around the deformed excited core as reported in [13] [14] [15].…”

“…And for the computation of resonant states, several theoretical approaches are employed. Some of those include the positive energy solution of the Faddeev equation by Cobis et al 1997 [17], complex coordinate rotation (CCR) by Csoto 1993 [18], Ayoma et al [19], the analytic computation of bound state energies by Tanaka et al 1997 [20], the algebraic version of resonating group method (RGM) by Vasilesky et al 2001 [21], continuum-discretized coupled-channels (CDCC) method clubbed to the cluster-orbital shell model (COSM) by Ogata et al 2013 [22], hyperspherical harmonics method (HHM) for scattering states by Danilin et al 1997 [23], etc. In most of the theoretical approaches, Jacobi coordinates are used to derive the relative coordinates after the separation of the center of mass motion.…”