Comment on “New modes of halo excitations in the6Henucleus”

Abstract

We try to explain the differences in the 6 He dipole strength function in [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 6 He 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.In a recent paper [1] the continuum properties of 6 He were discussed within a three body nnα model. The strength functions were computed using the hyperspherical harmonics approach. The authors argued that the main features of the continuum spectrum of the nnα system can be obtained using only a few hyperspherical harmonics with the hyper-spherical quantum number K ≤ 6, if one simultaneously renormalizes the nα interaction by introducing additional attraction.However the dipole strength function in [1] differs significantly from our recent calculation [2], where we used the same three-body model. The purpose of this comment is to explain these differences.We show that the continuum state calculations of the nnα system demand a much larger basis, K ≤ 100, compared to the bound state. In such case the simple prescription to renormalize the nα interaction aiming at the bound state might not be adequate for the continuum.The method we use is, in principle, similar to that of [1] -the angular part of the wave function is expanded in terms of the hyper-spherical harmonics and then the resulting system of coupled hyper-radial equations is solved. However our approach has the following modifications [3]: i) We use Faddeev rather than the Schrödinger equation; ii) Prior to solving the hyper-radial equations we calculate the eigenvalues λ n , as functions of the hyper-radius ρ, of the angular part of the Faddeev operator. The quantities λ n (ρ)ρ −2 then serve as effective potentials in the radial equations; iii) We use analytic large-distance solutions of the Faddeev equations for short range potentials [4] which greatly enhances the method and allows fully converged calculations.The nα interaction, originally fit to the scattering data, was somewhat modified in [1,5,6] in order to compensate for the limited basis,HereP l is a projection operator on the corresponding orbital momentum state l and s is the neutron spin. All lengths are in fm and energies in MeV. Due to the over attraction this interaction fails to reproduce the experimental nα phase shifts.For the nn interaction we use a simple Gaussian [7], similar to the the one used in [5]. The potential reproduces the experimental effective range in s-wave and scattering lengths in s-and p-waves, where s 1 , s 2 are the spins of the neutrons,Ŝ 12 is the usual tensor operator.In Fig. 1 we illustrate the convergence of the lowest angular eigenvalue using, as examples, calculations with K max = 9, K max = 19, and K max = 99. Obviously the basis limited to K < 9, used in [1], is by f...

Necessary conditions for accurate computations of three-body partial decay widths

“…The inadequacy of a small basis was exhibited in Ref. [37] for the 1 − excitation of the 6 He ground state. This was further emphasized in the fairly successful prediction of the similar 1 − strength function for 11 Li in Ref.…”

Three-body resonances: spectrum of two-nucleon halo nuclei

“…This method solves the Faddeev equations in coordinate space. This is shown in Fig.1, where the dominating angular eigenvalue is shown for different values of K max for the 1 states in 6 He. The eigenvalues of the angular part enter into the radial part as effective potentials [5] and they are the key quantities to be computed accurately in order to obtain also accurate three-body wave functions.…”

“…However this is not the case in nuclear physics. In the last few years the group from the Hokkaido University has been investigating systematically the excited (unbound) states of 6 He and 11 Li, where the complex scaling method is used on top of different methods like the cluster orbital shell model [10], the Hybrid-TV model [11], or the coupled rearrangement channel variational method [12]. In the last few years the group from the Hokkaido University has been investigating systematically the excited (unbound) states of 6 He and 11 Li, where the complex scaling method is used on top of different methods like the cluster orbital shell model [10], the Hybrid-TV model [11], or the coupled rearrangement channel variational method [12].…”

“…The arrows in Fig. Energies of the 0 · and 2 · states in 6 He, 6 Li, and 6 Be, obtained after the schematic calculation (second column), including also a spin-orbit core-nucleon interaction and the Pauli principle (third column), and including also an effective three-body force (third column). We see that these energies are clearly below the experimental ones (last column in the table), although the ordering is correct.…”

“…The main examples are 6 He and 11 Li, for which a vast amount of research work can be found in the literature (see [1] for a review). The main examples are 6 He and 11 Li, for which a vast amount of research work can be found in the literature (see [1] for a review).…”