Deeply quasi-bound state in single- and double- $\bar{K}$ K ¯ nuclear clusters

Abstract

New calculations of the quasi-bound state positions in K − K − pp kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three-and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models ofKN − πΣ potentials with one-and two-pole structure of Λ(1405) resonance and separable potential models forK-K and nucleonnucleon interactions, are used. The dependence of the resulting four-body binding energy on models of KN − πΣ interaction is investigated. We obtained the binding energy of the K − K − pp quasi-bound state ∼ 80-94 MeV with the phenomenologicalKN potentials. The width is about ∼ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give ∼ 24-31 MeV width.

The drip lines of kaonic nuclei

“…Similar phenomena can be found in 12 Be. On the contrary, a large amount of the 1d 3/2,5/2 -state neutrons locate in the range of 3.2 − 3.8 fm, where the central potentials 12 Be, 28 O, 30 Ne (solid lines) and their corresponding K − nuclei (dashed lines) with a 0 = 100, 300, and 500 MeV fm −3 . FIG.…”

“…However, 13,17,19 Be (N = 9, 13, 15) are unbound systems due to pair breaking. Therefore, the neutron drip line locates at 12 Be (N = 8). The proton drip line reaches at 6 Be (N = 2).…”

“…The proton drip line reaches at 6 Be (N = 2). Experimentally, the nuclei from 6 Be (N = 2) to 16 Be (N = 12) have been observed [56], but the experimental values of S n for 12 Be (N = 8) and S p for 7 B (N = 2) are negative. Therefore, the proton and neutron drip lines locate at 6 Be (N = 2) and 12 Be (N = 8), respectively.…”

“…The theoretical results of the total energies are in quite good agreement with the experimental values. All isotopes from 12 O (N = 4) to 28 O (N = 20) exist with negative e n and e p . The separation energies S n and S p of all nuclei with N = 5 − 16 are posi-FIG.…”

“…On the theoretical side, various models were used to study the properties of K − nuclei. For example, the antisymmetrized molecular dynamics model [7], the effective chiral Lagrangian for the kaon-baryon interaction combined with a nonrelativistic baryon-baryon interaction model [8], the chiral SU(3) model [9], the chiral meson-baryon coupledchannels interaction models [10], the non-relativistic Faddeev and Faddeev-Yakubovsky calculations [11,12]. For the density functional theory, several relativistic mean field (RMF) * xrzhou@phy.ecnu.edu.cn models explored many properties of light K − nuclei, such as level inversion, binding energy, decay widths, and density distributions [13][14][15][16][17].…”