Binding of antikaons and Lambda(1405) clusters in light kaonic nuclei

Abstract

The energy spectra of light-mass kaonic nuclei were investigated using the theoretical framework of the $0s$-orbital model with zero-range $\bar{K}N$ and $\bar{K}\bar{K}$ interactions of effective single-channel real potentials. The energies of the $\bar{K}NN$, $\bar{K}NNN$, $\bar{K}NNNN$, $\bar{K}\bar{K}N$, and $\bar{K}\bar{K}NN$ systems were calculated in the cases of weak- and deep-binding of the $\bar{K}N$ interaction, which was adjusted to fit the $\Lambda (1405)$ mass with the energy of the $\bar{K}N$ bound state. The results qualitatively reproduced the energy systematics of kaonic nuclei calculated via other theoretical approaches. In the energy spectra of the $\bar{K}NN$ and $\bar{K}\bar{K}NN$ systems, the lowest states $\bar{K}NN(J^{\pi },T=0^{-},1/2)$ and $\bar{K}\bar{K}NN(0^{+},0)$ were found to have binding energies approximately twice and four times as large as that of the $\bar{K}N(1/2^{-},0)$ state, respectively. Higher $(J^{\pi },T)$ states including $\bar{K}NN(1^{-},1/2)$, $\bar{K}\bar{K}NN(0^{+},1)$, and $\bar{K}\bar{K}NN(1^{+},1)$ were predicted at energies of 9--25 MeV below the antikaon-decay threshold. The effective $\Lambda (1405)$-$\Lambda (1405)$ interaction in the $\bar{K}\bar{K}NN$ system was also investigated via a $\bar{K}N+\bar{K}N$-cluster model. Strong and weak $\Lambda (1405)$-$\Lambda (1405)$ attractions were obtained in the $S^{\pi }=0^{+}$ and $S^{\pi }=1^{-}$ channels, respectively. The $\Lambda (1405)$-$\Lambda (1405)$ interaction in the $$\bar{K}\bar{K} NN$systemwascomparedwiththeeffective$d$-$d$interactioninthe$NNNN$ system, and the properties of dimer-dimer interactions in hadron and nuclear systems were discussed.

16 pages, 4 figures

References in corpus (16)

• Effective Kbar N interaction based on chiral SU(3) dynamics
• Faddeev calculation of a $K^{-}pp$ quasi-bound state
• Strange dibaryon resonance in the anti-KNN--piYN system
• Variational calculation of the ppK^- system based on chiral SU(3) dynamics
• Indication of a deeply bound compact K-pp state formed in the pp -> p Lambda K+ reaction at 2.85 GeV
• The basic K nuclear cluster K- pp and its enhanced formation in the p + p -> K+ + X reaction
• $\bar{K}NN$ quasi-bound state and the $\bar{K}N$ interaction: coupled-channel Faddeev calculations of the $\bar{K}NN-\pi \Sigma N$ system
• $K^{-}pp$ system with chiral SU(3) effective interaction
• Constraints on the chiral unitary $\bar{K}N$ amplitude from $\pi \Sigma K^{+}$ photoproduction data
• Energy dependence of barKN interactions and resonance pole of strange dibaryons
• Resonance energy of the barKNN-piYN system
• Variational calculations for K-few-nucleon systems
• anti-K anti-K N molecule state in three-body calculation
• The $\bar{K}NN$ system with chiral dynamics
• Search for strange tribaryon states in the inclusive ^4He(K^{-}_{stopped}, p) reaction
• Super strong nuclear force caused by migrating Kbar mesons - Revival of the Heitler-London-Heisenberg scheme in kaonic nuclear clusters