Deeply quasi-bound state in single- and double-$\bar{K}$ 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 of $\bar{K}N-\pi \Sigma$ potentials with one- and two-pole structure of $\Lambda$(1405) resonance and separable potential models for $\bar{K}$-$\bar{K}$ and nucleon-nucleon interactions, are used. The dependence of the resulting four-body binding energy on models of $\bar{K}N-\pi \Sigma$ interaction is investigated. We obtained the binding energy of the $K^{-}{K}^{-}pp$ quasi-bound state $\sim$ 80-94 MeV with the phenomenological $\bar{K}N$ potentials. The width is about $\sim$ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give $\sim$ 24-31 MeV width.

arXiv comment18 pages, 4 figures

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Cited by in corpus (5)

• Three- and four-body kaonic nuclear states: Binding energies and widths
• Structure, formation and decay of $\bar{K}NN$ system by Faddeev-AGS calculations
• Signature of $N^{\star }$ resonance in mass spectrum of the $K\bar{K}N$ decay channels
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• Possible Existence of ${}_{\varphi }^3$H, ${}_{\varphi }^4$H, ${}_{\varphi }^4$He, and ${}_{\varphi }^5$He Nuclei