Particle configurations in the $NN\bar{K}$ system

Abstract

Three-body $AAB$ model for the $NN\bar{K}(s_{NN}=0)$ kaonic cluster is considered based on the configuration space Faddeev equations. Within a single-channel approach, the difference between masses of nucleons and kaons and the charge independence breaking of nucleon-nucleon interaction are taken into consideration. We definite the particle configurations in the system according to the particle masses and pair potentials. There are two sets of the particle configurations, $pp{K}^{-}$, $np\overline{K^0}$ and $nn{\bar{K}}^0$, $np{K}^{-}$, charged and neutral. The three-body calculations are performed by applying $NN$ and $N\bar{K}$ phenomenological isospin-dependent potentials. The mass and energy spectra related to the particle configurations are presented. We evaluate the mass and energy uncertainties for the $NN\bar{K}$ model. An analogy to $NNN$ model for the ${}^3$H and ${}^3$He nuclei is proposed.

11 pages, 3 figures

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