Equivalency of Isospin and Particle Representations for NN{\bar K} Kaonic Clusters

In the framework of the Faddeev equations in configuration space the quasi-bound states of the kaonic cluster NN{\bar K} are considered using both the isospin and particle representations. Within the isospin formalism, the '' ppK^- '' cluster is determined as NN{\bar K}(s_NN=0) system (the other possible cluster is " dK^- ''). The alternative consideration of the kaonic clusters which was recently proposed (PRC 94, 054001-7 (2016)) is the isospinless ''particle model''. In this model, the system is presented as superposition of the ppK^- and pnK⁰ states which are possible due to a particle transition. We show the equivalency of isospin and particle representations using an unitary transformation of isospin basis. Such equivalency is possible under the assumption that the probabilities to find the system in the ppK^- or pnK⁰ state are equal. Numerical calculations using phenomenological potentials are presented for the case of weak coupling of the channels. The relation of the particle representation to the theory of two-level system is addressed and discussed.