Binding of antikaons and $$\varLambda (1405)$$ clusters in light kaonic nuclei

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