This review presents the current status of experimental searches and theoretical studies of antikaonic four-body $\bar{K}NNN$ and $\bar{K}\bar{K}NN$ clusters. Theoretical approaches within the framework of non-relativistic potential models used for the investigation of four-body $\bar{K}NNN$ and $\bar{K}\bar{K}NN$ clusters, such as the variational, Faddeev equations, and hyperspherical harmonics are considered. The results of calculations for the binding energies and the widths obtained within these methods by employing diverse sets of nucleon–nucleon, effective $\bar{K}N$, and antikaon–antikaon interactions are presented, discussed, and compared with the calculations using the method of hyperspherical harmonics in momentum representation. The presented results demonstrate that the quasibound state energy of antikaonic four-body $\bar{K}NNN$ and $\bar{K}\bar{K}NN$ clusters is not sensitive to the $NN$ interaction, and show a very strong dependence on the $\bar{K}N$ potential. Despite the strong short-range repulsion due to the $NN$ interaction in $K^{-}ppp$ and $K^{-}{K}^{-}pp$ and the weak $\bar{K}\bar{K}$ repulsion in $K^{-}{K}^{-}pp$, the antikaonic clusters $K^{-}ppp$ and $K^{-}{K}^{-}pp$ are strongly bound.

这篇综述介绍了反神教四体的实验研究和理论研究的现状。 $\overline{钾}NNN$ 和 $\overline{钾}\overline{钾}NN$集群。用于研究四体的非相对论势模型框架内的理论方法$\overline{钾}NNN$ 和 $\overline{钾}\overline{钾}NN$簇，例如变分方程、Faddeev 方程和超球面谐波被考虑在内。通过使用不同的核子-核子集，在这些方法中获得的结合能和宽度的计算结果，有效$\overline{钾}N$, 和 antikaon-antikaon 相互作用被呈现、讨论，并与使用动量表示中的超球面谐波方法的计算进行比较。结果表明，反正核四体的准束缚态能量$\overline{钾}NNN$ 和 $\overline{钾}\overline{钾}NN$ 集群不敏感 $NN$ 相互作用，并表现出非常强的依赖 $\overline{钾}N$潜在的。尽管有强烈的短程排斥$NN$ 互动 ${钾}^{-}ppp$ 和 ${钾}^{-}{钾}^{-}pp$ 和弱者 $\overline{钾}\overline{钾}$ 排斥在 ${钾}^{-}{钾}^{-}pp$, 反神子星团 ${钾}^{-}ppp$ 和 ${钾}^{-}{钾}^{-}pp$ 有很强的约束力。