Effects of $\Lambda$(1405) on the Structure of Multi-Antikaonic Nuclei

Multi-strangeness system in hadronic matter has received much attention toward understanding high-density QCD.Recently deeply bound antikaonic nuclear states have been studied extensively. We have investigated multi-antikaonic nuclei (MKN), where several $K^-$ mesons are bound in the nucleus. In this paper, we extend our framework to take into account the $\Lambda$(1405) ($\Lambda^{\ast}$) and consider its effects on the structure of the MKN. We base our study on the relativistic mean-field theory (RMF), coupled with $\bar K$-nucleon ($N$) and $\bar K-\bar K$ interactions which respect chiral symmetry. The $\Lambda^{\ast}$ is introduced as a pole contribution to the energy together with the range effects as the second-order perturbation with respect to the relevant axial-vector current. The density profiles of the nucleons and $K^-$ for the MKN are obtained. It is shown that the $I$=0 $\bar KN$ attraction is enhanced as a result of avoiding the $\Lambda^{\ast}$ pole. Therefore both protons and $K^-$ mesons become denser around the center of the MKN as compared with the previous result without the range terms and $\Lambda^{\ast}$. We also discuss behavior of the binding energy of the MKN by systematically changing the number of the embedded $K^-$, $|S|$.