Strong binding and shrinkage of single and double <span style="text-decoration: overline;"><i>K</i></span> nuclear systems (<i>K</i>⁻<i>pp</i>, <i>K</i>⁻<i>ppn</i>, <i>K</i>⁻<i>K</i>⁻<i>p</i> and <i>K</i>⁻<i>K</i>⁻<i>pp</i>) pred

Abstract

Non-relativistic Faddeev and Faddeev-Yakubovsky calculations were made for K−pp, K−ppn, K−K−p and K−K−pp kaonic nuclear clusters, where the quasi bound states were treated as bound states by employing real separable potential models for the K−-K− and the K−-nucleon interactions as well as for the nucleon-nucleon interaction. The binding energies and spatial shrinkages of these states, obtained for various values of the interaction, were found to increase rapidly with the interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the interaction in the dense nuclear medium are given. Using the Λ(1405) ansatz with a PDG mass of 1405 MeV/c2 for K−p, the following ground-state binding energies together with the wave functions were obtained: 51.5 MeV (K−pp), 69 MeV (K−ppn), 30.4 MeV (K−K−p) and 93 MeV (K−K−pp), which are in good agreement with previous results of variational calculation based on the Akaishi-Yamazaki coupled-channel potential. The K−K−pp state has a significantly increased density where the two nucleons are located very close to each other, in spite of the inner NN repulsion. Relativistic corrections on the calculated non-relativistic results indicate substantial lowering of the bound-state masses, especially of K−K−pp, toward the kaon condensation regime. The fact that the recently observed binding energy of K−pp is much larger (by a factor of 2) than the originally predicted one may infer an enhancement of the interaction in dense nuclei by about 25% possibly due to chiral symmetry restoration. In this respect some qualitative accounts are given based on “clearing QCD vacuum” model of Brown, Kubodera and Rho.

Investigation of the structure of the few body kaonic nuclei using the method of hyperspherical functions in momentum space

“…[2]. The light kaonic clusters KNN and KNNN represent a three-and four-body systems and theoretically can be treated in the framework of a few-body physics approaches: the variational method [1], [3] - [6], the method of Faddeev [7] - [13] and Faddeev-Yakubovsky [14] equations and the method of hyperspherical harmonics (HH) [15]. Variational calculations have been focused on using a phenomenological KN potential or KN effective interactions based on chiral SU(3) dynamics [16], [4], [5], while three-body calculations solving Faddeev equations in the formulation of Alt-Grassberger-Sandhas were used separable interactions.…”

Hyperon Resonance Λ(1405) and the K−pp Three-Body Resonance

“…At the present time, all theoretical calculations constrained with the availableKN data have reported that the binding energy of "K − pp" is less than 100 MeV [10]. Recently, several ideas are proposed to understand these signals at deep binding region: One scenario is that the enhancement ofKN potential occurs due to the partial restoration of chiral symmetry [16]. If theKN potential is enhanced by 17% compared with that in vacuum, the binding energy of "K − pp" increases to be 100 MeV.…”

\(\bar{K}\)N Interactions in the Nuclear Medium and \(\bar{K}\) Nuclear Quasi-Bound States

“…2 denoted by D [13], B [14], Y [15], M [16], and W [17]), and coupled channels genuine three-body Faddeev calculations (IK [18], IS [19], S [12], R1, R2, and RC [20]). The figure illustrates that the method of solving the 3-body problem (variational or Faddeev) is less important than the choice of the underlying interaction model.…”