  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 Kbar N interaction, were found
to increase rapidly with the Kbar N interaction strength. Their behaviors are
shown in a reference diagram, where possible changes by varying the KbarN
interaction in the dense nuclear medium are given. Using the Lambda(1405)
ansatz with a PDG mass of 1405 MeV/ c^2 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 KbarN 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.
