The sensitive correlations between the low-density halo structure and the high-density properties of the nuclear equation of state (EOS) are constructed in light kaonic nuclei with the relativistic mean-field theory. More specifically, the 1p 1/2 halo spreads out linearly with increasing the pressure and sound velocity square at supra-normal densities and decreasing the incompressibility at saturation density. These results suggest that the novel halo in light kaonic nuclei can serve as a sensitive indicator of the nuclear EOS of symmetric matter at supra-normal densities. The experimental production and detection of the light kaonic nuclei, yet to be available, is discussed in some details at last.
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