Two new low-lying $^6$He levels at excitation energies of about 2.4 and 2.9 MeV were observed in the experimental investigation of the p-$alpha$ coincidence spectra obtained by the $^3$H($^4$He,p$alpha$)2n four-body reaction at $E_{rm ,^4He}$ beam energy of 27.2 MeV. The relevant $E^*$ peak energy and $Gamma$ energy width spectroscopic parameters for such $^6$He$^*$ excited states decaying into the $alpha$+n+n channel were obtained by analyzing the bidimensional ($E_{rm p}$, $E_{rm alpha}$) energy spectra. The present new result of two low-lying $^6$He$^*$ excited states above the $^4$He+2n threshold energy of 0.974 MeV is important for the investigation of the nuclear structure of neutron rich light nuclei and also as a basic test for theoretical models in the study of the three-cluster resonance feature of $^6$He.
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