First measurement of the 2.4 and 2.9 MeV $^6$He three-cluster resonant states via the $^3$H($^4$He,p$\alpha$)2n four-body reaction

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.