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Measurements of the t-t and p-t coincidence events in the $^3$H ($\alpha$,ttp) reaction have been obtained at $E_\alpha$ incident energy of 67.2 MeV.Various appropriate angular configurations of detectors were chosen in order toobserve the population of the $^6$He$^*$ state at around 18 MeV. Itscontribution appears at the $E_{\rm tt}$ relative energy of 6.0 MeV by theanalysis of bidimensional spectra. We found the formation of the $^6$He excitedstate at $E^* = 18.3 \pm 0.2$ MeV (with a $\Gamma$ width of 1.1 $\pm$ 0.3 MeV)by the decay into the t+t binary channel, since the threshold energy of the t+tchannel is 12.31 MeV. In each analyzed bidimensional energy spectrum of($E_{\rm t}$, $E_{\rm t}$) and ($E_{\rm p}$, $E_{\rm t}$) coincidence eventsresonance structures are present due to the formation of both $^6$He$^*$ and$^4$He$^*$ excited states. Our results on the $E^*$ and $\Gamma$ valuesregarding the $^6$He$^*$ level of about 18 MeV are compared with the resultsobtained by other reactions. Moreover, we also found new $\Gamma$ width valuesof 0.7 $\pm$ 0.3 and 0.8 $\pm$ 0.4 MeV for the 14.0 $\pm$ 0.4 and 16.1 $\pm$0.4 MeV $^6$He levels, respectively.

Experimental evidence of the $^6$He level at $E^*$ = 18.3 MeV by the $^4$He+$^3$H three-body reaction