Reaction rate for two--neutron capture by $^4$He

Recent investigations suggest that the neutrino--heated hot bubble between the nascent neutron star and the overlying stellar mantle of a type--II supernova may be the site of the r--process. In the preceding $\alpha$--process building up the elements to $A \approx 100$, the $^4$He(2n,$\gamma$)$^6$He-- and $^6$He($\alpha$,n)$^9$Be--reactions bridging the instability gap at $A=5$ and $A=8$ could be of relevance. We suggest a mechanism for $^4$He(2n,$\gamma$)$^6$He and calculate the reaction rate within the $\alpha$+n+n approach. The value obtained is about a factor 1.6 smaller than the one obtained recently in the simpler direct--capture model, but is at least three order of magnitude enhanced compared to the previously adopted value. Our calculation confirms the result of the direct--capture calculation that under representative conditions in the $\alpha$--process the reaction path proceeding through $^6$He is negligible compared to $^4$He($\alpha$n,$\gamma$)$^9$Be.