  An introduction to nucleosynthesis, the creation of the elements in the big
bang, in interstellar matter and in stars is given. The two--step process
$^4$He(2n,$\gamma$)$^6$He and the reverse photodisintegration
$^6$He($\gamma$,2n)$^4$He involving the halo nucleus $^6$He could be of
importance in the $\alpha$--process in type--II supernovae. The reaction rates
for the above processes are calculated using three--body methods and show an
enhancement of more than three orders of magnitude compared to the previous
adopted value. Direct--capture calculations give similar values for the above
reaction rates. Therefore, this method was also used to calculate the reaction
rates of the two--step processes $^6$He(2n,$\gamma$)$^8$He and
$^9$Li(2n,$\gamma$)$^{11}$Li and the reverse photodisintegration of $^8$He and
$^{11}$Li that could be also of importance in the $\alpha$-process.
