  We consider theoretically the formation and stability of quasi-one
dimensional many-body excitons in GaAs quantum wire structures under external
photoexcitation conditions by solving the dynamically screened Bethe-Salpeter
equation for realistic Coulomb interaction. In agreement with several recent
experimental findings the calculated excitonic peak shows very weak carrier
density dependence upto (and even above) the Mott transition density,
$n_c\sim3\times10^5$ cm$^{-1}$. Above $n_c$ we find considerable optical gain
demonstrating compellingly the possibility of one-dimensional quantum wire
laser operation.
