The electronic structure of sigma-bonded silicon chains is calculated
in the tight-binding approximation. The exciton spectrum is calculated
by diagonalization of the full matrix of the Coulomb interaction taki
ng into account the electron-hole exchange interaction. The energy, th
e size and the radiative lifetime of excitons are computed as a functi
on of the size of the chain. The results show that chains of silicon a
toms are probably not at the origin of the visible luminescence of por
ous silicon but could explain its fast band in the blue.