  The transmission of silicon crystals irradiated by 24 GeV/c protons and
reactor neutrons has been measured for photon energies, $E{\gamma}$, between
0.95 and 1.3 eV. From the transmission data the absorption coefficient
${\alpha}$ is calculated, and from ${\alpha}(E_{\gamma})$ the fluence
dependence of the band-gap energy, $E_{gap}$, and the energy of transverse
optical phonons, $E_{ph}$, determined. It is found that within the experimental
uncertainties of about 1 meV neither $E_{gap}$ nor $E_{ph}$ depend on fluence
up to the maximum fluence of $1 \times 10^{17}$ cm$^{-2}$ of the measurements.
The value of $E_{gap}$ agrees within about 1 meV with the generally accepted
value, if an exciton-binding energy of 15 meV is assumed. A similar agreement
is found for $E_{ph}$. For the extraction of $E_{gap}$ and $E_{ph}$ the second
derivative of $\sqrt{{\alpha}(E{\gamma} )}$ smoothed with a Gaussian kernel has
been used.
