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The transmission of silicon crystals irradiated by 24 GeV/c protons and reactor neutrons has been measured for photon energies, E _γ , between 0.95 and 1.3 eV. From the transmission data the absorption coefficient α is calculated, and from α ( E _γ ) 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 × 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.