The Cryogenic Dark Matter Search (CDMS II) experiment aims to detect dark matter particles that elastically scatter from nuclei in semiconductor detectors. The resulting nuclear-recoil energy depositions are detected by ionization and phonon sensors. Neutrons produce a similar spectrum of low-energy nuclear recoils in such detectors, while most other backgrounds produce electron recoils. The absolute energy scale for nuclear recoils is necessary to interpret results correctly. The energy scale can be determined in CDMS II silicon detectors using neutrons incident from a broad-spectrum $^{252}$Cf source, taking advantage of a prominent resonance in the neutron elastic scattering cross section of silicon at a recoil (neutron) energy near 20 (182) keV. Results indicate that the phonon collection efficiency for nuclear recoils is $4.8^{+0.7}_{-0.9}$% lower than for electron recoils of the same energy. Comparisons of the ionization signals for nuclear recoils to those measured previously by other groups at higher electric fields indicate that the ionization collection efficiency for CDMS II silicon detectors operated at $sim$4 V/cm is consistent with 100% for nuclear recoils below 20 keV and gradually decreases for larger energies to $sim$75% at 100 keV. The impact of these measurements on previously published CDMS II silicon results is small.
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