  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.
