  We measure and explain scintillator non-proportionality and gamma quenching
of CaWO4 at low energies and low temperatures. Phonons that are created
following an interaction in the scintillating crystal at temperatures of 15mK
are used for a calorimetric measurement of the deposited energy, and the
scintillation light is measured with a separate cryogenic light detector.
Making use of radioactivity intrinsic to the scintillating crystal, the
scintillator non-proportionality is mapped out to electron energies <5keV. The
observed behavior is in agreement with a simple model based on Birks' law and
the stopping power dE/dx for electrons. We find for Birks' constant
$k_B=(18.5\pm0.7)$nm/keV in CaWO4. Gamma lines allow a measurement of the
reduced light yield of photons with respect to electrons, as expected in the
presence of scintillator non-proportionality. In particular, we show that
gamma-induced events in CaWO4 give only about 90 percent of the light yield of
electrons, at energies between 40keV and 80keV.
