  The rate of the direct decay of 40K to the ground state of 40Ar through
electron capture has not been experimentally reported. Aside from its inherent
importance for the theory of electron capture as the only such decay known of
its type (unique third-forbidden), this decay presents an irreducible
background in the DAMA experiment. We find that the presence of this
background, as well as others, poses a challenge to any interpretation of the
DAMA results in terms of a Dark Matter model with a small modulation fraction.
A 10ppb contamination of natural potassium requires a 20% modulation fraction
or more. A 20ppb contamination, which is reported as an upper limit by DAMA,
disfavors any Dark Matter origin of the signal. This conclusion is based on the
efficiency of detecting 40K decays as inferred from simulation. We propose
measures to help clarify the situation.
