The rate of the direct decay of ^ { 40 } \mathrm { K } to the ground state of ^ { 40 } \mathrm { Ar } 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 10 ppb contamination of natural potassium requires a 20 % modulation fraction or more .
A 20 ppb 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 ^ { 40 } \mathrm { K } decays as inferred from simulation .
We propose measures to help clarify the situation .