Pair production of light pseudoscalar particles in strong inhomogeneous fields by the Schwinger mechanism

We calculate the rate for pair production of light pseudoscalars by strong inhomogeneous and static electric (magnetic) fields. We show that, in the case of axions, the stability of atoms over cosmic lifetimes is jeopardised unless the Peccei-Quinn symmetry breaking scale $f_a$ is larger than ${\cal O} (10^{10} GeV)$.