In this paper we study the production of pairs in no-analytic potentials. It is a well-known fact that, when
the potential is analytic the average number of produced pairs is exponentially small in ?. On the other hand,
when the potential is no-analytic, using the W.K.B. method, we prove that the average number of produced
pairs is ?????, where ? is the regularity of the potential and ? is the fine structure constant. Finally, we
give a rigorous proof of the Schwinger’s formula.