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Probabilities of a pair of fermions and bosons creation in a static andspatially uniform electric field E are represented in the Schwinger formulas byinfinite series. It is believed that in weak fields the main contribution tothe probability is given by the first term of series, however the size of theremainder apparently was analyzed by nobody. We study the mathematicalstructure of the Schwinger series by using methods developed during lastdecades and prove that the given series allows an exact summation and thecontribution of remainder growths rapidly with the field strength. As a rule,it is argued that the pair of particles begin to be produced efficiently fromthe vacuum only in the fields of strength E >= E_cr. However, the directcalculation shows that the Schwinger formula for creation of e+e- pairs isvalid only at the field intensities of E < 0.0291*E_cr. At higher fields, theprobability of pair production in an unit space-time volume exceeds unity. Inthis regard, we refine the formula for the probability of pair creation andnumerically find that in the field of strength 2.95% of E_cr the pairproduction probability is almost 100%.

Properties of the Schwinger series and pair creation in strong fields