Vacuum polarization effect in intense laser fields

The probability of the electron-positron pair creation in vacuum by a time-dependent solution-like electric field is calculated. It has been found that, in order to have prominent pair production, the electric field intensity should be higher than the Schwinger threshold and the pulse duration should be longer than a threshold. The former condition guarantees that the electron in the negative energy state could gain enough energy to transit into a positive-energy state in Compton time. The latter condition is related to momentum requirement for the transition.