  Electron-positron pair creation due to combined nuclear Coulomb and strong
laser fields is investigated for the tunneling regime. The energy spectra and
angular distributions of the pair are found analytically for the first time.
The energy spectrum for each lepton exhibits a sharp maximum located well above
the threshold for any polarization of the laser field. The angular
distributions of leptons depend on the polarization: for the linear
polarization both leptons move predominantly along the laser beam direction;
for the circular polarization leptons are emitted in a thin-walled cone
centered on the laser beam. The spectral and angular distributions found are
governed by the intensity and frequency of the field, and the frequency
independent total pair creation rates comply with the previously known results.
A new method of calculation - the vicinal approximation - which uses the fact
that the pair production takes place in the close vicinity of the nucleus, is
suggested.
