  We analyze the one-photon mechanism of $e^+e^-$ pair production in the
collision of nonrelativistic nuclei. The contribution of electric quadrupole
radiation of virtual photon to the corresponding cross section is found. The
effect of the finite nuclear size is considered in detail. A comparison is made
with the contribution of electric dipole radiation of virtual photon and with
the contribution of the two-photon pair production mechanism. It is shown that
the contribution of electric quadrupole radiation is dominant in a wide range
of relative velocities. The cross section for the production of $e^+e^-$ pair
with the capture of an electron by one of the nuclei is also analyzed.
