We consider the production of electron-positron pairs by the interacti
on of relativistic superthermal electrons, generated by ultraintense l
aser pulses, with high-Z material. We discuss the laser and target par
ameters required in order to optimize the pair-production rate. We exp
lore the regime when the pairs, if sufficiently confined, can start to
exponentiate in number and explore the feasibility of achieving a pai
r density approaching 10(21) cm(-3), 1/50 th that of solid-ion density
. [S0031-9007(98)07766-7].