  A new method is used to investigate the tunneling between two weakly-linked
Bose-Einstein condensates confined in double-well potential traps. The
nonlinear interaction between the atoms in each well contributes to a finite
chemical potential, which, with consideration of periodic instantons, leads to
a remarkably high tunneling frequency. This result can be used to interpret the
newly found Macroscopic Quantum Self Trapping (MQST) effect. Also a new kind of
first-order crossover between different regions is predicted.
