  We study the dynamics of three-dimensional Bose-Einstein condensates confined
by double-well potentials using a two-mode model with an effective on-site
interaction energy parameter. The effective on-site interaction energy
parameter is evaluated for different numbers of particles ranging from a low
experimental value to larger ones approaching the Thomas-Fermi limit, yielding
important corrections to the dynamics. We analyze the time periods as functions
of the initial imbalance and find a closed integral form that includes all
interaction-driven parameters. A simple analytical formula for the
self-trapping period is introduced and shown to accurately reproduce the exact
values provided by the two-mode model. Systematic numerical simulations of the
problem in 3D demonstrate the excellent agreement of the two-mode model for
experimental parameters.
