  The effect of strongly repulsive interactions on the tunneling amplitude of
hard-sphere (HS) bosons confined in a simple cubic (sc) optical lattice plus
tight external harmonic confinement in continuous space is investigated. The
quantum variational Monte Carlo (VMC) and the variational path integral Monte
Carlo (VPI) techniques are used at zero temperature. The effects of the lattice
spacing $\pi/k$ on the tunneling amplitude is also considered. The occupancies
of the lattice sites as a function of the repulsion between the bosons are
further revealed. Our chief result is, that for a small number of bosons (N=8)
the overlap of the wave functions in neighboring wells does not change with an
increase of the repulsive interactions and changes only minimally for a larger
number of particles (N=40). The tunneling amplitude rises with a reduction in
the lattice spacing. In addition, the occupancy of the center of the trap
decreases in favor of a rise in the occupancy of the lattice sites at the edges
of the trap with increasing HS repulsion. Further, it was found that the energy
per particle at certain optical depths is insensitive to the number of
particles and variations in the HS diameter of the bosons. In order to support
our results, we compare the VMC results with corresponding VPI results.
