  The out-of-equilibrium quantum dynamics of a bosonic Josephson junction (BJJ)
with long-range interaction is studied in real space by solving the
time-dependent many-body Schr\"odinger equation numerically accurately using
the multiconfigurational time-dependent Hartree method for bosons. Having the
many-boson wave-function at hand we can examine the impact of the range of the
interaction on the properties of the BJJ dynamics, viz. density oscillations
and their collapse, self trapping, depletion and fragmentation, as well as the
position variance, both at the mean-field and many-body level. Explicitly, the
frequency of the density oscillations and the time required for their collapse,
the value of fragmentation at the plateau, the maximal and the minimal values
of the position variance in each cycle of oscillation and the overall pace of
its growth are key to our study. We find competitive effect between the
interaction and the confining trap. The presence of the tail part of the
interaction basically enhances the effective repulsion as the range of the
interaction is increased starting from a short, finite range. But as the range
becomes comparable with the trap size, the system approaches a situation where
all the atoms feel a constant potential and the impact of the tail on the
dynamics diminishes. There is an optimal range of the interaction in which
physical quantities of the junction are attaining their extreme values.
