  Since physics of the dark sector components of the Universe is not yet
well-understood, the phenomenological studies of non-minimal interaction in the
dark sector could possibly pave the way to theoretical and experimental
progress in this direction. Therefore, in this work, we intend to explore some
features and consequences of a phenomenological interaction in the dark sector.
We use the Planck 2018, BAO, JLA, KiDS and HST data to investigate two
extensions of the base $\Lambda$CDM model, viz., (i) we allow the interaction
among vacuum energy and dark matter, namely the I$\Lambda$CDM model, wherein
the interaction strength is proportional to the vacuum energy density and
expansion rate of the Universe, and (ii) the I$\Lambda$CDM scenario with free
effective neutrino mass and number, namely the $\nu$I$\Lambda$CDM model. We
also present comparative analyses of the interaction models with the companion
models, namely, $\Lambda$CDM, $\nu\Lambda$CDM, $w$CDM and $\nu w$CDM. In both
the interaction models, we find non-zero coupling in the dark sector up to 99\%
CL with energy transfer from dark matter to vacuum energy, and observe a
phantom-like behavior of the effective dark energy without actual ``phantom
crossing". The well-known tensions on the cosmological parameters $H_0$ and
$\sigma_8$, prevailing within the $\Lambda$CDM cosmology, are relaxed
significantly in these models wherein the $\nu$I$\Lambda$CDM model shows
consistency with the standard effective neutrino mass and number. Both the
interaction models find a better fit to the combined data compared to the
companion models under consideration.
