  We study the relation between the finite-range (meson-exchange) and
zero-range (point-coupling) representations of effective nuclear interactions
in the relativistic mean-field framework. Starting from the phenomenological
interaction DD-ME2 with density-dependent meson-nucleon couplings, we construct
a family of point-coupling effective interactions for different values of the
strength parameter of the isoscalar-scalar derivative term. In the
meson-exchange picture this corresponds to different values of the
$\sigma$-meson mass. The parameters of the isoscalar-scalar and
isovector-vector channels of the point-coupling interactions are adjusted to
nuclear matter and ground-state properties of finite nuclei. By comparing
results for infinite and semi-infinite nuclear matter, ground-state masses,
charge radii, and collective excitations, we discuss constraints on the
parameters of phenomenological point-coupling relativistic effective
interaction.
