  We study gravitationally bound, spherically symmetric equilibrium
configurations consisting of ordinary (neutron-star) matter and of a
phantom/ghost scalar field which provides the nontrivial topology in the
system. For such mixed configurations, we show the existence of static,
regular, asymptotically flat general relativistic solutions. Based on the
energy approach, we discuss the stability as a function of the core density of
the neutron matter for various sizes of the wormhole throat.
