  We analyze numerically the dynamical transition to spontaneous scalarization
in neutron stars in the framework of a scalar-tensor theory of gravity where
the scalar field is free but massive, and it is coupled non minimally to
gravity in the Jordan frame. We show that the quasi-static configuration of the
star that settles after the transition can avoid the observational constraints
imposed on the amount of scalarization by several observations in binary
systems due to the presence of the mass term, which suppresses the range of the
scalar field. We also study the impact of the scalar field mass on the total
mass of the star relative to the massless scenario.
