  We compute families of spherically symmetric neutron-star models in
two-derivative scalar-tensor theories of gravity with a massive scalar field.
The numerical approach we present allows us to compute the resulting spacetimes
out to infinite radius using a relaxation algorithm on a compactified grid. We
discuss the structure of the weakly and strongly scalarized branches of
neutron-star models thus obtained and their dependence on the linear and
quadratic coupling parameters $\alpha_0$, $\beta_0$ between the scalar and
tensor sectors of the theory, as well as the scalar mass $\mu$. For highly
negative values of $\beta_0$, we encounter configurations resembling a
"gravitational atom", consisting of a highly compact baryon star surrounded by
a scalar cloud. A stability analysis based on binding-energ calculations
suggests that these configurations are unstable and we expect them to migrate
to models with radially decreasing baryon density {\it and} scalar field
strength.
