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.
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