  Neutron stars (NSs) in scalar-tensor theories of gravitation with the
phenomenon of spontaneous scalarization can develop significant deviations from
general relativity. Cases with a massless scalar were studied widely. Here we
compare the NS scalarizations in the Damour--Esposito-Far{\`e}se theory, the
Mendes-Ortiz theory, and the $\xi$-theory with a massive scalar field.
Numerical solutions for slowly rotating NSs are obtained. They are used to
construct the X-ray pulse profiles of a pair of extended hot spots on the
surface of NSs. We also calculate the tidal deformability for NSs with
spontaneous scalarization which is done for the first time with a massive
scalar field. We show the universal relation between the moment of inertia and
the tidal deformability. The X-ray pulse profiles, the tidal deformability, and
the universal relation may help to constrain the massive scalar-tensor theories
in X-ray and gravitational-wave observations of NSs, including the Neutron star
Interior Composition Explorer (NICER) satellite, Square Kilometre Array (SKA)
telescope, and LIGO/Virgo/KAGRA laser interferometers.
