  We study the structure of neutron stars in scalar-tensor theories for the
nonminimal coupling of the form $(1+\kappa \xi \phi^{2})\cal R$. We solve the
hydrostatic equilibrium equations for two different types of scalar field
potentials and three different equations of state representative of different
degrees of stiffness. We obtain the mass-radius relations of the configurations
and determine the allowed ranges for the term $\xi\phi^2$ at the center of the
star and spatial infinity based on the measured maximum value of the mass for
neutron stars and the recent constraints on the radius coming from
gravitational wave observations. Thus we manage to limit the deviation of the
model from general relativity. We examine the possible constraints on the
parameters of the model and compare the obtained restrictions with the ones
inferred from other cosmological probes that give the allowed ranges for the
coupling constant only. In the case of the Higgs-like potential, we also find
that the central value for the scalar field cannot be chosen arbitrarily but it
depends on the vacuum expectation value of the field. Finally, we discuss the
effect of the scalar field potential on the mass and the radius of the star by
comparing the results obtained for the cases considered here.
