  In this present work, we suggest studying neutron star with a conformal
coupling by using the analytical expressions of realistic equations of state.
The equations of perturbed and nonperturbed metrics, scalar field and the
pressure of the matter are derived in order to observe the effects of the
conformal coupling on the mass, radius and tidal love number of polar and axial
types. The numerical and the analytical analysis show a different comportment
of our model from GR by varying the value of the parameters in the model. We
showed also for a particular case that the scalar field becomes vanished
outside the star which will give us the opportunity to investigate the
behaviour tidal love number of our model. Finally, a comparison between the
results of our model and the outcome from the signal of gravitational waves,
coming from the fusion of binary neutron star, was performed using the
universal relations $C$-$\Lambda$.
