  The aim of this work is to study the possible effects and biases on the
radius constraints for rotation-powered millisecond pulsars when using Thomson
approximation to describe electron scattering in the atmosphere models, instead
of using exact formulation for Compton scattering. We compare the differences
between the two models in the energy spectrum and angular distribution of the
emitted radiation. We also analyse a self-generated synthetic phase-resolved
energy spectrum, based on Compton atmosphere and the most X-ray luminous
rotation-powered millisecond pulsars observed by the Neutron star Interior
Composition ExploreR (NICER). We derive constraints for the neutron star
parameters using both the Compton and Thomson models. The results show that the
method works by reproducing the correct parameters with the Compton model.
However, biases are found in size and the temperature of the emitting hot spot,
when using the Thomson model. The constraints on the radius are still not
significantly changed, and therefore the Thomson model seems to be adequate if
we are interested only in the radius measurements using NICER.
