  We consider the effect of a logarithmic f(R) theory, motivated by the form of
the one-loop effective action arising from gluons in curved spacetime, on the
structure of relativistic stars. In addition to analysing the consistency
constraints on the potential of the scalar degree of freedom, we discuss the
possibility of observational features arising from a fifth force in the
vicinity of the neutron star surface. We find that the model exhibits a
chameleon effect that completely suppresses the effect of the modification on
scales exceeding a few radii, but close to the surface of the neutron star, the
deviation from General Relativity can significantly affect the surface redshift
that determines the shift in absorption (or emission) lines. We also use the
method of perturbative constraints to solve the modified
Tolman-Oppenheimer-Volkov equations for normal and self-bound neutron stars
(quark stars).
