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We reexamine the static and spherical symmetric compact star configuration in the R 2 model of the F (R) gravity theory. With asymptotic solutions for the additional scalar degrees of freedom, we refine analysis on the external geometry and settle the scalar-hair problem argued in previous works.Performing the numerical integration of the modified Tolman-Oppenheimer-Volkoff equations as a two-boundaries-value problem, we further discuss the scalar-field distribution inside the compact stars and its influence on the mass-radius relation. We show that the chameleon potential plays an essential role in determining the scalar-field profile inside the star. The scalar field often behaves as a quintessential field that effectively decreases the mass of compact stars with lower central energy density.

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