Context. Few unified equations of state for neutron star matter, in which core and crust are described using the same nuclear model, are available. However the use of non-unified equations of state with simplified matching between the crust and core has been shown to introduce uncertainties in the radius determination, which can be larger than the expected precision of the next generation of X-ray satellites. Aims. We aim to eliminate the dependence of the radius and mass of neutron stars on the detailed model for the crust and on the crust-core matching procedure. Methods. We solved the approximate equations of the hydrostatic equilibrium for the crust of neutron stars and obtained a precise formula for the radius that only depends on the core mass and radius, the baryon chemical potential at the core-crust interface, and at the crust surface. For a fully accreted crust one needs, additionally, the value of the total deep crustal heating per one accreted nucleon. Results. For typical neutron star masses, the approximate approach allows us to determine the neutron star radius with an error ~ 0.1% ( ~ 10 m, equivalent to a 1% inaccuracy in the crust thickness). The formalism applies to neutron stars with a catalyzed or a fully accreted crust. The difference in the neutron star radius between the two models is proportional to the total energy release due to deep crustal heating. Conclusions. For a given model of dense matter describing the neutron star core, the radius of a neutron star can be accurately determined independent of the crust model with a precision much better than the ~ 5% precision expected from the next generation of X-ray satellites. This allows us to circumvent the problem of the radius uncertainty that may arise when non-unified equations of state for the crust and core are used.
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