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Background: Proton and neutron radii are fundamental quantities of atomic nuclei. To study the sizes of short-lived unstable nuclei, there is a need for an alternative to electron scattering. Purpose: The recent paper by Horiuchi et al. [Phys. Rev. C 89, 011601(R) (2014)] proposed a possible way of extracting the matter and neutron-skin thickness of light-to medium-mass nuclei using total reaction cross section, sigma(R). The analysis is extended to medium to heavy nuclei up to lead isotopes with due attention to Coulomb breakup contributions as well as density distributions improved by paring correlation. Methods: We formulate a quantitative calculation of sigma(R) based on the Glauber model including the Coulomb breakup. To substantiate the treatment of the Coulomb breakup, we also evaluate the Coulomb breakup cross section due to the electric dipole field in a canonical-basis-time-dependent-Hartree-Fock-Bogoliubov theory in the three-dimensional coordinate space. Results: We analyze sigma(R) 's of 103 nuclei with Z = 20, 28, 40, 50, 70, and 82 incident on light targets, (1,2) H, He-4, and (12) C. Three kinds of Skyrme interactions are tested to generate those wave functions. To discuss possible uncertainty due to the Coulomb breakup, we examine its dependence on the target, the incident energy, and the Skyrme interaction. The proton is a most promising target for extracting the nuclear sizes as the Coulomb excitation can safely be neglected. We find that the so-called reaction radius, sigma(R) = root sigma(R)/pi, for the proton target is very well approximated by a linear function of two variables, the matter radius and the skin thickness, in which three constants depend only on the incident energy. We quantify the accuracy of sigma(R) measurements needed to extract the nuclear sizes. Conclusions: The proton is the best target because, once the incident energy is set, its a(R) is very accurately determined by only the matter radius and neutron-skin thickness. If sigma(R) 's at different incident energies are measured, one can determine both the proton and neutron radii for unstable nuclei as well. The total reaction cross sections calculated in this paper are given as Supplemental Material for the sake of future measurements

Extracting nuclear sizes of medium to heavy nuclei from total reaction cross sections