The ground state properties including radii, density distribution and one neutron separation energy for C, N, O and F isotopes up to the neutron drip line are systematically studied by the fully self-consistent microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) theory. With the proton density distribution thus obtained, the charge-changing cross sections for C, N, O and F isotopes are calculated using the Glauber model. Good agreement with the data has been achieved. The charge changing cross sections change only slightly with the neutron number except for proton-rich nuclei. Similar trends of variations of proton radii and of charge changing cross sections for each isotope chain is observed which implies that the proton density plays * e-mail: mengj@pku.edu.cn 1 important role in determining the charge-changing cross sections.PACS numbers: 21.10. Gv, 24.10.Cn, 25.45.De Key words: Relativistic Continuum Hartree-Bogoliubov (RCHB) theory, charge-changing cross section, neutron-rich light nuclei, exotic nuclei Typeset using REVT E X 2 Recent progresses in the accelerator and detection techniques all around the world have made it possible to produce and study the nuclei far away from the stability line -so called "EXOTIC NUCLEI". Based on the measurement of interaction cross section with radioactive beams at relativistic energy, novel and entirely unexpected features has appeared: e.g., the neutron halo and skin as the rapid increase in the measured interaction cross-sections in the neutron-rich light nuclei [1,2].Systematic investigation of interaction cross sections for an isotope chain or an isotone chain can provide a good opportunity to study the density distributions over a wide range of isospin [3,4]. However the contribution from proton and neutron are coupled in the measurement of interaction cross section. To draw conclusion on the differences in proton and neutron density distributions definitely, a combined analysis of the interaction cross section and other experiment on either proton or neutron alone are necessary.The charge-changing cross section which is the cross section for all processes which result in a change of the atomic number for the projectile can provide good opportunity for this purpose. In Ref.[5], the total charge-changing cross section σ cc for the light stable and neutron-rich nuclei at relativistic energy on a carbon target were measured. We will study σ cc theoretically by using the fully self-consistent and microscopic relativistic continuum Hartree-Bogoliubov (RCHB) theory and the Glauber Model in the present letter.The RCHB theory [6][7][8], which is an extension of the relativistic mean field (RMF) [9][10][11] and the Bogoliubov transformation in the coordinate representation, can describe satisfactorily the ground state properties for nuclei both near and far from the β-stability line and from light to heavy or super heavy elements, as well as for the understanding of pseudo-spin symmetry in finite nuclei [12][13][14][15]. A remarkable success of the RCHB t...