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We present the proton-total reaction cross sections σR by comparing the experimental data with the Glauber model calculation using four sets of nucleon-nucleon cross sections used in literature (free nucleon-nucleon cross sections (NNCS),phenomenological NNCS,Bruckner-type NNCS and Pauli NNCS) and different nuclear densities for symmetric and asymmetric nuclei.For light symmetric target nuclei,the experimental σR data are well reproduced by the former three NNCS with the ground state density distributions of relativistic mean-field theory.On the other hand,for asymmetry heavier target nuclei,the calculations of the σ R data depend significantly on the nuclear density distribution at large radius in the low energy region.The experimental σR of these nuclei are well reproduced by the empirical 3pF density distribution and the in-medium NNCS.The neutron surface distributions are also discussed based on the 3 pF nuclear charge distributions.