K-condensation and quark deconfinement phase transitions in neutron stars are investigated.We use themodified quark-meson coupling model for hadronic phase and the MIT bag model for quark phase.With the equationof state (EOS) solved self-consistently,we discuss the properties of neutron stars.We find that the EOS of pure hadronmatter with condensed K^- phase should be ruled out by the redshift for star EX00748-676,while EOS containingunpaired quark matter phase with B^(1/4) being about 180 MeV could be consistent with both this observation and thebest measured mass of star PSR 1913+16.But if the recent inferred massive star among Terzan 5 with M>1.68M_⊙is confirmed,all the present EOSes with condensed phase and decor,fined phase would be ruled out.
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