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We use a modified SU(2) chiral sigma model to study nuclear matter at highdensity using mean field approach. We also study the phase transition ofnuclear matter to quark matter in the interior of highly dense neutron stars.Stable solutions of Tolman-Oppenheimer-Volkoff equations representing hybridstars are obtained with a maximum mass of 1.69 $M_{\odot}$, radii around 9.3kms and a quark matter core constituting nearly 55-85 % of the star radii.Comment: 19 pages, 9 figures, accepted for Mod. Phys. Letts.

PHASE TRANSITION AND HYBRID STAR IN AN SU(2) CHIRAL SIGMA MODEL