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We investigate the properties of the hadron-quark mixed phase, often termedthe \textit{pasta} phase, expected to exist in the cores of massive neutronstars. To construct the equations of state (EoS), we combine an analyticalrepresentation based on the APR EoS for hadronic matter with the MIT bag modelfeaturing vector interactions for quark matter. For modeling the mixed phase,we utilize the compressible liquid drop model that consistently accounts forfinite-size and Coulomb effects. Unlike most previous analyses that treatedsurface tension as a constant free parameter and neglected curvature tension,we employ microphysical calculations using the multiple reflection expansionformalism to determine these parameters, while also ensuring theirself-consistency with the EoS. We construct an extensive set of mixed hybridEoSs by varying model parameters, solve the stellar structure equations toobtain neutron star mass-radius relationships, and select the models thatsatisfy current astrophysical constraints. Our findings closely align withcalculations using a constant surface tension in terms of EoS stiffness andresulting stellar structure. However, they reveal significant differences inthe types of geometric structures and their prevalence ranges within the mixedphase. Specifically, curvature effects enhance the emergence of tubes andbubbles at high densities despite the large value of surface tension, whilesuppressing the existence of drops and rods at low densities.

Quark-hadron pasta phase in neutron stars: the role of medium-dependent surface and curvature tensions