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We explore effects of the light vector $U$-boson, which is weakly coupled tonucleons, on the transition density $\rho_{t}$ and pressure $P_{t}$ at theinner edge separating the liquid core from the solid crust of neutron stars.Three methods, i.e., the thermodynamical approach, the curvature matrixapproach and the Vlasov equation approach are used to determine the transitiondensity $\rho_{t}$ with the Skyrme effective nucleon-nucleon interactions. Wefind that the $\rho_{t}$ and $P_{t}$ depend on not only the ratio of couplingstrength to mass squared of the $U$-boson $g^{2}/\mu ^{2}$ but also its mass$\mu $ due to the finite range interaction from the $U$-boson exchange. Inparticular, our results indicate that the $\rho_{t}$ and $P_{t}$ are sensitiveto both $g^{2}/\mu ^{2}$ and $\mu $ if the $U$-boson mass $\mu $ is larger thanabout 2 MeV. Furthermore, we show that both $g^{2}/\mu ^{2}$ and $\mu $ canhave significant influence on the mass-radius relation and the crustal fractionof total moment of inertia of neutron stars. In addition, we study the exchangeterm contribution of the $U$-boson based on the density matrix expansionmethod, and demonstrate that the exchange term effects on the nuclear matterequation of state as well as the $\rho_{t}$ and $P_{t}$ are generallynegligible.

Effects of the U-boson on the inner edge of neutron star crusts