  We study the neutron star core-crust transition density $\rho_t$ with the
inclusion of the vacuum polarization in the dielectric function in the
nonlinear relativistic Hartree approach (RHAn). It is found that the strong
correlation between the $\rho_{t}$ and the scalar meson mass $m_{\sigma}$
strikingly overwhelms the uncertainty of the nuclear equation of state in the
RHAn models, in contrast to the usual awareness that $\rho_{t}$ is
predominantly sensitive to the isovector nuclear potential and symmetry energy.
The accurate extraction of $\rho_{t}$ through the future gravitational wave
measurements can thus provide a strong constraint on the longstanding
uncertainty of $m_{\sigma}$, which is of significance to better infer the
vacuum property. As an astrophysical implication, it suggests that the
correlation between $\rho_t$ and $m_\sigma$ is very favorable to reconcile the
difficulty in reproducing the large crustal moment of inertia for the pulsar
glitches with the well constrained symmetry energy.
