Properties of $N^{\ast }$(1535) at Finite Density in the Extended Parity-Doublet Models

We improve so called naive'' and mirror’’ models for the positive and negative parity nucleons, $N$ and $N^{\ast }$, by introducing nonlinear terms allowed by chiral symmetry. Both models in this improvement reproduce the observed nucleon axial charge in free space and reveal interesting density dependence of the axial charges for $N$ and $N^{\ast }$, and the doublet masses. A remarkable difference between the two models is found in the off-diagonal axial charge, $g_{AN{N}^{\ast }}$, which could appear either as suppression or as enhancement of $N^{\ast }\to \pi N$ decay in the medium.