  We improve so called ``naive'' and ``mirror'' models for the positive and
negative parity nucleons, $N$ and $N^{*}$, 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 $N^*$, and the doublet masses. A
remarkable difference between the two models is found in the off-diagonal axial
charge, $g_{ANN^*}$, which could appear either as suppression or as enhancement
of $N^* \to \pi N$ decay in the medium.
