  We analyze the propagatory nucleus-acoustic wave (NAW) modes excitable in the
completely degenerate (CD) core and in its nearly degenerate (ND) ambience of
the ONe and CO white dwarfs (WDs). It is based on three-component spherical
hydrodynamic quantum plasma consisting of tiny non-thermal quantum electrons,
classical thermal light nuclear species (LNS), and classical thermal heavy
nuclear species (HNS). The inner concentric layer-wise electronic pressures are
judiciously modelled. The electronic energy distribution governed by the
Fermi-Dirac (FD) thermostatistical distribution law involves both the
thermodynamical temperature and chemical potential. Our exploration emphasizes
on the transition state between the thermodynamical temperature and the Fermi
temperature for the borderline regions of intermediate degeneracy. A normal
spherical mode analysis procedurally yields a sextic generalized linear
dispersion relation highlighting the plasma multiparametric dependency of the
NAW-features. A numerical illustrative platform is constructed to investigate
the full NAW propagatory and dispersive behaviours. We demonstrate that the NAW
in ONe (CO) WDs exhibits sensible growth characteristics at near the
transcritical (supercritical) wave zone. The temperature-sensitivity of the
NAW-growth is more (less) prominent in ONe (CO) WDs. It could be hopefully
useful to see the internal structure of compact astroobjects from the
asteroseismic probe-perspective of collective quantum interaction processes.
