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A rigorous theoretical investigation is made of arbitrary amplitude nucleus acoustic solitary waves (SWs) in a fully ionized multi-nucleus plasma system (consisting of thermally degenerate electron species and non-degenerate warm light as well as heavy nucleus species). The pseudo-potential approach, which is valid for the arbitrary amplitude SWs, is employed. The subsonic and supersonic nucleus-acoustic SWs (which are found to be compressive) along with their basic features are identified. The basic properties of these subsonic and supersonic nucleus-acoustic SWs are found to be significantly modified by the effects of non and ultra-relativistically degenerate electron species, dynamics of heavy nucleus species, number densities as well as adiabatic temperatures of light and heavy nucleus species, etc. It shown that the presence of heavy nucleus species with non-degenerate (isothermal) electron species supports the existence of subsonic nucleus-acoustic SWs, and that the effects of electron degeneracies and light and heavy nucleus temperatures reduce the possibility for the formation of these subsonic nucleus-acoustic SWs. The amplitude of the supersonic nucleus-acoustic SWs in the situation of non-relativistically degenerate electron species is much smaller than that of ultra-relativistically degenerate electron species, but is much larger than that of isothermal electron species. The rise of adiabatic temperature of light or heavy nucleus species causes to decrease (increase) the amplitude (width) of the subsonic and supersonic nucleus acoustic SWs. On the other hand, the increase in the number density of light or heavy nucleus species causes to increase (decrease) the amplitude (width) of the subsonic and supersonic nucleus acoustic SWs. The results of this investigation are found to be applicable in laboratory, space, and astrophysical plasma systems.