  Heavy nuclei can be synthetized or entrained in gamma-ray bursts (GRBs) with
implications on the high-energy neutrino emission. By means of a Monte-Carlo
algorithm, we model nuclear cascades and investigate their impact on the
neutrino production considering kinetic dominated jets (in the internal shock
model, including a dissipative photosphere) as well as Poynting flux dominated
jets (for a jet model invoking internal-collision-induced magnetic reconnection
and turbulence, ICMART). We find that the ICMART model allows for efficient
nuclear cascades leading to an overall larger neutrino fluence than in the
other two jet models. The survival of nuclei and inefficient nuclear cascades
lead to an overall reduction of the neutrino fluence up to one order of
magnitude. However, if nuclei are disintegrated, the neutrino fluence may be
comparable to the one emitted from a jet loaded with protons. Exploring the
parameter space of jet properties, we conclude that the composition and the
bulk Lorentz factor have significant impact on the efficiency of nuclear
cascades as well as the spectral shape of the expected neutrino fluence. On the
other hand, the neutrino spectral distribution is less sensitive to the
power-law index of the accelerated population of protons or heavier nuclei. For
what concerns the diffuse emission of neutrinos from GRBs, we find that the
uncertainty due to the jet composition can be at most comparable to the one
related to the GRB cosmological rate.
