  We calculate the density fluctuations of net baryon number up to sixth order
induced by the interactions of nuclear matter, and explore their relationship
with the nuclear liquid-gas phase transition (LGPT), including the stable and
metastable phase as well as the region far from the phase transition. The
results show that dramatic density fluctuations exist in the vicinity of LGPT,
and the hyperorder density fluctuations are more sensitive than the lower order
ones to the interactions and structural properties of nuclear matter. The study
also indicates that, even far away from the critical region of LGPT, the
hadronic interactions can still lead to significant hyperorder density
fluctuations. In combination with the chemical freeze-out line fitted from the
experimental data, the derived results can be referred to investigate the
chiral phase transition, nuclear LGPT, as well as the analysis of related
experimental signals.
