  Nontopological fermionic solitons exist across a diverse range of particle
physics models and have rich cosmological implications. This study establishes
a general framework for calculating fermionic soliton profiles under arbitrary
scalar potentials, utilizing relativistic mean field theory to accurately
depict the interaction between the fermion condensate and the background scalar
field. Within this framework, the conventional fermion bound states are
revealed as a subset of fermionic solitons. In addition, we demonstrate how the
analytical formulae in previous studies are derived as special cases of our
algorithm, discussing the validity of such approximations. Furthermore, we
explore the phenomenology of fermionic solitons, highlighting new formation
mechanisms and evolution paths, and reconsidering the possibility of collapse
into primordial black holes.
