Title: Comprehensive classification for Bose-Fermi mixtures,
Abstract: We present analytical studies of a boson-fermion mixture at zero temperature
with spin-polarized fermions. Using the Thomas-Fermi approximation for bosons
and the local-density approximation for fermions, we find a large variety of
different density shapes. In the case of continuous density, we obtain analytic
conditions for each configuration for attractive as well as repulsive
boson-fermion interaction. Furthermore, we analytically show that all the
scenarios we describe are minima of the grand-canonical energy functional.
Finally, we provide a full classification of all possible ground states in the
interpenetrative regime. Our results also apply to binary mixtures of bosons.