  We study binary atomic boson-fermion mixtures confined in one dimensional box
potentials by few-body theory with contact interactions and mean-field
many-body theory with density-density interactions. A variety of correlations
and structures arise as the inter- and intra- species interactions are tuned.
Both few-body and many-body results show that miscible phase and three-chunk
phase separation are directly observable in the density profiles. Meanwhile,
two-chunk phase separation can be inferred from the few-body correlations and
many-body density profiles. We present phase diagrams of selected types of
atomic mixtures to show where different structures survive. The few-body
analysis demonstrates that two-body correlation functions can reveal
information relevant to the results from many-body calculations or experiments.
From the many-body density profiles in the phase-separation regime, we extract
the healing lengths of each species and explain the scaling behavior by an
energy-competition argument.
