  Using Density Matrix renormalization group (DMRG), we study the ground state
properties of spin one-half fermions and scalar bosons in the soft-core limit,
with weak s-wave inter and intra species interactions. We considered the system
subject to one-dimensional (1D) optical lattice and a superimposed potential at
zero temperature, in the framework of Bose-Fermi-Hubbard model. We found that
for certain fillings and interaction parameters, a transmutation occurs between
the ground states of bosons and fermions when the densities are exchanged. We
too report that the density distributions of bosons and fermions overlap with
each other in a bosonic and fermionic Mott plateau, when the interaction
parameters fulfill the relationship $U_{BB}>U_{BF}<U_{BF}$. We also find that
the fermions are repelled out of the central region of the trap for
sufficiently strong $U_{FF}$ interaction, exhibiting phase separation of Bose
and Fermi components.
