  We investigate theoretically the behavior of a one-dimensional interacting
Bose-Fermi mixture with equal masses and equal repulsive interactions between
atoms at finite temperature in the scheme of thermodynamic Bethe ansatz.
Combining the Yang-Yang thermodynamic formalism with local-density
approximation in a harmonic trap, we calculate the density distribution of
bosons and fermions numerically by treating the radially and axially excited
states as discrete and continuous ones, respectively. Our result from exactly
solvable solutions may be used as a touchstone for one-dimensional interacting
Bose-Fermi mixture for experimental data fitting where mean-field theoretical
approaches fail.
