  We utilized high-energy-resolution resonant inelastic X-ray scattering (RIXS)
at both the Ta and Ni $L_3$-edges to map out element-specific particle-hole
excitations in Ta$_2$NiSe$_5$ across the phase transition. Our results reveal a
momentum dependent gap-like feature in the low energy spectrum, which agrees
well with the band gap in element-specific joint density of states calculations
based on ab initio estimates of the electronic structure in both the low
temperature monoclinic and the high temperature orthorhombic structure. Below
$T_c$, the RIXS energy-momentum map shows a minimal gap at the Brillouin zone
center ($\sim$ 0.16 eV), confirming that Ta$_2$NiSe$_5$ possesses a direct band
gap in its low temperature ground state. However, inside the gap, no signature
of anticipated collective modes with an energy scale comparable to the gap size
can be identified. Upon increasing the temperature to above $T_c$, whereas the
gap at the zone center closes, the RIXS map at finite momenta still possesses
the gross features of the low temperature map, suggesting a substantial mixing
between the Ta and Ni orbits in the conduction and valence bands, which does
not change substantially across the phase transition. Our experimental
observations and comparison to the theoretical calculations lend further
support that the phase transition and the corresponding gap opening in
Ta$_2$NiSe$_5$ is largely structural by nature with possible minor contribution
from the putative exciton condensate.
