  The nuclear structure dependence of direct reactions that remove a pair of
like or unlike nucleons from a fast $^{12}$C projectile beam are considered.
Specifically, we study the differences in the two-nucleon correlations present
and the predicted removal cross sections when using $p$-shell shell-model and
multi-$\hbar\omega$ no-core shell-model (NCSM) descriptions of the two-nucleon
overlaps for the transitions to the mass $A$=10 projectile residues. The NCSM
calculations use modern chiral two-nucleon and three-nucleon (NN+3N)
interactions. The $np$-removal cross sections to low-lying $T$=0, $^{10}$B
final states are enhanced when using the NCSM two-nucleon amplitudes. The
calculated absolute and relative partial cross sections to the low energy
$^{10}$B final states show a significant sensitivity to the interactions used,
suggesting that assessments of the overlap functions for these transitions and
confirmations of their structure could be made using final-state-exclusive
measurements of the $np$-removal cross sections and the associated momentum
distributions of the forward travelling projectile-like residues.
