  A widely accepted practice for treating deuteron breakup in $A(d,p)B$
reactions relies on solving a three-body $A+n+p$ Schr\"odinger equation with
pairwise $A$-$n$, $A$-$p$ and $n$-$p$ interactions. However, it was shown in
[Phys. Rev. C \textbf{89}, 024605 (2014)] that projection of the many-body
$A+2$ wave function into the three-body $A+n+p$ channel results in a
complicated three-body operator that cannot be reduced to a sum of pairwise
potentials. It contains explicit contributions from terms that include
interactions between the neutron and proton via excitation of the target $A$.
Such terms are normally neglected. We estimate the first order contribution of
these induced three-body terms and show that applying the adiabatic
approximation to solving the $A+n+p$ model results in a simple modification of
the two-body nucleon optical potentials. We illustrate the role of these terms
for the case of $^{40}$Ca($d,p$)$^{41}$Ca transfer reactions at incident
deuteron energies of 11.8, 20 and 56 MeV, using several parameterisations of
nonlocal optical potentials.
