  A quadratic semiclassical theory, regarding the interaction of gravity with a
massive scalar quantum field, is considered in view of the renormalizable
energy-momentum tensor in a multi-dimensional curved spacetime. According to
it, a self-consistent coupling between the square curvature term R^{2} and the
quantum field \Phi should be introduced in order to yield the "correct"
renormalizable energy-momentum tensor in quadratic gravity theories. The
subsequent interaction discards any higher-order derivative terms from the
gravitational field equations, but, in the expence, it introduces a geometric
source term in the wave equation for the quantum field. Unlike the conformal
coupling case (R\Phi ^{2}), this term does not represent an additional "mass"
and, therefore, the quantum field interacts with gravity not only through its
mass (or energy) content (~\Phi ^{2}), but also, in a more generic way
(R^{2}\Phi). Within this context, we propose a general method to obtain
mode-solutions for the quantum field, by means of the associated Green's
function in an anisotropic six-dimensional background.
