  Non-minimally coupled curvature-matter gravity models are an interesting
alternative to the Theory of General Relativity and to address the dark energy
and dark matter cosmological problems. These models have complex field
equations that prevent a full analytical study. Nonetheless, in a particular
limit, the behavior of a matter distribution can, in these models, be described
by a Schr\"odinger-Newton system. In nonlinear optics, the Schr\"odinger-Newton
system can be used to tackle a wide variety of relevant situations and several
numerical tools have been developed for this purpose. Interestingly, these
methods can be adapted to study General Relativity problems as well as its
extensions. In this work, we report the use of these numerical tools to study a
particular non-minimal coupling model that introduces two new potentials, an
attractive Yukawa potential and a repulsive potential proportional to the
energy density. Using the imaginary-time propagation method we have shown that
stationary solutions arise even at low energy density regimes.
