  In this paper we study the impact of a scalar exchange on the dark matter
relic abundance by solving a plasma-modified Schroedinger equation. A
simplified model is considered where a Majorana dark matter fermion is embedded
in a U(1)$'$ extension of the Standard Model and couples with a dark Higgs via
a Yukawa interaction. We find that the dark-Higgs exchange can increase the
overclosure bounds significantly. For the largest (smallest) value of the
Yukawa coupling examined in this work, the dark matter mass is lifted from 5
TeV (0.55 TeV) to 27 TeV (0.70 TeV).
