  We study Dick quark-antiquark potential (up to a color factor)
$V_D(r)={-\alpha_s \over r} + gf \sqrt{N_c \over {2(N_c-1)}} \ln[exp(2mr)-1]$
in the heavy meson sector. This potential emerges from an effective
dilaton-gluon coupling inspired from string theory and proves to be linearly
rising at large distances which ensures quark confinement. The
semi-relativistic wave equation which appears in the theory of relativistic
quark-antiquark bound states is used. This equation is cast into a constituent
second order Schr\"{o}dinger-like equation with the inclusion of relativistic
corrections up to order $(v/c)^{2}$ in the quark speeds. The resulting equation
is solved for Dick potential via the Shifted-$l$ expansion technique (SLET).
The obtained results show that the spin-averaged energy levels of heavy-mesons
are well explained and agree with other potential models or QCD sum rules
predictions. Moreover, as a by-product, our analysis assign to the dilaton a
mass around 56.9 MeV lying within the range of many theoretical scenario of
dilatonic mass.
