  The double folding (DF) approach is one of the widely used methods for
finding nucleus-nucleus interaction potential. In the present work, the
influence of the nuclear matter density on the DF potential and on the Coulomb
barrier parameters is studied systematically for collisions of spherical
nuclei. The value of the parameter $B_Z=Z_P Z_T/(A_P^{1/3}+A_T^{1/3})$
(estimating the Coulomb barrier height) varies in these calculations from 10
MeV up to 150 MeV. The novel feature of this study is that the nuclear
densities came from the Relativistic Mean Field approach (RMF). For the
nucleon-nucleon effective interaction, the M3Y forces with the finite range
exchange term and density dependence are employed. The above barrier fusion
cross sections are calculated within the framework of the trajectory model with
surface friction. Results are compared with the previous study in which the
nuclear density came from the Hartree-Fock (HF) calculations and with the high
precision experimental data. This comparison demonstrates that i) agreement
between the theoretical and experimental cross sections obtained with RMF and
HF densities is of the same quality and ii) the values of the only adjustable
parameter (friction strength) obtained with RMF and HF densities strongly
correlate.
