The goal of this research is to explore the nuclear fusion reactions among heavy nuclei in the dense crusts of neutron stars. Nuclear fusion reactions of atomic nuclei and strange quark matter nuggets are also considered. These reactions are also known as pycnonuclear reactions. This study uses one of the best available nucleon-nucleon potential to calculate pycnonuclear reaction rates, which is the density-dependent Michigan 3-range Yukawa (M3Y) potential. M3Y has both attractive and repulsive contributions. In previous studies the less realistic Sao Paulo nucleon-nucleon potential has been used. This potential does not contain a repulsive contribution. Comparing the pycnonuclear reaction rates of both nucleon-nucleon potentials will reveal the significance of the repulsion part found in the M3Y. The repulsion is expected to decrease the total pycnonuclear reaction rates in the neutron star's crust. These reaction rates are key inputs for nuclear reaction network calculations, which predict which atomic nuclei exist at a certain density in the crust of a neutron star.