We analyze fusion reactions in dense matter composed of one or two atomic nuclei types. We pay special attention to the Coulomb tunneling problem. We compare results of the Path Integral Monte Carlo (PIMC) calculations by Militzer and Pollock (Phys. Rev. B 71, 134303, 2005) of Coulomb tunneling in nuclear reaction in dense one component matter with semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean field potential. We apply the mean field model to the reactions in mixtures of atomic species. We carefully analyze results of the extensive Monte Carlo calculations of mean field potential in one component plasma and in binary ionic mixtures and describe this results by simple fitting expression. Respective reaction rates are calculated and approximated by simple analytical expression applicable in a wide range of parameters. We analyze Gamow-peak energies of reacting ions in various reaction regimes. We discuss theoretical uncertainties of nuclear reaction rates taking burning in ¹²C-¹⁶O mixture as an example.

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