We analyze thermonuclear and pycnonuclear fusion reactions in dense matter containing atomic nuclei of different types .
We extend a phenomenological expression for the reaction rate , proposed recently by Gasques et al . ( ( 11 ) ) for the one-component plasma of nuclei , to the multi-component plasma .
The expression contains several fit parameters which we adjust to reproduce the best microscopic calculations available in the literature .
Furthermore , we show that pycnonuclear burning is drastically affected by an ( unknown ) structure of the multi-component matter ( a regular lattice , a uniform mix , etc . ) .
We apply the results to study nuclear burning in a ^ { 12 } { C } ^ { 16 } { O } mixture .
In this context we present new calculations of the astrophysical S -factors for carbon-oxygen and oxygen-oxygen fusion reactions .
We show that the presence of a CO lattice can strongly suppress carbon ignition in white dwarf cores and neutron star crusts at densities \rho \gtrsim 3 \times 10 ^ { 9 } g cm ^ { -3 } and temperatures T \lesssim 10 ^ { 8 } K .