Fusion reactions in multicomponent dense matter

Abstract

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. [Phys. Rev. C 72, 025806 (2005)] for the one-component plasma of nuclei, to the multicomponent 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 multicomponent matter (a regular lattice, a uniform mix, etc.). We apply the results to study nuclear burning in a ${}^{12}C{\text{\ensuremath{-}}}^{16}O$ 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 C-O lattice can strongly suppress carbon ignition in white dwarf cores and neutron star crusts at densities $\ensuremath{\rho}\ensuremath{\gtrsim}3\ifmmode\times\else\texttimes\fi{}{10}^{9}$ g cm${}^{\ensuremath{-}3}$ and temperatures $T\ensuremath{\lesssim}{10}^{8}$ K.