Large collection of astrophysicalSfactors and their compact representation

Abstract

Numerous nuclear reactions in the crust of accreting neutron stars are strongly affected by a dense plasma environment. Simulations of superbursts, deep crustal heating, and other nuclear burning phenomena in neutron stars require astrophysical $S$ factors for these reactions (as a function of center-of-mass energy $E$ of colliding nuclei). A large database of $S$ factors is created for about 5000 nonresonant fusion reactions involving stable and unstable isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si. It extends the previous database of about 1000 reactions involving isotopes of C, O, Ne, and Mg. The calculations are performed using the S\~ao Paulo potential and the barrier penetration formalism. All calculated $S$ data are parameterized by an analytic model for $S(E)$ proposed before [Phys. Rev. C 82, 044609 (2010)] and further elaborated here. For a given reaction, the present $S(E)$ model contains three parameters. These parameters are easily interpolated along reactions involving isotopes of the same elements with only seven input parameters, giving an ultracompact, accurate, simple, and uniform database. The $S(E)$ approximation can also be used to estimate theoretical uncertainties of $S(E)$ and nuclear reaction rates in dense matter, as illustrated for the case of the ${}^{34}$Ne${+}^{34}$Ne reaction in the inner crust of an accreting neutron star.