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We propose a physically transparent analytic model of astrophysical S-factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for non-resonant fusion reactions. For any given reaction, the S(E)-model contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parameterize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with 9 parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important 12C+12C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E <= 2-3 MeV).
Numerous nuclear reactions in the crust of accreting neutron stars are strongly affected by dense plasma environment. Simulations of superbursts, deep crustal heating and other nuclear burning phenomena in neutron stars require astrophysical S-factor
Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2
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