A simple analytic model for astrophysical S-factors

Abstract

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).

13 pages, 5 figures, Phys. Rev. C, accepted

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• The effect of 12C + 12C rate uncertainties on the evolution and nucleosynthesis of massive stars
• Horizons: Nuclear Astrophysics in the 2020s and Beyond
• Urca cooling pairs in the neutron star ocean and their effect on superbursts
• Thermonuclear fusion in dense stars: Electron screening, conductive cooling, and magnetic field effects
• Large collection of astrophysical S-factors and its compact representation
• Impacts of the New Carbon Fusion Cross Sections on Type Ia Supernovae
• Effects of $NN$ potentials on $p$ nuclides in the A$\sim$100-120 region
• Glassy quantum nuclear pasta in neutron star crusts
• Electron screening effect on stellar thermonuclear fusion
• Enhanced dynamics in fusion of neutron-rich oxygen nuclei at above-barrier energies
• Strong plasma screening in thermonuclear reactions: Electron drop model
• Cross-section measurements of radiative proton-capture reactions in ${}^{112}$Cd at energies of astrophysical interest
• Dispersion relations applied to double-folding potentials from chiral EFT
• Theoretical exploration of $S$-factors for nuclear reactions of astrophysical importance
• Swelling of nuclei embedded in neutron-gas and consequences for fusion
• An Investigation of radiative proton-capture reactions in the Cd-In mass region
• Low-pressure THGEM-based operation with Ne+H2 Penning mixtures
• Constraining Accreted Neutron Star Crust Shallow Heating with the Inferred Depth of Carbon Ignition in X-ray Superbursts
• Assessing the impact of valence sd neutrons and protons on fusion