Nuclear fusion in dense matter: Reaction rate and carbon burning

Abstract

In this paper we analyze the nuclear fusion rate between equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime). The rate is determined by Coulomb barrier penetration in dense environments and by the astrophysical S-factor at low energies. We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate which covers all cases. The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate. The results are illustrated for the example of the ^{12}C+^{12}C fusion reaction. This reaction is very important for the understanding of nuclear burning in evolved stars, in exploding white dwarfs producing type Ia supernovae, and in accreting neutron stars. The S-factor at stellar energies depends on a reliable fit and extrapolation of the experimental data. We calculate the energy dependence of the S-factor using a recently developed parameter-free model for the nuclear interaction, taking into account the effects of the Pauli nonlocality. For illustration, we analyze the efficiency of carbon burning in a wide range of densities and temperatures of stellar matter with the emphasis on carbon ignition at densities rho > 10^9 g/cc.Comment: 22 pages, 6 figures, accepted for publication in PR

Effects of mutual excitations in the fusion of carbon isotopes

“…There is, unfortunately, a very large uncertainty in the predicted fusion cross sections for 12 C+ 12 C that are needed in a stellar environment [1], partly because the cross sections are difficult to measure down to the low energies that are of interest, and partly because the data contain strong resonance structures that make it difficult to extrapolate the measured cross sections to low energy. In order to get some constraints on the extrapolation it is instructive to analyze the existing fusion data for 13 C+ 13 C by Trentalange et al [2] and Charvet et al [3], and also of the 12 C+ 13 C data by Dayras et al [4] and Notani et al [5], because these data do not exhibit strong resonance features.…”

Large collection of astrophysicalSfactors and their compact representation

“…Their physics is described, for instance, by Salpeter and Van Horn [5] and applied in later work (e.g. [6,7,25,31] and references therein). Pycnonuclear reactions occur at high densities and involve very neutron-rich nuclei [16,17], immersed in a see of free neutrons available in the inner crust.…”

“…S(E)-factors calculated using the São Paulo potential have been compared previously [6,25,28] with experimental data and with theoretical calculations performed using other models such as coupled-channels and fermionic molecular dynamics ones. Let us stress that the calculated values of S(E) are uncertain due to nuclear physics effects -due to using the São Paulo model with the NL3 nucleon density distribution.…”

“…The plasma effects were described by Salpeter and Van Horn [5] (also see [6,7,25,31,33] and references therein). They modify the interaction potential U (r) but mainly at sufficiently large r, typically larger than nuclear scales, whereas we discuss the nuclear physics effects which influence U (r) at smaller r. It is commonly thought that the plasma physics and nuclear physics effects are distinctly different and can be considered separately.…”

“…Such isotopes can appear during nuclear burning in stellar matter, particularly, in the cores of white dwarfs and envelopes of neutron stars. The calculations have been performed using the São Paulo potential in the frame of the barrier penetration model [25]. Nuclear densities of reactants have been obtained in Relativitic Hartree-Bogoliubov (RHB) theory [26] employing the NL3 parametrization for relativistic mean field Lagrangian [27] and Gogny D1S force for pairing.…”