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

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. (2005) for the one-component plasma of nuclei, to the multi-component 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 multi-component matter (a regular lattice, a uniform mix, etc.). We apply the results to study nuclear burning in a carbon_12-oxygen_16 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 CO lattice can strongly suppress carbon ignition in white dwarf cores and neutron star crusts at densities > 3e9 g cm^{-3} and temperatures T<1e8 K.Comment: 16 pages, 5 figures, to appear in Phys. Rev.

The temperature in the crust of an accreting neutron star, which comprises its outermost kilometre, is set by heating from nuclear reactions at large densities, neutrino cooling and heat transport from the interior. The heated crust has been thought to affect observable phenomena at shallower depths, such as thermonuclear bursts in the accreted envelope. Here we report that cycles of electron capture and its inverse, β(-) decay, involving neutron-rich nuclei at a typical depth of about 150 metres, cool the outer neutron star crust by emitting neutrinos while also thermally decoupling the surface layers from the deeper crust. This 'Urca' mechanism has been studied in the context of white dwarfs and type Ia supernovae, but hitherto was not considered in neutron stars, because previous models computed the crust reactions using a zero-temperature approximation and assumed that only a single nuclear species was present at any given depth. The thermal decoupling means that X-ray bursts and other surface phenomena are largely independent of the strength of deep crustal heating. The unexpectedly short recurrence times, of the order of years, observed for very energetic thermonuclear superbursts are therefore not an indicator of a hot crust, but may point instead to an unknown local heating mechanism near the neutron star surface.

X-ray observations of transiently accreting neutron stars during quiescence provide information about the structure of neutron star crusts and the properties of dense matter. Interpretation of the observational data requires an understanding of the nuclear reactions that heat and cool the crust during accretion, and define its nonequilibrium composition. We identify here in detail the typical nuclear reaction sequences down to a depth in the inner crust where the mass density is ρ = 2 × 10 12 g cm −3 using a full nuclear reaction network for a range of initial compositions. The reaction sequences differ substantially from previous work. We find a robust reduction of crust impurity at the transition to the inner crust regardless of initial composition, though shell effects can delay the formation of a pure crust somewhat to densities beyond ρ = 2 × 10 12 g cm −3 . This naturally explains the small inner crust impurity inferred from observations of a broad range of systems. The exception are initial compositions with A ≥ 102 nuclei, where the inner crust remains impure with an impurity parameter of Q imp ≈ 20 due to the N = 82 shell closure. In agreement with previous work we find that nuclear heating is relatively robust and independent of initial composition, while cooling via nuclear Urca cycles in the outer crust depends strongly on initial composition. This work forms a basis for future studies of the sensitivity of crust models to nuclear physics and provides profiles of composition for realistic crust models.

Despite much effort in the past decades, the C-burning reaction rate is uncertain by several orders of magnitude, and the relative strength between the different channels 12 C( 12 C, α) 20 Ne, 12 C( 12 C, p) 23 Na, and 12 C( 12 C, n) 23 Mg is poorly determined. Additionally, in C-burning conditions a high 12 C+ 12 C rate may lead to lower central C-burning temperatures and to 13 C(α, n) 16 O emerging as a more dominant neutron source than 22 Ne(α, n) 25 Mg, increasing significantly the s-process production. This is due to the chain 12 C(p, γ ) 13 N followed by 13 N(β+) 13 C, where the photodisintegration reverse channel 13 N(γ, p) 12 C is strongly decreasing with increasing temperature. Presented here is the impact of the 12 C+ 12 C reaction uncertainties on the s-process and on explosive p-process nucleosynthesis in massive stars, including also fast rotating massive stars at low metallicity. Using various 12 C+ 12 C rates, in particular an upper and lower rate limit of ∼50,000 higher and ∼20 lower than the standard rate at 5 × 10 8 K, five 25 M stellar models are calculated. The enhanced s-process signature due to 13 C(α, n) 16 O activation is considered, taking into account the impact of the uncertainty of all three C-burning reaction branches. Consequently, we show that the p-process abundances have an average production factor increased up to about a factor of eight compared with the standard case, efficiently producing the elusive Mo and Ru proton-rich isotopes. We also show that an s-process being driven by 13 C(α, n) 16 O is a secondary process, even though the abundance of 13 C does not depend on the initial metal content. Finally, implications for the Sr-peak elements inventory in the solar system and at low metallicity are discussed.

We have performed for the first time a comprehensive study of the sensitivity of r-process nucleosynthesis to individual nuclear masses across the chart of nuclides. Using the latest version (2012) of the Finite-Range Droplet Model, we consider mass variations of ±0.5 MeV and propagate each mass change to all affected quantities, including Q-values, reaction rates, and branching ratios. We find such mass variations can result in up to an order of magnitude local change in the final abundance pattern produced in an r-process simulation. We identify key nuclei whose masses have a substantial impact on abundance predictions for hot, cold, and neutron star merger r-process scenarios and could be measured at future radioactive beam facilities.

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 São 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 12 C+ 12 C 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).

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