THEORETICAL ESTIMATES OF STELLARe^–CAPTURES. I. THE HALF-LIFE OF⁷Be IN EVOLVED STARS

Abstract

The enrichment of Li in the Universe is still unexplained, presenting various puzzles to astrophysics. One open issue is that of obtaining reliable estimates for the rate of e − -captures on 7 Be, for T and ρ conditions different from the solar ones. This is of crucial importance to model the Galactic nucleosynthesis of Li. In this framework, we present here a new theoretical method for calculating the e − -capture rate in conditions typical of evolved stars. Furthermore, we show how our approach compares with state-of-the-art techniques for solar conditions, where various estimates are available. Our computations include: i) "traditional" calculations of the electronic density at the nucleus, to which the e − -capture rate for 7 Be is proportional, for different theoretical approaches including the Thomas-Fermi, Poisson-Boltzmann and Debye-Hückel (DH) models of screening, ii) a new computation, based on a formalism that goes beyond the previous ones, adopting a mean-field "adiabatic" approximation to the scattering process. The results obtained with the new approach as well as with the traditional ones and their differences are discussed in some detail, starting from solar conditions, where our approach and the DH model essentially converge to the same solution. We then analyze the applicability of both our method and the DH model to a rather broad range of T and ρ values, embracing those typical of red giant stars, where both bound and continuum states contribute to the capture. We find that, over a wide region of the parameter space explored, the DH approximation does not really stand, so that the more general method we suggest should be preferred. As a first application, we briefly reanalyze the 7 Li abundances in RGB and AGB stars of the Galactic Disk in the light of a revision in the Be-decay only; we however underline that the changes we find in the electron density at the nucleus would induce effects also on the electron screening (for p-captures on Li itself, as well as for other nuclei) so that our new approach might have rather wide astrophysical consequences.

ASTROPHYSICAL IMPACT OF THE UPDATED9Be(p,α)6Li AND10B(p,α)7Be REACTION RATES AS DEDUCED BY THM

“…The study of the 10 B(p,α) 7 Be reaction is of importance in nuclear astrophysics because of the difficulty in measuring the corresponding S(E)-factor at Gamow energies and the astrophysical community's interest in the production/destroying processes of the unstable 7 Be isotope (see, for instance, Simonucci et al 2013). Indeed, the 8.701 MeV excited level of 11 C dominates the S(E)-factor trend at low-energies, being this an s-wave resonance in the 10 B-p system at 10 keV.…”

Primordial Nucleosynthesis

“…[33,34]. It is well known that the lifetime of 7 Be that decays by electron capture is modified in a plasma [35]. However, because of the Boltzmann suppression factor, at T <0.5 GK, the electron density is too low to provide the required reduction factor of ≈3000 on its 53 days half-life.…”

Lithium abundances in AGB stars and a new estimate for the7Be life-time

“…The situation worsens at physical conditions of the H-burning shell in Red Giants, where λ D might be smaller than λ DB . A comparison between the decay rate (λ) of 7 Be in the layers between the convective envelope and the H-burning shell during the fourth inter-pulse period of a 2M AGB star, adopting data by [19] (red line) and the one extrapolated by [17] (black line). λ is plotted as a function of T and ρ (left and right panel, respectively).…”

“…Simonucci et al 2013 [19] explore the problem of electron captures on 7 Be in stellar environments introducing a new treatment, in which electrons are considered as a Fermi gas and a mean-field adiabatic approximation to the scattering process is used. This is justified by the fact that the Debye-Hückel approach can be derived as a two-step approximation of the more general Thomas-Fermi model, by using the linearized Maxwell-Boltzmann distribution.…”

“…In this way electron captures might be computed over a much wider range of T and ρ, with a more precise estimate of the contributions from both bound and free electronic states to the capture. We refer to the paper by [19] for further details about the electron density modeling and the calculation of the 7 Be half-life. Here we want to underline that the results of the quoted paper agree well with the previous findings for the Sun (so that no changes to the solar neutrino problem are introduced).…”