THEORETICAL ESTIMATES OF STELLAR e− CAPTURES. I. THE HALF-LIFE OF 7Be IN EVOLVED STARS

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 7Be for T and ρ conditions that are different from the solar ones. This is of crucial importance for modeling the Galactic nucleosynthesis of Li. In this framework, we present here a new theoretical method for calculating the e− capture rate in typical conditions for 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 (1) “traditional” calculations of the electronic density at the nucleus, to which the e− capture rate for 7Be is proportional, for different theoretical approaches including the Thomas–Fermi, Poisson–Boltzmann, and Debye–Hückel (DH) models of screening; and (2) 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 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 7Li abundances in red giant branch and asymptotic giant branch stars of the Galactic disk in light of a revision in the Be decay only; however, we emphasize that the changes we find in the electron density at the nucleus would also induce effects 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.

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