Finite-range effects in dilute Fermi gases at unitarity

We develop a theoretical method going beyond the contact-interaction approximation frequently used in mean-field theories of many-fermion systems, based on the low-energy T-matrix of the pair potential to rigorously define the effective radius of the interaction. One of the main consequences of our approach is the possibility to investigate finite-density effects, which are outside the range of validity of approximations based on delta-like potentials. We apply our method to the calculation of density dependent properties of an ultracold gas of 6Li atoms at unitarity, whose two-body interaction potential is calculated using ab initio quantum chemistry methods. We find that density effects will be significant in ultracold gases with densities one order of magnitude higher than those attained in current experiments.Comment: 7 pages, 3 figures. v2: Corrected typos in the main text and in the reference

A Bird's Eye View on the Concept of Multichannel Scattering with Applications to Materials Science, Condensed Matter, and Nuclear Astrophysics

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Theoretical Estimates of Stellar e-Captures. I. The half-life of 7Be in Evolved Stars

The Li enrichment in the Universe still presents various puzzles to astrophysics. One open issue is that of obtaining estimates for the rate of e-captures on 7Be, for T and rho conditions different from solar. This is important to model the Galactic nucleosynthesis of Li. In this framework, we present a new theoretical method for calculating the e-capture rate in conditions typical of evolved stars. 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 7Be is proportional, for different theoretical approaches including the Thomas--Fermi, Poisson--Boltzmann and Debye--Hueckel (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 our approach as well as with the traditional ones and their differences are discussed in some detail, starting from solar conditions, where our method and the DH model converge to the same solution. We then analyze the applicability of the various models to a rather broad range of T and rho values, embracing those typical of red giant stars. We find that, over a wide region of the parameter space explored, the DH approximation does not stand, and the more general method we suggest is preferable. We then briefly reanalyze the 7Li abundances in RGB and AGB stars of the Galactic Disk using the new Be-decay rate. We also underline that the different values of the electron density at the nucleus we find should induce effects on electron screening (for p-captures on Li itself, as well as for other nuclei) so that our new approach might have wide astrophysical consequences.Comment: Astrophts. Journal Feb. 1, 201

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

In most cases RGB and AGB stars with M <= 2M(circle dot) destroy Li (which is instead synthesized trough electron-captures on Be-7). This occurs through the combined operation of mixing processes and proton captures, when H-burning operates close to the envelope. Observed Li abundances are however difficult to explain, as they cover a wide spread. Various uncertainties affect model attempts, but so far the largest one concerns the processes of bound and free e-captures on Be-7, hence its life-time, whose known estimates are valid only for solar conditions. RGB and AGB stages have temperatures and densities below the envelope covering a wide range and differing from solar by up to a factor of five for T and up to five orders of magnitudes for rho, hence extrapolations are unreliable. Recently, we presented an estimate of the Be-7 half-life based on a fully quantistic method that goes beyond the Debye-Huckel approximation. Here we discuss its consequences on Li nucleosynthesis in low mass AGB stars