Theoretical estimations for the astrophysical S-factor and the d(alpha,gamma)6Li reaction rates are obtained on the base of the two-body model with the alpha-d potential of a simple Gaussian form, which describes correctly the phase-shifts in the S-,
P-, and D-waves, the binding energy and the asymptotic normalization constant in the final S-state. Wave functions of the bound and continuum states are calculated by using the Numerov algorithm of a high accuracy. A good convergence of the results for the E1- and E2- components of the transition is shown when increasing the upper limit of effective integrals up to 40 fm. The obtained results for the S-factor and reaction rates in the temperature interval 10E+6 K < T < 10E+10 K are in a good agreement with the results of Ref. A.M. Mukhamedzhanov, et.al., Phys. Rev., C 83, 055805 (2011), where the authors used the known asymptotical form of wave function at low energies and a complicated potential at higher energies.
The neutron-rich $^{11}$Li halo nucleus is unique among nuclei with known separation energies by its ability to emit a proton and a neutron in a $beta$ decay process. The branching ratio towards this rare decay mode is evaluated within a three-body m
odel for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e. a lower bound $6 times 10^{-12}$ obtained with a pure Coulomb wave and an upper bound $5 times 10^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausible values between between $0.8 times 10^{-10}$ and $2.2 times 10^{-10}$ with most probable total energies of the proton and neutron between 0.15 and 0.3 MeV.
The 16O(p,gamma)17F reaction rate is revisited with special emphasis on the stellar temperature range of T=60-100 MK important for hot bottom burning in asymptotic giant branch (AGB) stars. We evaluate existing cross section data that were obtained s
ince 1958 and, if appropriate, correct published data for systematic errors that were not noticed previously, including the effects of coincidence summing and updated effective stopping powers. The data are interpreted by using two different models of nuclear reactions, that is, a potential model and R-matrix theory. A new astrophysical S-factor and recommended thermonuclear reaction rates are presented. As a result of our work, the 16O(p,gamma)17F reaction has now the most precisely known rate involving any target nucleus in the mass A >= 12 range, with reaction rate errors of about 7% over the entire temperature region of astrophysical interest (T=0.01-2.5 GK). The impact of the present improved reaction rate with its significantly reduced uncertainties on the hot bottom burning in AGB stars is discussed. In contrast to earlier results we find now that there is not clear evidence to date for any stellar grain origin from massive AGB stars.
