Comparative study of the direct α+d→6Li+γ astrophysical capture reaction in few-body models

Abstract A comparative analysis of the astrophysical S factor and the reaction rate for the direct α ( d , γ ) 6 Li capture reaction, and the primordial abundance of the 6Li element, resulting from two-body and three-body cluster models is presented. It is shown that the two-body model, based on the exact-mass prescription, can not correctly describe the dependence of the isospin-forbidden E1 S factor on energy and does not reproduce the temperature dependence of the reaction rate from the direct LUNA data. It is demonstrated that the isospin-forbidden E1 astrophysical S factor is very sensitive to the orthogonalization procedure of Pauli-forbidden states within the three-body model. On the other hand, the E2 S factor does not depend on the orthogonalization method. This insures that the orthogonolizing pseudopotentials method yields a very good description of the LUNA collaboration's low-energy direct data. At the same time, the SUSY transformation significantly underestimates the data from the LUNA collaboration. On the other hand, the energy dependence of the E1 S factor are the same in both methods. The best description of the LUNA data for the astrophysical S factor and the reaction rates is obtained within the three-body orthogonolizing pseudopotential models. It yields a value of ( 0.67 ± 0.01 ) × 10 − 14 for the 6Li/H primordial abundance ratio, consistent with the estimate ( 0.80 ± 0.18 ) × 10 − 14 of the LUNA collaboration. For the Li 6 / 7 Li abundance ratio an estimate ( 1.30 ± 0.12 ) × 10 − 5 is obtained in good agreement with the Standard Model prediction.