Theoretical study of the α+d→Li6+γ astrophysical capture process in a three-body model. II. Reaction rates and primordial abundance

Abstract

The astrophysical S-factor and reaction rate of the direct capture process α+d → 6 Li + γ, as well as the abundance of the 6 Li element are estimated in a three-body model. The initial state is factorized into the deuteron bound state and the α + d scattering state. The final nucleus 6 Li(1+) is described as a three-body bound state α + n + p in the hyperspherical Lagrange-mesh method. Corrections to the asymptotics of the overlap integral in the Sand D-waves have been done for the E2 Sfactor. The isospin forbidden E1 S-factor is calculated from the initial isosinglet states to the small isotriplet components of the final 6 Li(1+) bound state. It is shown that the three-body model is able to reproduce the newest experimental data of the LUNA collaboration for the astrophysical S-factor and the reaction rates within the experimental error bars. The estimated 6 Li/H abundance ratio of (0.67 ± 0.01) × 10 −14 is in a very good agreement with the recent measurement (0.80 ± 0.18) × 10 −14 of the LUNA collaboration.

Comparative study of the direct $α+d$ $\rightarrow$ $^6$Li + $γ$ astrophysical capture reaction in few-body models

“…A resulting three-body wave function contains a small isotriplet component of about 0.5 %. That small isotriplet component is responsible for the forbidden E1 transition and the new direct data of the LUNA collaboration for the S factor and the reaction rates have been reproduced within the experimental error bars [10,18,19]. The estimated 6 Li/H abundance ratio of (0.67 ± 0.01) × 10 −14 agreed well with the value of (0.80±0.18)×10 −14 , extracted by the LUNA collaboration [5].…”

“…As was shown within the three-body model [10,19], at energies below 100 keV the E1 S factor is important, while beyond this region the E2 S factor becomes dominant. For the calculation of the three-body α + p + n bound state wave function of the 6 Li nucleus, a realistic α − N potential [21] was used which includes a Pauliforbidden state in the S wave.…”

“…For the solution of the abundance problem of lithium isotopes, the three-body models [10,18,19] are developed beyond the two-body approaches. These models include an important contribution of the isospin mixing which is responsible for the isospin-forbidden E1 transition from the initial isosinglet states to the isotriplet components of the 6 Li ground state.…”

3He(α,γ)7Be and 3H(α,γ)7Li reaction rates and implication for Big Bang nucleosynthesis in the potential model

“…On the other hand, recent direct measurements of the LUNA collaboration 6 and theoretical development [7][8][9][10] within the potential model have done an important step toward the correct estimation of the primordial abundance of the 6 Li element.…”

Determination of the asymptotic normalization coefficient (nuclear vertex constant) for α + d →6Li from the new direct measured d(α,γ)6Li data and its implication for extrapolating the d(α,γ)6Li astrophysical S factor at Big Bang energies

“…The most late theoretical calculations of S 24 (E) have been performed within different two-body [10][11][12][13][14][15] and three-body [16][17][18][19] potential models as well as semimicroscopic 20 and microscopic 21,22 models. These methods show considerable spread in the calculated S 24 (E) at Big Bang energies and the result depends noticeably on a specific model used.…”