Theoretical analysis of the astrophysical S-factor for the capture reaction α + d → 6Li + γ in the two-body model

Abstract

Theoretical estimates for the astrophysical S-factor and the rate of the reaction d (α, γ) 6 Li were obtained on the basis of the two-body model involving an α−d potential that has a simple Gaussian form and which describes correctly S-, P -, and D-wave phase shifts, the binding energy, and the asymptotic normalization coefficient for the S-wave bound state. The wave functions for the bound and continuum channels were calculated with the aid of the highly precise Numerov algorithm. The results for the contributions of the E1 and E2 transition components reveal a good convergence as the upper limit in the effective integrals increases up to 40 fm. The results obtained for the astrophysical S-factor and the rate of the reaction d(α, γ) 6 Li in the temperature range of 10 6 K ≤ T ≤ 10 10 K agree well with the results of the calculations performed by A.M. Mukhamedzhanov and his coauthors [Phys. Rev. C 83, 055805 (2011)] by using the known asymptotic form of the wave function at low energies and a complicated two-body potential at higher energies.

Theoretical study of theα+d→Li6+γastrophysical capture process in a three-body model

“…3 the contribution of the E2-transition operator to the astrophysical S-factor is demonstrated for different initial partial waves 3 D 1 , 3 D 2 and 3 D 3 . As can be seen from the figure the estimations are essentially less than the corresponding numbers for the two-body model [21]. The magnitude of underestimation is larger at low astrophysical energies.…”

“…Finally, in Fig. 6 we compare the obtained theoretical results with the estimations of the two-body model [21] and experimental data from Refs. [8][9][10]12].…”

“…[19] is based on the well-known asymptotic form of the two-body α+d boundstate wave function at low energies and a complicated potential derived from the original Woods-Saxon potential via the integro-differential transformation at higher energies. Recently these results have been reproduced with a much simpler α − d potential of the Gaussian form describing both bound state (ANC, binding energy) and scattering state (phase shifts in the S, P , D-waves) properties [21] of the α + d system.…”

“…From the theoretical side, different two-body and three-body potential models [14][15][16][17][18][19][20][21] and ab initio approaches [22] have been developed. These studies have demonstrated that the main contribution to the process at energies around and beyond the 3 + resonance comes from the E2 transition.…”

Influence of orthogonalization procedure on astrophysical S-factor for the direct α + d →6Li + γ capture process in a three-body model

“…The Schrödinger equation is solved using a highly accurate Lagrange-Laguerre mesh method[21]. It yields E d =-2.202 MeV for the deuteron ground-state energy with the number of mesh points N = 40 and a scaling parameterh d = 0.40.The scattering wave function of the α − d relative motion is calculated with a deep potential of Dubovichenko[22] with a small modification in the S-wave[10]: V (S) d (R) = −92.44 exp(−0.25R 2 ) MeV. The potential parameters in the 3 P 0 , 3 P 1 , 3 P 2 and 3 D 1 , 3 D 2 , 3 D 3 partial waves are the same as in Ref [22]…”