Modified two-body potential approach to the peripheral direct capture astrophysical [formula omitted] reaction and asymptotic normalization coefficients

Abstract

A modified two-body potential approach is proposed for determination of both the asymptotic normalization coefficient (ANC) (or the respective nuclear vertex constant (NVC)) for the A + a → B (for the virtual decay B → A + a ) from an analysis of the experimental S-factor for the peripheral direct capture a + A → B + γ reaction and the astrophysical S-factor, S ( E ) , at low experimentally inaccessible energy regions. The approach proposed involves two additional conditions which verify the peripheral character of the considered reaction and expresses S ( E ) in terms of the ANC. The connection between NVC (ANC) and the effective range parameters for Aa-scattering is derived. To test this approach we reanalyse the precise experimental astrophysical S-factors for t + α → Li 7 + γ reaction at energies E ⩽ 1200 keV [C.R. Brune et al., Phys. Rev. C 50 (1994) 2205]. The same Wood–Saxon potential form both for the bound ( t + α )-state wave function and for the αt-scattering wave function is used to guarantee selfconsistency. New estimates have been obtained for the values of the ANC's (the NVC's) for the α + t → Li 7 (g.s.), α + t → Li 7 (0.478 MeV) and of S ( E ) at E ⩽ 50 keV . These ANC values have been used for getting information about the “indirect” measured values of the effective range parameters and the p-wave phase shift for αt-scattering in the energy range of 100 ≲ E ≲ 180 keV .