Modified two-body potential approach to the peripheral direct capture astrophysical a+A→B+γ reaction and asymptotic normalization coefficients

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 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 (g.s.), (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.