Asymptotic normalization coefficients of resonant and bound states from the phase shifts for αα and α12 C scattering
Abstract
Recently we have published a paper [Irgaziev, Phys. Rev. C 91, 024002 (2015)] where the S-matrix pole method (SMP) which is only valid for resonances has been developed to derive a new explicit expression for the asymptotic normalization coefficient (ANC), and is applied to the low-energy resonant states of nucleon+α and α+12C systems. The SMP results are compared with the effective-range expansion method (EFE) results. In the present paper the SMP and EFE plus the Pad\'e-approximation are applied to study the excited 2+ resonant states of 8Be. A contradiction is found between descriptions of the experimental phase shift data for αα scattering and of the 8Be resonant energy for 2+ state. Using the EFE method, we also calculate the ANC for the 8Be ground 0+ state with a very small width. This ANC agrees well with the value calculated using the known analytical expression for narrow resonances. In addition, for the α+12C states1- and 3- the SMP results are compared with the Pad\'e-approximation results. We find that the Pad\'e-approximation improves a resonance width description compared with the EFE results. The EFE method is also used to calculate the ANCs for the bound 16O ground 0+ state and for the excited 1- and 2+ levels which are situated near the threshold of α+12C channel.
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