Asymptotic normalization coefficients of resonant and bound states from the phase shifts for $\alpha \alpha$ and ${\alpha }^{12}\mathrm{C}$ 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$+\alpha$ and $\alpha {+}^{12}\mathrm{C}$ systems. The SMP results are compared with the effective-range expansion method (EFE) results. In the present paper the SMP and EFE plus the Padé-approximation are applied to study the excited 2${}^{+}$ resonant states of ${}^8\mathrm{Be}$. A contradiction is found between descriptions of the experimental phase shift data for $\alpha \alpha$ scattering and of the ${}^8\mathrm{Be}$ resonant energy for 2${}^{+}$ state. Using the EFE method, we also calculate the ANC for the ${}^8\mathrm{Be}$ 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 $\alpha {+}^{12}\mathrm{C}$ states1${}^{-}$ and 3${}^{-}$ the SMP results are compared with the Padé-approximation results. We find that the Padé-approximation improves a resonance width description compared with the EFE results. The EFE method is also used to calculate the ANCs for the bound ${}^{16}\mathrm{O}$ ground 0${}^{+}$ state and for the excited 1${}^{-}$ and 2${}^{+}$ levels which are situated near the threshold of $\alpha {+}^{12}\mathrm{C}$ channel.

9 pages, 3 figures, 1 table

References in corpus (2)

• Effect of Coulomb Forces on the Position of the Pole in the Scattering Amplitude and on Its Residue
• Resonance-state properties from a phase shift analysis with the $S$-matrix pole method and the effective-range method

Cited by in corpus (10)

• Ab initio alpha-alpha scattering
• On the phase-shift parameterization and ANC extraction from elastic-scattering data
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering
• Extrapolation of scattering data to the negative-energy region II
• Extrapolation of scattering data to the negative-energy region
• Effective-range function methods for charged particle collisions
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the sharp resonant $0_3^{+}$ state of ${}^{16}$O
• The energies and ANCs for 5Li resonances deduced from experimental p-$\alpha$ scattering phase shifts using the effective-range and $\Delta$ methods