Resonance-state properties from a phase shift analysis with the $S$-matrix pole method and the effective-range method

Abstract

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANC of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the $S$-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the ${}^5\mathrm{He},{}^5\mathrm{Li}$, and ${}^{16}\mathrm{O}$ concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the $p_{3/2}$ and $p_{1/2}$ resonance states of the nuclei ${}^5\mathrm{He}$ and ${}^5\mathrm{Li}$ and compare them with the results obtained by the $S$-matrix pole method. ANC values are found which can be used to calculate the reaction rate through the ${}^{16}\mathrm{O}$ resonances which lie slightly above the threshold for the ${\alpha }^{12}\mathrm{C}$ channel.

8 pages, 3 tables, 5 figures

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Cited by in corpus (9)

• On the phase-shift parameterization and ANC extraction from elastic-scattering data
• 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
• Asymptotic normalization coefficients of resonant and bound states from the phase shifts for $\alpha \alpha$ and ${\alpha }^{12}\mathrm{C}$ scattering
• Extrapolation of scattering data to the negative-energy region
• Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system
• New method of analytic continuation of elastic-scattering data to the negative-energy region and asymptotic normalization coefficients for ${}^{17}$O and ${}^{13}$C
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
• The energies and ANCs for 5Li resonances deduced from experimental p-$\alpha$ scattering phase shifts using the effective-range and $\Delta$ methods