Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering

Abstract

A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $\Delta$-method, is proved and developed. This method was proposed in Ref. [O. L. Ramírez Suárez and J.-M. Sparenberg, arXiv: 1602.04082 [nucl-th] (2016)] but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function $K_l(k^2)$ is actually defined by the Coulomb term. One of the resulting effects is the wrong description of energy behavior of the elastic scattering phase shift ${\delta }_l$ reproduced from the fitted total effective-range function $K_l(k^2)$. This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this $\Delta$-method to calculate the pole position values and the ANC. We apply it to the vertices ${}^4\mathrm{He}+{}^{12}\mathrm{C}⟷{}^{16}\mathrm{O}$ and ${}^3\mathrm{He}+{}^4\mathrm{He}⟷{}^7\mathrm{Be}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the ${}^{16}\mathrm{O}$ bound final states as well as to the ${}^7\mathrm{Be}⟷{}^7\mathrm{Be}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the ${}^{16}\mathrm{O}$ bound final states as well as to the ${}^7\mathrm{Be}$.

11 pages, 6 figures, 1 table

References in corpus (4)

• Asymptotic normalization coefficients from ab initio calculations
• Extrapolation of scattering data to the negative-energy region
• 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)

• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• 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
• Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system
• Cluster effective field theory and nuclear reactions
• Determination of asymptotic normalization coefficients for the channel ${}^{16}$O$\to \alpha {+}^{12}$C. Excited state ${}^{16}$O($0^{+};6.05$ MeV)
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
• The $S$ matrices of elastic $\alpha$-${}^{12}$C scattering at low energies in effective field theory
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the sharp resonant $0_3^{+}$ state of ${}^{16}$O