Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory

Abstract

The elastic $\alpha$-${}^{12}$C scattering for $l=0,1,2,3$ channels at low energies is studied, including the energies of excited bound states of ${}^{16}$O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the $0_2^{+}$, $1_1^{-}$, $2_1^{+}$, $3_1^{-}$ states of ${}^{16}$O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O reaction.

arXiv comment18 pages, 10 eps figures, version accepted for publication in Phys. Rev. C

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• Nuclear effective field theory: status and perspectives
• The $S_{E1}$ factor of radiative $\alpha$ capture on ${}^{12}$C in cluster effective field theory
• 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)
• The $S$ matrices of elastic $\alpha$-${}^{12}$C scattering at low energies in effective field theory
• Radiative proton capture on ${}^{15}\mathrm{N}$ within effective field theory
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the sharp resonant $0_3^{+}$ state of ${}^{16}$O
• The $S_{E1}$ factor of radiative $\alpha$ capture on ${}^{12}$C in effective field theory
• Fixing effective range parameters in elastic $\alpha$-${}^{12}$C scattering: an impact on resonant $2_4^{+}$ state of ${}^{16}$O and $S_{E2}$ factor of ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O
• Analysis of elastic $\alpha$-${}^{12}$C scattering with global optimization in the cluster effective field theory