The $S$ matrices of elastic $\alpha$-${}^{12}$C scattering at low energies in effective field theory

Abstract

The elastic $\alpha$-${}^{12}$C scattering at low energies for $l=0,1,2,3,4,5,6$ is studied in effective field theory. We discuss the construction of the $S$ matrices of elastic $\alpha$-${}^{12}$C scattering in terms of the amplitudes of sub-threshold bound and resonant states of ${}^{16}$O, which are calculated from the effective Lagrangian. The parameters appearing in the $S$ matrices are fitted to the phase shift data below the $p$-${}^{15}$N breakup threshold energy, and we find that the phase shifts are well described within the theory.

28 pages, 13 figures; version accepted for publication in Physical Review C

References in corpus (10)

• The 12C(a,g)16O reaction and its implications for stellar helium burning
• alpha-alpha Scattering in Halo Effective Field Theory
• Constraining the 6.05 MeV 0${}^{+}$ and 6.13 MeV 3${}^{-}$ cascade transitions in the ${}^{12}$C($\alpha$,$\gamma$)${}^{16}$O reaction using the Asymptotic Normalization Coefficients
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• Nonrelativistic Effective Field Theory with a Resonance Field
• 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)
• Radiative proton capture on ${}^{15}\mathrm{N}$ within effective field theory

Cited by in corpus (2)

• 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