Elastic $\alpha$-${}^{12}$C scattering at low energies in cluster effective field theory

Abstract

The elastic $\alpha$-${}^{12}$C scattering at low energies is studied employing an effective field theory in which the $\alpha$ and ${}^{12}$C states are treated as elementary-like fields. We discuss scales of the theory at stellar energy region that the ${}^{12}$C($\alpha$, $\gamma$)${}^{16}$O process occurs, and then obtain an expression of the elastic scattering amplitudes in terms of effective range parameters. Using experimental data of the phase shifts for $l=0,1,2$ channels at low energies, for which the resonance regions are avoided, we fix values of the parameters and find that the phase shifts at the low energies are well reproduced by using three effective range parameters for each channel. Furthermore, we discuss problems and uncertainties of the present approach when the amplitudes are extrapolated to the stellar energy region.

17 pages, 8 eps figures, version accepted for publication in Eur. Phys. J. A

References in corpus (13)

• Frontiers in Nuclear Astrophysics
• alpha-alpha Scattering in Halo Effective Field Theory
• Proton-proton fusion in pionless effective theory
• Low energy proton-proton scattering in effective field theory
• Causality constraints for charged particles
• The long and winding road from chiral effective Lagrangians to nuclear structure
• Constraining Low-Energy Proton Capture on Beryllium-7 through Charge Radius Measurements
• Elastic $\alpha$-${}^{12}$C scattering at low energies in cluster effective field theory
• Ordinary muon capture on a proton in manifestly Lorentz invariant baryon chiral perturbation theory
• Narrow resonances and short-range interactions
• Recent results in nuclear astrophysics
• $pp\to pp{\pi }^0$ near threshold in pionless effective theory
• ${}_{\Lambda \Lambda }^{6}He$ in cluster effective field theory

Cited by in corpus (11)

• Nuclear effective field theory: status and perspectives
• Elastic $\alpha$-${}^{12}$C scattering at low energies in cluster effective field theory
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• The $S_{E1}$ factor of radiative $\alpha$ capture on ${}^{12}$C in cluster effective field theory
• Cluster effective field theory and nuclear reactions
• 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
• 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
• The $S_{E1}$ factor of radiative $\alpha$ capture on ${}^{12}$C in effective field theory
• Analysis of elastic $\alpha$-${}^{12}$C scattering with global optimization in the cluster effective field theory