Analysis of elastic $\alpha$-${}^{12}$C scattering with global optimization in the cluster effective field theory

Abstract

We analyze the elastic $\alpha$-${}^{12}$C scattering including the contribution of resonance states below the $p$-${}^{15}$N breakup threshold energy. We use the cluster effective field theory in which scattering amplitude is expanded in terms of the effective range expansion parameters for the angular momentum states from $l=0$ to $l=6$. The amplitude contains 37 parameters, which are determined by fitting to 11 392 differential cross section data points of the elastic $\alpha$-${}^{12}$C scattering. To optimize the fitting process, we implement the differential evolution (DE) algorithm, which performs a global search over the high-dimensional parameter space and consistently converges to the same minimum ${\chi }^2$ value across independent runs, suggesting proximity to the global minimum within the explored domain. In parallel, the Markov chain Monte Carlo (MCMC) method is used to crosscheck the DE results and to estimate the parameter uncertainties. The best fit yields ${\chi }^2/N\simeq 6.2$ for the elastic scattering data. Using the determined 37 parameters, we calculate the differential cross sections and the phase shifts of the elastic $\alpha$-${}^{12}$C scattering and compare the results with experimental data and those of an $R$-matrix analysis. Our result of the cross section agrees with the experimental data as accurately as an $R$-matrix analysis. The results demonstrate that the cluster effective field theory, combined with global optimization and uncertainty quantification based on DE-MCMC methods, provides a reliable and systematic framework for applications to low energy phenomena relevant to stellar evolution and nucleosynthesis.

32 pages, 8 figures

References in corpus (13)

• The 12C(a,g)16O reaction and its implications for stellar helium burning
• Proton-proton fusion in pionless effective theory
• Low energy proton-proton scattering in effective field theory
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• Analysis of nuclear structure in a converging expansion scheme
• Quasi-elastic electron scattering with KIDS nuclear energy density functional
• Spin Polarization in $\gamma d\to \vec{n}p$ at Low Energies with a Pionless Effective Field Theory
• Non-radial oscillations of hadronic neutron stars, quark stars, and hybrid stars : Calculation of $f$, $p$, and $g$ mode frequencies
• Influence of the effective mass on the properties of nuclear matter at finite density and temperature
• Nuclear mass table in density functional approach inspired by neutron-star observations
• $f$ and $p$ mode oscillation of proto-neutron stars with systematic variation of the nucleon effective mass
• Hadron-quark phase transition in the neutron star with vector MIT bag model and Korea-IBS-Daegu-SKKU functional
• 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