Low-energy bound states, resonances, and scattering of light ions

Abstract

We describe bound states, resonances and elastic scattering of light ions using a $\delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients, effective-range parameters, and phase shifts, we adjust the two parameters of the potential to some of these observables and make predictions for the nuclear systems $d+\alpha$, $\mbox{$^3$He}+α$, $\mbox{$^3$He}+α$, $\alpha +\alpha$, and $p+\mbox{$^{16}$O}$. We identify relevant momentum scales for Coulomb halo nuclei and propose how to apply systematic corrections to the potentials. This allows us to quantify statistical and systematic uncertainties. We present a constructive criticism of Coulomb halo effective field theory and compute the unknown charge radius of ${}^{17}$F.

arXiv comment18 pages, 8 figures

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• Bayesian analysis of capture reactions ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$
• Nuclear Structure at the Crossroads
• Universal physics of bound states of a few charged particles
• Resonant and Scattering States in the $\alpha +\alpha$ System from the Non-Localized Cluster Model
• $\beta$-delayed proton emission from ${}^{11}$Be in effective field theory
• Nonrelativistic Effective Field Theory with a Resonance Field
• Coupled-channels treatment of ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ in effective field theory
• Bayesian method for fitting the low-energy constants in chiral perturbation theory