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Abstract |
In this talk I will show how an Effective Field Theory for weakly-bound few-body systems ("Halo EFT") aids the modeling and understanding of light nuclei in the $p$-shell. After introducing Halo EFT I will discuss two examples of its use. First, I will describe our recent analysis of the reaction $^3$He($\alpha$, $\gamma$)~[1]. In this case we take $^3$He and $^4$He as the effective degrees of freedom and work to next-to-leading order in the EFT. We use a Bayesian analysis to perform the extrapolation of higher-energy data to solar energies and find a markedly smaller uncertainty to previous evaluations, as well as significant constraints on $^3$He-$^4$He scattering parameters. Second, I will demonstrate that a three-body ($\alpha$-neutron-proton) model of $^6$Li exhibits a correlation between the deuteron-$\alpha$ scattering length and the $^6$Li binding energy~[2]. Such correlations appear generically in three-body systems with weak binding (cf. the Phillips line in the $A=3$ system) and can be understood as a consequence of the requirement that the EFT be renormalized. The emergence of such a correlation in the presence of $p$-wave nucleon-$\alpha$ interactions is particularly striking, as is the fact that it is rather insensitive to the actual values of the $p$-wave phase shifts. I will close by discussing the implications of this finding for model and EFT treatments of $^6$He and $^6$Li. |
