Cluster Effective Field Theory

Doctoral thesis, 2016

Halo nuclei are loosely bound systems consisting of a core plus valence nucleon(s). In so called Halo, or Cluster, effective field theory, the core of the halo nucleus is treated as an effective degree-of-freedom without internal structure. As such, Cluster effective field theory is a low-energy model, appropriate for the typical momentum scales of halo physics. The advantages of using effective field theory are the systematic way of improving results, by including higher orders in the momentum expansion, and the rigorous error estimates that are available at each order. In this thesis we present a formalism for treating one-proton and two-neutron halo nuclei in effective field theory, with an emphasis on charge radii, astrophysical S-factors, and the renormalization of three-body states. We also discuss a new power-counting scheme for heavy-core systems and introduce finite-size contributions. For one-proton halo nuclei we derive formalism for S- and P-wave systems, which we exemplify by studying the one-proton halo states 17F* and 8B, respectively. Of particular significance are: (i) our calculation of the radiative capture cross section of 16O(p,gamma)17F* to fifth order in the S-wave system and (ii) our derivation of a leading-order correlation between the charge radius of 8B and the threshold S-factor of 7Be(p,gamma)8B for the P-wave system. Our alternative power counting for halo nuclei with a heavy core leads to a new organizational principle that demotes the naive leading-order contributions to the charge radius for neutron halos. Additionally, in this new power counting we include the finite-size effects of the constituents explicitly into the field theory and derive how their finite sizes contribute to the charge radius of S- and P-wave one-neutron and one-proton halo states. For two-neutron halo systems we derive the field-theory integral equations to study both bound and resonant states. We apply the formalism to the 0+ channel of 6He. In this three-body field theory we include both the 3/2- and the 1/2- channels of the alpha-n subsystem, together with the 0+ channel of the n-n part. Furthermore, we include the relevant three-body interactions and analyze, in particular, the renormalization of the system.