Abstract
Halo/Cluster Effective Field Theory describes halo/cluster nuclei in an expansion in the small ratio of the size of the core(s) to the size of the system. Even in the point-particle limit, neutron-halo nuclei have a finite charge radius, because their center of mass does not coincide with their center of charge. This point-particle contribution decreases as 1/A_mathrm {c}, where A_mathrm {c} is the mass number of the core, and diminishes in importance compared to other effects, e.g., the size of the core to which the neutrons are bound. Here we propose that for heavy cores the EFT expansion should account for the small factors of 1/A_mathrm {c}. As a specific example, we discuss the implications of this organizational scheme for the inclusion of finite-size effects in expressions for the charge radii of halo nuclei. We show in particular that a short-range operator could be the dominant effect in the charge radius of one-neutron halos bound by a P-wave interaction. The point-particle contribution remains the leading piece of the charge radius for one-proton halos, and so Halo EFT has more predictive power in that case.
Highlights
Constituent-size effects can be accounted for in effective field theories (EFTs), where they appear through derivative interactions
We show that for one-neutron halos bound by a P-wave interaction this effect may be as important as the long-distance contributions to the halo’s charge radius that have been previously computed in HEFT [22]
An appendix discusses the corresponding results for proton halos, where considering factors of 1/Ac does not lead to any change in the hierarchy of the various physical mechanisms that contribute to the charge radius
Summary
Constituent-size effects can be accounted for in effective field theories (EFTs), where they appear through derivative interactions. Clusterized systems, with much smaller energies and larger radii, are characterized by scales beyond the pion scales. The generic existence of such systems can be understood as a consequence of a fine-tuning in QCD, which introduces a lighter momentum scale א ∼ 30 MeV [10,11]. For such loosely bound systems we can devise EFTs that exploit the separation of scales without involving pions explicitly. In these EFTs one considers processes with typical momenta klo, such that klo khi,
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