Abstract
Background: In recent years properties of light rare isotopes have been measured with high accuracy. At the same time, the theoretical description of light nuclei has made enormous progress, and properties of, e.g., the helium isotopes can now be calculated ab initio. These advances make those rare isotopes an ideal testing ground for effective field theories (EFTs) built on cluster degrees of freedom.
Purpose: Systems with widely separated intrinsic scales are well suited to an EFT treatment. The Borromean halo nucleus exhibits such a separation of scales. In this work an EFT in which the degrees of freedom are the valence neutrons () and an inert -core () is employed. The properties of can then be calculated using the momentum-space Faddeev equations for the bound state to obtain information on at leading order (LO) within the EFT.
Results: The virtual state and the resonance in give the two-body amplitudes which are input to our LO three-body Halo EFT calculation. We find that without a genuine three-body interaction the two-neutron separation energy of is strongly cutoff dependent. We introduce a “three-body” operator which renormalizes the system, adjusting its coefficient to reproduce the of . The Faddeev components are then cutoff independent for cutoffs of the order of, and above, the breakdown scale of the Halo EFT.
Conclusions: As in the case of a three-body system where only resonant -wave interactions are present, one three-body input is required for the renormalization of the EFT equations that describe at LO. However, in contrast to the -wave-only case, the running of the LO counterterm does not exhibit discrete scale invariance, due to the presence of the -wave interaction.
- Received 13 May 2014
- Revised 8 August 2014
DOI:https://doi.org/10.1103/PhysRevC.90.044004
©2014 American Physical Society