Finite-size effects in heavy halo nuclei from effective field theory

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/Ac, where Ac 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/Ac. 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. I. INTRODUCTIONTheoretical models of many-body systems usually treat the constituent particles as having no internal structure. This point-particle approximation is also used in cluster models, e.g., for the description of halo systems [1-3], even though one might encounter situations for which the core is rather large. Finite-size effects are included a posteriori, but can become significant for certain observables. As an example, the total charge radius is usually calculated by simply adding in quadrature [4] the charge radii of the constituents and the calculated point-particle radius, see e.g. the calculation of charge radii for neutron-rich helium isotopes in the Gamow Shell Model [5]. Instead, it would be useful to construct a framework in which finite-size effects can be included systematically.Constituent-size effects can be accounted for in effective field theories (EFTs), where they appear through derivative interactions. For example, the nucleon charge radius (and, more generally, nucleon form factors) can be calculated [6] in Chiral Perturbation Theory (ChPT) in an expansion in powers of k π /M QCD , where k π ∼ 150 MeV is a momentum scale associated with the lightest carrier of the nuclear force, the pion, and M QCD ∼ 1 GeV is the characteristic mass scale of QCD. The relevant pion parameters are its mass and decay constant. Chiral EFT [7] is a generalization of ChPT to a typical nucleus, for which the binding energy per nucleon is B/A ∼ k 2 π /M QCD and the radius R ∼ A 1/3 /k π . The nuclear charge radius includes the sum of the nucleons' radii plus many-body effects generated by internucleon interactions and currents [8]. We would like to have a similar framework for clusterized systems.Clusterized systems, with much smaller energies and larger radii, are additionally characterized by scales beyond the pion scales. These nuclei can be viewed as a collection of valence nucleons orbiting around either no core (few...

Halo EFT for 31Ne in a spherical formalism

“…Such effects can be included at NLO by treating excited states of the core as explicit fields or via counterterms. See [47] for a discussion of this issue in the case of the charge radius.…”

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

“…(4) is elementary and this expression is well known [2,38]; for a recent EFT discussion of contributions to charge radii in halo nuclei we refer the reader to Ref. [39]. We note that the consistency of any two-ion model (or EFT) requires that the distance between the two ions is larger than the sum of their individual charge radii.…”

“…As this expectation value can be very large (compared to C 2 l E), the contribution of a derivative contact such as δ(r−R + ) 2 ∆/(2m) must be large in size, too, when compared to C 2 l E. This analysis suggests that systematic improvements to Coulomb systems should be based on a Coulomb-corrected derivative expansion such as Eq. (39), rather than on a purely derivative expansion as done in Coulomb halo EFT.…”