Helium halo nuclei from low-momentum interactions

Abstract

Abstract. We present ground-state energies of helium halo nuclei based on chiral low-momentum interactions, using the hyperspherical-harmonics method for 6 He and coupled-cluster theory for 8 He, with correct asymptotics for the extended halo structure. MotivationThe physics of strong interactions gives rise to new structures in neutron-rich nuclei. One prominent example are the helium halo nuclei, 6 He and 8 He, with two or four loosely-bound neutrons forming an extended halo around the 4 He core. 6 He is the lightest halo nucleus and the lightest Borromean system in nature. Recently, a combination of nuclear and atomic physics techniques enabled a new era of precision measurements of the ground-state energies (masses) and charge radii of 6 He [1,2] and 8 He [3,4]. Their reproduction poses extraordinary challenges for nuclear theory that will advance ab-initio methods and our understanding of nuclear forces.The existing ab-initio calculations with traditional nucleon-nucleon (NN) and three-nucleon (3N) potentials are based on the Green's Function Monte Carlo (GFMC) method [5] and the No-Core Shell Model (NCSM) [6]. In addition, there are larger-scale NCSM results but restricted to NN interactions [7] and Fermionic Molecular Dynamics studies based on a unitary-correlated NN interaction plus a two-body potential introduced to mimic 3N effects [8].One of the central advances in nuclear theory has been the development of effective field theory (EFT) and the renormalization group (RG) to nuclear forces. While light nuclei have been investigated using the NCSM [9], there are no results for helium halo nuclei based on chiral NN and 3N interactions. This is due to the challenges of the loosely-bound halo and the extended structure of the wave function. In this paper, we present results of an effort to study helium halo nuclei based on chiral EFT. These combine the RG evolution to low-momentum interactions with the ab-initio hyperspherical-harmonics method for 6 He and coupled-cluster theory for 8 He. Our work goes beyond the previous investigation [10] of the helium isotopes by studying the cutoff variation, as a tool to probe the effects of many-body forces, and we present first results based on the exact hyperspherical-harmonics expansion for 6 He, which is more difficult to describe in coupled-cluster theory due to its open-shell nature [10].2 Effective field theory and the renormalization group for nuclear forces Nuclear interactions depend on a resolution scale, which we denote by a generic momentum cutoff Λ, and the Hamiltonian is always given by an effective theory for NN and corresponding a

Matter and charge radius of6He in the hyperspherical-harmonics approach

“…The value obtained from the exponential extrapolation of the HH results with error bar obtained as explained in [24] is also shown. One can readily see that the convergence is faster when the lowest cutoff Λ = 1.8 fm −1 is used, because the inter- [24] and plotted together with the new EIHH results. The value obtained from the exponential extrapolation of the HH results with the corresponding error bar (see [24]) is also shown.…”

“…Similar enhancements of the V low k chiral potential. The extrapolated HH results are shown as a reference and compared to the coupled cluster results from [24].…”

“…As opposed to a shell model expansion, the use of the hyperspherical basis enables to better describe the exponential fall-off of the nuclear wave function, which is important to provide precise results for 6 He. This work also goes beyond our first study [24], since here we present converged results for the energy and new calculations of radii for 6 He, where the use of the effective interaction method enables to speed up the convergence. This paper is organized as follows.…”

“…In [24] we used a HH expansion to study the energy of 6 He with V low k potentials. A rather slow convergence was observed, especially for the larger values of Λ, and we therefore performed an exponential extrapolation of the variational HH energies to the infinite Hilbert space.…”

First Direct Mass Measurement of the Two-Neutron Halo NucleusHe6and Improved Mass for the Four-Neutron HaloHe8

“…6 He and 8 He are the lightest known halo nuclei and, due to their few-nucleon (A 10) structure, are amenable to different ab-initio calculations based on microscopic nuclear forces [11][12][13][14][15]. Therefore, they represent an ideal testing ground for nuclear structure theory, leading to a deeper understanding of the strong interaction in neutron-rich systems.…”