Development of an accurate formalism to predict properties of two-neutron halo nuclei: case study of $^{22}$C

Abstract

When moving away from stability or in loosely-bound systems, few-body clusterized structures like two-neutron halo nuclei appear. These emerge from the interplay between the many- and few-body degrees of freedom, and/or strong coupling between bound and continuum states. This motivates the development of models that can accurately describe few-body dynamics while enforcing shell effects. This work has two goals: understanding how to accurately enforce the Pauli principle in few-body models, as well as presenting new technical developments that allow for more robust and cheaper three-body calculations. We focus on properties of the two-neutron halo 22C, but expect the conclusions to apply to other few-body systems. We use a three-body, hyperspherical harmonics formalism combined with the R-matrix method. We compare predictions for properties of 22C starting from phenomenological interactions and using two methods to remove Pauli-forbidden states, the projection and supersymmetric methods. We also present the algorithms and derivations used. Additionally, we explore model space truncations that allow for reduced computational time. We show convergence of the calculation of both bound and scattering states for $K_{max}\sim 40$. The two methods to enforce the Pauli-exclusion principle lead to different predictions of 22C properties; the projection method is more accurate. We find one efficient channel truncation that reduces the computational cost of our calculations by 20%. Our study clarifies that the projection method is more accurate than the supersymmetric one to enforce the Pauli-exclusion principle. Technical and algorithmic developments enable accurate and efficient computation of two-neutron halo properties. This development paves the way to robust uncertainty quantification in three-body predictions, and is a useful starting point to tackle more complex systems and observables.

Figures (11)

• Figure 1: Definition of T-basis (in black)and Y-basis (in red and blue) coordinates and particle spins .
• Figure 2: Root-mean-square hyperradius of bound states calculated with different $K_{max}$ cutoffs.
• Figure 3: Amplitudes of the lowest angular momentum partial waves in the $0^+$ ground state at $-0.5$ MeV calculated with projection and supersymmetry. $l_x,l_y$ angular momenta are in the T-basis and $l_a,l_b$ angular momenta are in the Y-basis.
• Figure 4: Dalitz plots of the ground state solutions with $K_{max}=30$ for projection (left) and supersymmetry (right). Note that $r_{nn}=x/\sqrt{\mu_{nn}}$
• Figure 5: Wavefunctions of the two largest partial waves in each case, projection plotted with solid lines and supersymmetry with dashed. The total amplitude of the chosen partial waves for projection (supersymmetry) are: 0.54(0.83), 0.30(0.02)