Continuum Systems in the No-Core Shell Model

Abstract

The progress of ab initio nuclear structure in the past two decades revealed the need to incorporate continuum degrees of freedom. They are indispensable in the treatment of nuclear structure and for connecting theory to experiments performed at the extremes of low-energy many-body scattering. Many-body continuum calculation are a challenging task. It makes sense to build on the proven ab initio bound-state methods, if possible. In this work, we present combinations of the ab initio nuclear structure method of the No-Core Shell Model (NCSM) with two approaches that give access to observables in the nuclear continuum. These methods are the Harmonic Oscillator Representation of Scattering Equations (HORSE) and the Analytic Continuation in the Coupling Constant (ACCC). The focus is on the determination of resonance parameters, which is motivated by the possible existence of a resonating four-neutron J = 0+ state, the tetraneutron, proposed by a recently conducted experiment. We employ various state-of-the-art Chiral Effective Field Theory (χEFT) interactions. We first introduce the HORSE method and its simplification, the Single-State HORSE, which belong to the so-called J-matrix methods. The J-matrix approach uses the tridiagonality of the kinetic energy in a specific basis representation to connect an interior, interacting region, to an exterior, free region. With the Single-State HORSE method, we calculate tetraneutron phase shifts derived in a hyperspherical framework. We use various Similarity Renormalization Group evolved χEFT interactions and two phenomenological potentials, studying their effects on phase shifts. The calculations are performed in large NCSM model spaces. The phase shifts are in line with the existence of a resonance, showing characteristic features of such states. We further show a way of obtaining a hyperspherical basis within the framework of the Jacobi-NCSM. This paves the way for future studies involving full HORSE Green's function. The second method used to investigate resonances, with an application to the dineutron and tetraneutron, is the ACCC. The method provides access to resonances on the complex k-plane by using the analytic properties of the Jost function as a function of a coupling constant. It relies solely on bound-state calculations by artificially binding the system to obtain energies at different coupling strengths, which are fitted by Pade approximants and extrapolated to the initial interaction strength. We show two different binding procedures, an additional four-body potential constructed on matrix element level from the smallest NCSM model spaces, dubbed eigenvector binding. This is motivated by the desire to avoid bound substructures. The second procedure is a straightforward multiplication of the interaction matrix elements by a factor. The dineutron results show that the binding methods do not falsely produce resonances. The tetraneutron results support a resonance in the case of eigenvector binding, but not so for the direct matrix element modification.