Unified ab initio approach to bound and unbound states: no-core shell model with continuum and its application to 7He

TL;DR

This paper presents a new ab initio method called no-core shell model with continuum (NCSMC) that unifies bound and scattering states in nuclear physics, demonstrating improved convergence and application to 7He.

Contribution

The paper introduces the NCSMC, combining NCSM and NCSM/RGM, to accurately describe bound, resonant, and scattering states in nuclei within a single framework.

Findings

Enhanced convergence over traditional methods.

Successful application to unbound 7He nucleus.

Unified treatment of bound and continuum states.

Abstract

We introduce a unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model (NCSM), a bound-state technique, with the no-core shell model/resonating group method (NCSM/RGM), a nuclear scattering technique. This new ab initio method, no-core shell model with continuum (NCSMC), leads to convergence properties superior to either NCSM or NCSM/RGM while providing a balanced approach to different classes of states. In the NCSMC, the ansatz for the many-nucleon wave function includes: i) a square-integrable A-nucleon component expanded in a complete harmonic oscillator basis; ii) a binary-cluster component with asymptotic boundary conditions that can properly describe weakly-bound states, resonances and scattering; and, in principle, iii) a three-cluster component suitable for the description of, e.g., Borromean halo nuclei and reactions with final three-body states. The Schroedinger equation is transformed into a system of coupled-channel integral-differential equations that we solve using a modified microscopic R-matrix formalism within a Lagrange mesh basis. We demonstrate the usefulness of the approach by investigating the unbound 7He nucleus.