Unified<i>ab initio</i>approach to bound and unbound states: No-core shell model with continuum and its application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mrow/><mml:mn>7</mml:mn></mml:msup></mml:math>He

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 and (ii) a binary-cluster component with asymptotic boundary conditions that can properly describe weakly bound states, resonances, and scattering. The Schr\"odinger 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 ${}^{7}$He nucleus.