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

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.

Ab initio description of the exotic unbound 7He nucleus

The neutron rich exotic unbound 7He nucleus has been the subject of many experimental investigations. While the ground-state 3/2- resonance is well established, there is a controversy concerning the excited 1/2- resonance reported in some experiments as low-lying and narrow (E_R ~ 1 MeV, Gamma < 1 MeV) while in others as very broad and located at a higher energy. This issue cannot be addressed by ab initio theoretical calculations based on traditional bound-state methods. We introduce a new unified approach to nuclear bound and continuum states based on the coupling of the no-core shell model, a bound-state technique, with the no-core shell model/resonating group method, a nuclear scattering technique. Our calculations describe the ground-state resonance in agreement with experiment and, at the same time, predict a broad 1/2- resonance above 2 MeV.