Unifiedab initioapproach to bound and unbound states: No-core shell model with continuum and its application to7He

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 Schrödinger 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.

Alternative similarity renormalization group generators in nuclear structure calculations

“…More generally, if a (starting) potential has only weak matrix elements in the basis states with N >N gen , it will be only mildly affected by the SRG transformation generated by the flow operator G B s . As long as we can reach a basis with, e.g., N max ≥ N gen , we can solve the many-nucleon problem of such a Hamiltonian within, e.g., the NCSMC method [17]. It is then counterproductive to SRG transform such a Hamiltonian using, e.g., the standard G s =T rel and generate many-body terms in the process.…”

Deuteron-induced nucleon transfer reactions within anab initioframework: First application top-shell nuclei

“…For such matrix elements, which are comparatively much less computationally intensive, we will adopt the formalism and codes developed in Refs. [18,19]. For the sake of completeness, we outline the main features of the NCSMC approach in Appendix A 2.…”

“…the composite nucleus in the reaction. This extension, which we call no-core shell model with continuum (NC-SMC) [18,19], accelerates the convergence of the calculation by providing a more efficient description of the short-range physics at the A-body level that is hard to capture within the cluster ansatz of the NCSM/RGM formalism.…”

Spectroscopy ofHe7using theBe9(HeRenzi1, Raabe2, Randisi3 et al. 2016Phys. Rev. C5010View full textAdd to dashboardCite

“…The latter 6 He(2 + ) configuration also plays a crucial role in the wave function of 7 He 5/2 − state [20,23,24].…”

“…Selecting the one-neutron-knockout channel, they observed a clear deviation of the 6 He +n invariant mass spectrum from the expected R-matrix lineshape. Their result was interpreted as the 7 He ground state in addition to a low-lying J π = 1/2 − state at [20], variational Monte Carlo (VMC) [25], a and no core shell model (NCSM) [24] calculations. For CSM calculations only the real part of the values are reported.…”