Ab initiosymplectic no-core shell model

Abstract

The no-core shell model (NCSM) is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. The symplectic no-core shell model (Sp-NCSM) aspires to extend the scope of the NCSM beyond the p-shell region by augmenting the conventional spherical harmonic oscillator basis with the physically relevant symplectic Sp(3, R) symmetry-adapted configurations of the symplectic shell model that describe naturally the monopole-quadrupole vibrational and rotational modes, and also partially incorporate α-cluster correlations. In this review, the models underpinning the Sp-NCSM approach, namely, the NCSM, the Elliott SU(3) model and the symplectic shell model, are discussed. Following this, a prescription for constructing translationally invariant symplectic configurations in the spherical harmonic oscillator basis is given. This prescription is utilized to unveil the extent to which symplectic configurations enter into low-lying states in 12 C and 16 O nuclei calculated within the framework of the NCSM with the JISP16 realistic nucleon-nucleon interaction. The outcomes of this proof-of-principle study are presented in detail.

Efficacy of the SU(3) scheme for ab initio large-scale calculations beyond the lightest nuclei

“…The potential gains from the SA-NCSM have also been demonstrated in our earlier study where we found that ab initio wavefunctions of 12 C and 16 O calculated by the no-core shell model (NCSM) [4] project well onto a symmetry-adapted subspace that is only a tiny fraction of the corresponding complete model space [34][35][36]. While the SA-NCSM states can be obtained through a unitary transformation from the basis used in the NCSM, and hence span the entire space, the growth of the model space within the SA-NCSM framework can be managed, as shown here, by down-selecting to the physically relevant states as determined through symmetry considerations.…”

“…The SA-NCSM framework allows one to down-select from all possible configurations to a subset that tracks with an inherent preference of a system towards low-spin and high-deformation dominance -and symplectic multiples thereof in high-N max spaces [18] -as revealed to be important in realistic NCSM wavefunctions [34][35][36].…”

Emergence of rotational bands inab initiono-core configuration interaction calculations of the Be isotopes

“…In ab initio no-core configuration interaction (NCCI) approaches -such as the no-core shell model (NCSM) [14,15], no-core full configuration (NCFC) [16], importance-truncated NCSM (IT-NCSM) [17,18], nocore Monte Carlo shell model (MCSM) [19], and symmetry-adapted NCSM (SA-NCSM) [20,21] methods -the nuclear many-body bound-state eigenproblem is formulated as a Hamiltonian matrix diagonalization problem. The Hamiltonian is represented with respect to a basis of antisymmetrized products of singleparticle states, generally harmonic oscillator states.…”

What a wonderful world — simplicity within complexity

“…Symmetry patterns revealed in results of ab initio studies and the SA-NCSM model The ab initio symmetry-adapted no-core shell model (SA-NCSM) [2] adopts the first-principle concept and utilizes a many-particle basis that is reduced with respect to the physically relevant SU(3)⊃SO(3) subgroup chain. This allows the full model space to be down-selected to the physically relevant space [1,5]. The significance of the SU(3) group for a microscopic description of the nuclear collective dynamics can be seen from the fact that it is the symmetry group of the Elliott model [6,7,8], and a subgroup of the Sp(3, R) symplectic model [9].…”