Ab initio methods for obtaining accurate predictions of nuclear structure directly from inter-nucleon interactions require enormous computational resources. In no-core configuration interaction approaches, the accuracy of the predictions depends on our ability to solve the Hamiltonian eigenproblem in a basis large enough to capture the essential properties of a nuclear many-body system within limited computational resources. However, the basis size grows rapidly with the number of nucleons and calculations quickly become intractable.
The symplectic no-core configuration interaction (SpNCCI) framework seeks to reduce the necessary basis size by carrying out calculations in an Sp(3,R) symplectic basis. In the symplectic basis, states are organized into subspaces forming Sp(3,R) irreducible representations (irreps). The efficacy of this framework depends on the extent to which the wavefunctions are dominated by specific Sp(3,R) irreps and are thereby accurately described in a basis restricted to the dominantly contributing irreps.
The first steps toward achieving the goal of reducing the basis size by using the Sp(3,R) symmetry are carried out in this thesis. (1) The necessary mathematical and computational framework is developed for large-scale ab initio calculations in a symplectic basis. Preliminary calculations of 3He, 6Li, 7Be and 8Be are carried out. (2) The evolution of the accuracy of energies, radii and E2 transitions strengths in 3He and 6Li are analyzed with respect to a simple truncations of the basis by Sp(3,R) irrep to gain the necessary insight for developing more efficient truncation schemes. (3) Decompositions of 6Li, 7Be and 8Be wavefunctions by their Sp(3,R) content are analyzed to identify which Sp(3,R) irreps dominantly contribute. These decomposition reveal that most of the low-lying wavefunctions project onto a few Sp(3,R) irreps. Moreover, families of states emerge which are characterized by having the same dominant Sp(3,R) content.
The Sp(3,R) symmetry also provides a useful classification scheme for analyzing emergent collective phenomena. An excited rotational band belonging to the same Sp(3,R) family as the ground state rotational band is identified in the energy spectra of both 7Be and 8Be, using the Sp(3,R) and U(3) decompositions of the band members’ wavefunctions.