Symplectic no-core configuration interaction framework for nuclear structure

TL;DR

The paper introduces the SpNCCI framework, a symmetry-adapted approach for nuclear structure calculations that directly computes matrix elements in an Sp(3,R) basis, improving efficiency and symmetry encoding.

Contribution

It develops a method to perform nuclear many-body calculations using an Sp(3,R) symmetry basis and introduces a recurrence relation for matrix elements, enhancing computational efficiency.

Findings

Matrices of two-body operators are computed directly in the Sp(3,R) basis.

A recurrence relation expresses matrix elements in terms of simpler basis states.

A method for decomposing operators into U(3) tensor components is presented.

Abstract

We present the symplectic no-core configuration interaction (SpNCCI) framework, in which the nuclear many-body problem is solved a symmetry-adapted basis that explicitly encodes approximate symmetries associated with nuclear collectivity and deformation. In this framework, calculations are carried out in a basis organized into Sp(3,R) irreducible representations (irreps), each of which can be expressed as an infinite tower of U(3) irreps. In this framework, matrices of realistic relative two-body operators, such as the nuclear Hamiltonian, are computed directly in the Sp(3,R) many-body basis, obviating the need to expand all Sp(3,R) many-body states in, e.g., a U(3)-coupled configuration basis. Instead, many-body matrix elements are obtained via a recurrence relation that expresses a given matrix element in terms of matrix elements between basis states with fewer oscillator quanta. To use this recurrence method for computing matrix elements of relative two-body operators, we must first expand each operator into components of U(3) tensors. To this end, we present a method for decomposing arbitrary operators into U(3) tensor components.