Construction of the center-of-mass free space for the SU(3) no-core shell model

TL;DR

This paper develops a method to isolate the center-of-mass free subspace in the SU(3) no-core shell model, enabling exact removal of spurious states and improving nuclear structure calculations.

Contribution

It introduces a null-space solution approach for constructing the nonspurious subspace in the SU(3) NCSM based on the center-of-mass harmonic oscillator operator.

Findings

Successfully constructs the center-of-mass free subspace for light nuclei.

Provides an algorithm for matrix representation of Bcm.

Demonstrates the dimensions of the nonspurious space in example nuclei.

Abstract

We address the removal of states with center-of-mass excitation from the SU(3) no-core shell model [SU(3)-NCSM] space, i.e., construction of the nonspurious subspace. A procedure is formulated based on solution of the null-space problem for the center-of-mass harmonic oscillator lowering operator Bcm, operating at the level of SU(3) irreducible representations. Isolation of the center-of-mass free subspace for the SU(3)-NCSM provides the foundation for exact removal of center-of-mass dynamics in the proposed Sp(3,R) symplectic no-core shell model. We outline the construction process for the matrix representation of Bcm, present the algorithm for obtaining the nonspurious space, and examine the dimensions obtained for center-of-mass free SU(3) subspaces in representative light nuclei.