Construction of the center-of-mass free space for the SU(3) no-core shell model
arXiv:1211.3187 · doi:10.1016/j.nuclphysa.2012.11.003
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.
14 pages, 5 figures; to be published in Nucl. Phys. A