Construction of the center-of-mass free space for the image no-core shell model

We address the removal of states with center-of-mass excitation from the image no-core shell model [image-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 image, operating at the level of image irreducible representations. Isolation of the center-of-mass free subspace for the image-NCSM provides the foundation for exact removal of center-of-mass dynamics in the proposed image symplectic no-core shell model. We outline the construction process for the matrix representation of image, present the algorithm for obtaining the nonspurious space, and examine the dimensions obtained for center-of-mass free image subspaces in representative light nuclei.