Classification and construction of six-quark basis states from parity eigenfunctions for NN processes

Six-quark configurations relevant to N-N scattering and bound states are constructed from parity eigenfunctions which can be obtained from any static independent particle model. The two lowest, one even and one odd, parity orbitals are considered. In the (TS) = (10) and (01) sectors, there are 16 orthogonal color-singlet configurations of various orbital-spin-isospin symmetries; there are 7 in the (00) sector and 25 in the (11) sector. The results obtained are compared with the cluster model approach for single particle s states in each sector. In that model, certain p^n s^{6-n} components disappear from the wave function in the zero-separation limit, whereas the parity eigenfunctions representation preserves a symmetry between even and odd parity states (with respect to the centre of mass). Furthermore, cluster model configurations have been limited three-quark clusters, which also limits the number of basis states. It is demonstrated here how parity eigenfunctions can be constructed from cluster model functions, and utilized to build the "missing" basis states.