Toward optimizing the basis states in the nucleon-pair approximation: Variational factorization

In this paper we study low-lying states based on the nucleon-pair approximation to the nuclear shell model with our focus on the optimization of basis states constructed by using $SDGI$ (nucleon pair with spin zero, two, four, and six) nucleon pairs. We find that the low-lying states in the very large and complex $SDGI$ nucleon-pair configuration space can be well represented by much smaller basis states optimized by the variational factorization method of Papenbrock and collaborators [Phys. Rev. C 67, 051303(R) (2003)] (after modifications). This considerably facilitates studies of deformed nuclei in terms of the nucleon-pair approximation.