Low-lying shell-model states may be approximated accurately by a sum over products of proton and neutron states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue problems. Application of this method to $sd$-shell nuclei, $pf$-shell nuclei, and to no-core shell-model problems shows that very accurate approximations to the exact solutions may be obtained. Their energies, quantum numbers, and overlaps with exact eigenstates converge exponentially fast as the number of retained factors is increased.

• Received 13 August 2003

DOI:https://doi.org/10.1103/PhysRevC.69.024312