  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.
