Factorization of shell-model ground states

We present a method that accurately approximates the shell-model ground state by products of suitable states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional eigenvalue problems. The power of this method is demonstrated by computations of ground states and low-lying excitations in $\mathrm{sd}$-shell and $\mathrm{pf}$-shell nuclei.