  The nucleon-pair approximation (NPA) can be a compact alternative to full
configuration-interaction (FCI) diagonalization in nuclear shell-model spaces,
but selecting good pairs is a long-standing problem. While seniority-based
pairs work well for near-spherical nuclides, they do not work well for deformed
nuclides with strong rotational bands. We propose an alternate approach. We
show how one can write any Slater determinant for an even number of particles
as a general pair condensate, from which one can project out pairs of good
angular momentum. We implement this by generating unconstrained Hartree-Fock
states in a shell model basis and extracting $S$, $D$, and $G$ pairs. The
subsequent NPA calculations yield good agreement with FCI results using the
same effective interactions.
