  In this paper we model low-lying states of atomic nuclei in the nucleon-pair
approximation of the shell model, using three approaches to select collective
nucleon pairs: the generalized seniority scheme, the conjugate gradient method,
and the Hartree-Fock approach. We find the collective pairs obtained from the
generalized seniority scheme provides a good description for nearly spherical
nuclei, and those from the conjugate gradient method or the Hartree-Fock
approach work well for transitional and deformed nuclei. Our NPA calculations
using collective pairs with angular momenta 0, 2, and 4 (denoted by $SDG$
pairs) reproduce the nuclear shape evolution in the $N=26$ isotones, $^{46}$Ca,
$^{48}$Ti, $^{50}$Cr, and $^{52}$Fe, and yield good agreement with full
configuration-interaction calculations of low-lying states in medium-heavy
transitional and deformed nuclei: $^{44-48}$Ti, $^{48}$Cr, $^{50}$Cr,
$^{52}$Fe, $^{60-64}$Zn, $^{64,66}$Ge, $^{84}$Mo, and $^{108-112}$Xe. Finally,
using the $SDGI$-pair approximation we describe low-lying states of
$^{112,114}$Ba, cases difficult to reach by conventional
configuration-interaction methods.
