  It is shown that the renormalized nuclear deformations in different mass
regions can be globally scaled by two probability partition factors of
Boltzmann-like distribution, which are derived from the competing valence $np$
and like-nucleon interactions. The partition factors are simply related to the
probabilities of anti-parallel and fully-aligned orientations of the angular
momenta of the neutrons and protons in the valence $np$ pairs, responsible for
spherical- and deformed-shape phases, respectively. The partition factors
derived from the renormalized deformations are also present in the new scaling
law for the energies of the first $2^+$ states. A striking concordance between
the distributions of the renormalized deformations and of the newly introduced
parameter for the energies of the first $2^+$ states over the extended mass
region from Ge to Cf is achieved, giving strong support to the existence of two
phases: anti-aligned and fully-aligned subsets of $np$ pairs.
