  Some results for two distinct but complementary exactly solvable algebraic
models for pairing in atomic nuclei are presented: 1) binding energy
predictions for isotopic chains of nuclei based on an extended pairing model
that includes multi-pair excitations; and 2) fine structure effects among
excited $0^+$ states in $N \approx Z$ nuclei that track with the proton-neutron
($pn$) and like-particle isovector pairing interactions as realized within an
algebraic $sp(4)$ shell model. The results show that these models can be used
to reproduce significant ranges of known experimental data, and in so doing,
confirm their power to predict pairing-dominated phenomena in domains where
data is unavailable.
