We explore, within the framework of an algebraic $\text{sp}\left(4\right)$ shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired $0^{+}$ states of atomic nuclei in the $40⩽A⩽100$ mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron ($pn$) and like-particle isovector pairing interactions as well as interactions with higher $J$ multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the $N=Z$ region, and the like-particle and $pn$ isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.

• Received 2 October 2003

DOI:https://doi.org/10.1103/PhysRevC.69.024313