In this paper, we make use of transition sum rules to study isoscalar and isovector pairing correlations in $T=0$ states of seven self-conjugate nuclei, ${}^{96}\mathrm{Cd}$, ${}^{94}\mathrm{Ag}$, ${}^{92}\mathrm{Pd}$, ${}^{90}\mathrm{Rh}$, ${}^{48}\mathrm{Cr}$, ${}^{46}\mathrm{V}$, and ${}^{44}\mathrm{Ti}$. Four typical pairing correlation schemes are investigated, including (i) isoscalar spin-aligned (SA), (ii) isoscalar spin-one (SO), (iii) isovector lowest-seniority (LS), and (iv) isovector $SDG$ pair approximations. Our systematic calculations demonstrate that the SA pairing strongly suppresses Gamow-Teller transitions, while the SO pairing reduces electric quadrupole transition strengths. Comparisons with experimental data show that the SA pairing picture accurately describes high-spin isomers with relatively long half-lives, whereas the isovector pairing (LS/$SDG$) modes is more favored by low-spin ground states. In addition, we investigate the robustness of these conclusions by extending our calculations from single-$j$ to multi-$j$ shells with realistic shell-model interactions.

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• Collective levels
• Nuclear forces
• Nuclear structure & decays
• Pairing mechanisms
• Sum rules
• Shell model