Discrimination between isoscalar and isovector pairing correlations using transition sum rules

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.