This work analyzes fusion data for the medium-heavy systems ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ and ${}^{58}\mathrm{Ni}+{}^{54}\mathrm{Fe}$ and the medium-light systems ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ and ${}^{36}\mathrm{S}+{}^{64}\mathrm{Ni}$, and compares them with previous results for ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$. While all the systems exhibit negative $Q$ values and signatures of fusion hindrance, the lighter systems do not show a maximum in the astrophysical $S$ factor or a substantial increase in the logarithmic slope at the lowest measured energies. To elucidate these differences, fusion cross sections derived from interaction potentials calculated within the Skyrme energy density functional (SEDF) approach are examined. The analysis indicates that Skyrme forces with a softer incompressibility modulus $K$ $\approx 216\mathrm{MeV}$ best describe the behavior of the medium-heavy systems, where an $S$-factor maximum and an increase in the barrier height emerge at low energies. Applying the same methodology to ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ and ${}^{36}\mathrm{S}+{}^{64}\mathrm{Ni}$ suggests that observing a similar steep falloff in their fusion excitation functions may require measurements at lower bombarding energies. Estimates indicate that energies of approximately $E$ $\approx 44\mathrm{MeV}$ for ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ and $E$ $\approx 50\mathrm{MeV}$ for ${}^{36}\mathrm{S}+{}^{64}\mathrm{Ni}$ corresponding to cross sections of roughly 0.8 and 3 nb, respectively, may be necessary to reveal this behavior.

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• Low & intermediate energy heavy-ion reactions
• Nuclear fusion
• Nuclear reactions
• S-factor